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Erster Unvollständigkeitssatz

Der erste Unvollständigkeitssatz lässt sich wie folgt allgemein formulieren:

Sei T ein formales System, welches natürliche Zahlen mit Addition und Multiplikation beschreiben kann. Dann gilt eine der folgenden Möglichkeiten:

• Es gibt wahre arithmetische Formeln, die in T nicht beweisbar sind.
• Es gibt falsche arithmetische Formeln, die in T beweisbar sind.

Ist T ausreichend stark, lässt sich die Aussage wie folgt präzisieren:

Sei T ein formales System, in dem das System Q interpretierbar ist. Dann gilt eine der folgenden Möglichkeiten:

• Es gibt wahre arithmetische Formeln, die in T nicht beweisbar sind.
• T ist widersprüchlich.

Dabei ist Q (auch Robinson-Arithmetik) eine schwache Form der Arithmetik in Prädikatenlogik erster Stufe. Diese verfügt über die Konstante 0 „null“, die Nachfolgerfunktion S, welche intuitiv zu einer gegebenen Zahl eins addiert, sowie die Funktionen + für Addition und ✕ für Multiplikation. Sie hat folgende Axiome, die elementare Eigenschaften der natürlichen Zahlen und der arithmetischen Operationen formalisieren:

• Null hat keinen Vorgänger: Sx ≠ 0
• Wenn x+1 = y+1 gilt, dann ist x=y: (Sx = Sy) → x = y
• Jede Zahl ist gleich Null oder hat einen Vorgänger: y=0 ∨ ∃x (Sx = y)
• Rekursive Definition von Addition und Multiplikation:
  • x + 0 = x
  • x + Sy = S(x + y)
  • x ✕ 0 = 0
  • x ✕ Sy = (x ✕ y) + x

Im Folgenden wird angenommen, dass T das System Q selbst ist. Der Beweis lässt sich genauso in jedem anderen System durchführen, in dem sich die Arithmetik so interpretieren lässt, dass sich alle Funktionen aus Q so durch Ausdrücke des neuen Systems definieren lassen, dass alle Theoreme von Q in Theoreme des anderen Systems übergehen. Gödel bewies den Satz ursprünglich für das viel stärkere System der Principia Mathematica. Ebenso lässt sich der Beweis in der Zermelo-Fraenkel-Mengenlehre durchführen, die als einziges nichtlogisches Zeichen die Elementrelation $\in$ hat, in der Zahlen aber als Mengen interpretiert werden können, sodass alle Theoreme von Q als Theoreme der Mengenlehre interpretierbar sind.

Der Beweis zerfällt in vier Teile:

1. Arithmetisierung der Syntax: Jeder Formel der Theorie wird eine Zahl, die sogenannte Gödelnummer, zugewiesen, aus der sich die Formel wieder effektiv rekonstruieren lässt. Diese Nummerierung wird auf endliche Folgen von Formeln erweitert.
2. Arithmetisierung der Beweisbarkeitsrelation: Eine Formel Beweis(x, y) wird konstruiert, sodass für jedes Paar von Zahlen n und m, Beweis(n, m) genau dann wahr ist, wenn n die Gödelnummer eines Beweises einer Formel ist, deren Gödelnummer m ist.
3. Konstruktion des Gödelsatzes: Es wird eine Formel konstruiert, die informell besagt „Ich bin nicht beweisbar.“, der sogenannte Gödelsatz.
4. Nachweis der Unbeweisbarkeit: Es wird gezeigt, dass der Gödelsatz weder bewiesen noch widerlegt werden kann.

Arithmetisierung der Syntax

Das Hauptproblem bei der Ausführung des oben beschriebenen Beweises scheint zunächst darin zu liegen dass bei der Konstruktion einer Aussage p, die äquivalent zu „p ist unbeweisbar“, p eine Referenz auf p enthalten muss. Gödels Lösung ist, zu zeigen, dass Aussagen auf eine solche Weise Zahlen zugewiesen werden können, dass das Beweisen einer Aussage dadurch ersetzt werden kann, dass überprüft wird, ob die der Aussage zugewiesene Zahl eine gewisse arithmetische Eigenschaft hat. Dies ermöglicht die Konstruktion einer selbstbezüglichen Formel, die unendlichen Regress vermeidet.

Der erste Schritt des Beweises besteht somit darin, Formeln und endliche Folgen von Formeln (injektiv) auf natürliche Zahlen abzubilden. Diese Zahlen heißen Gödelnummern der Formeln. Es sind verschiedene Verfahren bekannt, Gödelnummern zuzuweisen. Die folgende Gödelnummerierung orientiert sich an der von Douglas Hofstadter in Gödel, Escher, Bach benutzten. Zunächst wird jedem Symbol der Sprache der Arithmetik eine Zahl zugeordnet, ähnlich dem ASCII-Code, der jedem Buchstaben eine eindeutige Zahl zuordnet:

Nummer Symbol Bedeutung 666 0 Null 123 S Nachfolgerfunktion 111 = Gleichheit 112 + Addition 236 ✕ Multiplikation 362 ( linke Klammer 323 ) rechte Klammer

Nummer Symbol Bedeutung 262 $x$ eine Variable 163 $'$ Strich (für weitere Variablen x', x'', …) 333 $\exists$ Existenzquantor 626 $\forall$ Allquantor 161 $\land$ logisches und 616 $\lor$ logisches oder 223 $\neg$ Negation

Die Gödelnummer einer Formel erhält man durch Aneinanderreihung der Gödelnummern für jedes Symbol der Formel. Die Gödelnummern der Symbole werden durch 0 getrennt, da keine Gödelnummer eines Symbols eine 0 enthält. Damit kann jede Formel eindeutig aus ihrer Gödelnummer rekonstruiert werden. Die Gödelnummer einer Formel F wird mit G(F) bezeichnet.

Mit dieser Gödelnummerierung erhält beispielsweise der Satz, der das Kommutativgesetz der Addition ausdrückt, $\forall x\forall x'(x+x'=x'+x)$ die Nummer:

626 0 262 0 626 0 262 0 163 0 362 0 262 0 112 0 262 0 163 0 111 0 262 0 163 0 112 0 262 0 323

(die Leerzeichen dienen nur der Lesbarkeit.) Nicht alle Zahlen repräsentieren Formeln, beispielsweise steht

111 0 626 0 112 0 262

für "$=\forall +x$", was keine korrekte Formel ist.

Da jede natürliche Zahl durch wiederholte Anwendung der Nachfolgeroperation S auf 0 erhalten werden kann, hat jede natürliche Zahl eine Gödelnummer. So ist beispielsweise die Gödelnummer für 4, SSSS0, gleich:

123 0 123 0 123 0 123 0 666.

Die Zuweisung von Gödelnummern kann auf endliche Folgen von Formeln erweitert werden. Um die Gödelnummer einer endlichen Folge von Formeln zu erhalten werden die Nummern die Formeln hintereinander geschrieben und jeweils durch zwei Nullen getrennt. Da die Gödelnummer einer Formel nie zwei aufeinanderfolgende Nullen enthält, kann jede Formel der Folge eindeutig rekonstruiert werden.

Es ist wichtig, dass die formale Arithmetik einige einfache Tatsachen beweisen kann. Insbesondere muss sie beweisen können, dass jede Zahl eine Gödelnummer hat. Ebenso muss sie beweisen, dass es für die Gödelnummer einer Formel F(x) mit einer freien Variable und eine Zahl m die Gödelnummer einer Formel F(m) gibt, in der alle Vorkommen von x durch die Gödelnummer von m ersetzt wurden, und dass man diese Gödelnummer aus der ersten durch eine effektive Prozedur erhalten kann.

Die Beweisbarkeitsrelation

Das formale System besitzt Axiome und Schlussregeln, aus denen die Formeln des Systems bewiesen werden können. Ein formaler Beweis im System ist somit eine Kette von Formeln, in der jede entweder ein Axiom ist oder sich durch eine Schlussregel aus früheren Formeln gewinnen lässt.

Da das formale System rekursiv aufzählbar ist, kann man effektiv entscheiden, ob eine gegebene Zahl Gödelnummer eines Axioms ist. Im Falle des endlich axiomatisierten Systems Q genügt es sogar, zu überprüfen, ob die Zahl zur Gödelnummer einer der sieben Axiome gleich ist.

Ableitungsregeln können als binäre Relationen zwischen Gödelnummern von Folgen von Formeln repräsentiert werden. So gibt es beispielsweise eine Ableitungsregel D₁, durch die man aus den Formeln S₁,S₂ die Formel $S_{1}\wedge S_{2}$ erhält. Dann besagt die Relation R₁ zu dieser Ableitungsregel, dass n genau dann in Relation zu m steht (n R₁m gilt), wenn n die Gödelnummer einer Liste von Formeln ist, die S₁ und S₂ enthält, und wenn m die Gödelnummer einer Liste von Formeln ist, die aus den Formeln in der von n kodierten Liste besteht und zusätzlich $S_{1}\wedge S_{2}$ enthält. Da jede Ableitungsregel eine einfache formale Vorschrift ist, ist es möglich, effektiv zu entscheiden, ob zwei Zahlen n und m in Relation R₁ stehen.

Der zweite Schritt ist, zu zeigen, dass diese Gödelnummerierung benutzt werden kann, um den Begriff der Beweisbarkeit auszudrücken. Angenommen die Theorie hat die Axiome A₁, A₂, A₃, … und die Ableitungsregeln: D₁, D₂, D₃, … . R₁, R₂, R₃, … seien die zugehörigen Relationen.

Ein Beweis einer Formel S ist eine Kette von Formeln, in denen jede entweder ein Axiom ist, oder aus früheren Aussagen durch eine Ableitungsregel entsteht, und in der die letzte Aussage S ist. Damit lässt sich die Gödelnummer eines Beweises mit der oben angegebenen Methode zur Kodierung endlicher Folge von Formeln definieren. Zudem lässt sich eine Formel Beweis(x,y) definieren, die für zwei Zahlen x and y genau dann wahr (und beweisbar) ist, wenn x die Gödelnummer eines Beweises von S ist, und y = G(S) ist.

Beweis(x,y) ist eine arithmetische Relation, ebenso wie etwa "x+y = 6", nur beträchtlich komplizierter. Gegeben eine solche Relation R(x,y), ist für alle spezifischen Zahlen n und m entweder die Formel R(m,n) oder ihre Negation $\lnot$R(m,n) beweisbar, aber nicht beide. Dies liegt daran, dass die Relation zwischen den Zahlen auf einfache Weise „überprüft“ werden kann. Die Konstruktion der Formel Beweis hängt entscheidend davon ab, dass die Theorie rekursiv aufzählbar ist; ohne diese Annahme wäre die Formel nicht konstruierbar.

Damit lässt sich nun eine Formel Beweisbar(y) definieren, die die metasprachliche Aussage „F ist beweisbar“ repräsentiert: F ist beweisbar, wenn es eine Zahl x gibt, die einen Beweis für F kodiert:

Beweisbar(y) = ∃ x (Beweis(x, y))

Dabei ist "Beweisbar(y)" ebenso wie "Beweis(x, y)" nur eine Abkürzung für eine bestimmte, sehr lange, arithmetische Formel; die Symbol "Beweis" und "Beweisbar" selbst gehört nicht zur Sprache des Systems.

Ein wichtiges Merkmal der Formel Beweisbar(y) ist, dass Beweisbar(G(p)) beweisbar ist, wenn p beweisbar ist. Denn wenn p beweisbar ist, dann existiert ein Beweis mit Gödelnummer n. Dann ist Beweisbar(n, G(p)) wahr und, wie oben dargelegt, beweisbar. Damit ist erst recht die schwächere Existenzaussage ∃ x Beweisbar(x, G(p)) beweisbar.

Diagonalisierung

Der nächste Schritt besteht darin, eine Aussage zu konstruieren, die ihre eigene Unbeweisbarkeit behauptet. Hierzu lässt sich das Diagonallemma anwenden. Dieses besagt, dass es in der Arithmetik und stärkeren formalen Systemen für jede Formel F(x) mit freier Variable x eine Aussage p gibt, sodass das System die Äquivalenz

p ↔ F(G(p)).

beweist. Man erhält also eine Formel mit der intuitiven Bedeutung „Ich habe die Eigenschaft F(x).“ Wenn man für F die Negation von Beweisbar(x) einsetzt, erhält man die Aussage p mit der Bedeutung „Meine Gödelnummer ist die Gödelnummer einer unbeweisbaren Formel“, also „Ich bin unbeweisbar“.

Die Formel p ist nicht direkt gleich zu ¬Beweisbar(G(p)); vielmehr besagt p, dass man, wenn man eine gewisse Berechnung ausführt, die Nummer einer unbeweisbaren Aussage erhält. Wenn man nun diese Berechnung durchführt, zeigt sich aber, dass die entstehende Zahl die Gödelnummer von p selbst ist. Diese Konstruktion ähnelt folgender natürlichsprachigen Aussage:

"ist in Anführungszeichen und gefolgt von sich selbst unbeweisbar." ist in Anführungszeichen und gefolgt von sich selbst unbeweisbar.

Dieser Satz bezieht sich nicht direkt auf sich selbst, aber man erhält die ursprüngliche Aussage, wenn man die angegebene Umformung durchführt, und damit behauptet der Satz seine eigene Unbeweisbarkeit. Der Beweis des Diagonallemmas benutzt eine ähnliche Methode.

Beweis der Unabhängigkeit des Gödelsatzes

Man nehme nun an, dass das formale System ω-konsistent, und damit konsistent, ist. Sei p die Aussage, die im vorangehenden Abschnitt konstruiert wurde.

Wenn p beweisbar wäre, dann wäre Bew(G(p)) beweisbar. Aber p ist äquivalent zur Negation von Bew(G(p)). Damit wäre das System inkonsistent, da es eine Aussage und ihre Negation beweisen würde. Also kann p nicht beweisbar sein, da die Theorie nach Voraussetzung konsistent ist.

Wenn die Negation von p beweisbar wäre, dann wäre Bew(G(¬ p)) beweisbar. Aber keine natürliche Zahl n kann die Gödelnummer eines Beweises von p sein, da p nicht beweisbar ist. Damit ermöglicht das System einerseits die Konstruktion einer Zahl mit einer bestimmten Eigenschaften, aber beweist andererseits für jede Zahl n, dass diese die Eigenschaft nicht hat. Dies ist in einem ω-konsistenten System unmöglich. Damit ist die Negation von p nicht beweisbar.

Damit ist die Aussage p unentscheidbar: sie kann im gewählten System weder bewiesen noch widerlegt werden. Damit ist das System entweder ω-inkonsistent oder unvollständig. Diese Argumentation lässt sich auf jedes formale System, das die Voraussetzungen erfüllt, anwenden. Damit sind alle formalen Systeme, die die Voraussetzungen erfüllen, entweder ω-inkonsistent oder unvollständig.

Dabei ist zu bemerken, dass p auch dann nicht beweisbar ist, wenn das System konsistent und ω-inkonsistent ist. Die Annahme der ω-Konsistenz ist nur dazu nötig, zu zeigen, dass die Negation von p nicht beweisbar ist.

Wenn man versucht, die Unvollständigkeit zu beseitigen, indem man eine der unbeweisbaren Formeln p oder nicht p als Axiom hinzufügt, erhält man ein neues formales System. Auf dieses lässt sich der gleiche Prozess anwenden und man erhält wieder eine Aussage der Form „Ich bin im neuen System nicht beweisbar.“ und das neue System ist wieder entweder ω-inkonsistent oder unvollständig.

Verallgemeinerung von Rosser

Wie im vorangehenden Abschnitt gezeigt, erlaubt die Konstruktion des Gödelsatzes zunächst nur den Beweis der Unvollständigkeit für ω-konsistente Systeme. J. Barkley Rosser zeigte 1936, dass sich mit der gleichen Technik die Unvollständigkeit auch für ω-inkonsistente Systeme zeigen lässt.

Durch das Diagonallemma lässt sich ein Satz konstruieren, der die metasprachliche Bedeutung „Wenn es einen Beweis für mich gibt, dann gibt es einen kürzeren Beweis für meine Negation.“ hat. Dieser Satz wird auch als Rossersatz R bezeichnet:

$T\vdash R\leftrightarrow \forall y(Beweis(\mathbf {G} (R),y)\rightarrow \exists z<yBeweis(\mathbf {G} (\neg R),z))$

Angenommen R ist beweisbar und es gibt einen Beweis mit Gödelnummer n. Dann gibt es eine Zahl m < n, die Gödelnummer eines Beweises der Negation von R ist. Damit beweist das formale System einen Satz und seine Negation, ist also inkonsistent.

Nun nehme man an, das System sei konsistent und der Rossersatz sei widerlegbar, wobei es einen Beweis für die Negation mit Gödelnummer n gibt. Da das System konsistent ist, ist R nicht beweisbar. Dann ist beweisbar:

$T\vdash \forall y(y\leq n\rightarrow \neg Beweis(\mathbf {G} (R),y))$

Da es keinen Beweis für R gibt, gibt es auch keinen Beweis mit Gödelnummer kleiner gleich n. Damit ist die Formel wahr. Da es nur endlich viele Zahlen kleiner n gibt, ist die Formel äquivalent zu einer quantorenfreien Formel $(\neg Beweis(\mathbf {G} (R),0))\wedge (\neg Beweis(\mathbf {G} (R),1))\wedge ...\wedge (\neg Beweis(\mathbf {G} (R),n))$ und damit auch beweisbar.

$T\vdash \forall y(n<y\rightarrow \exists z<y\ Beweis(\mathbf {G} (\neg R),z))$

Für jede Zahl größer n findet man eine kleinere Zahl, die Nummer eines Beweises von $\neg R$ ist. Dies folgt direkt daraus, dass n eine solche Nummer ist.

Damit lässt sich aber durch Kontraposition und Modus Ponens beweisen:

$T\vdash \forall y(Beweis(\mathbf {G} (R),y)\rightarrow \exists z<yBeweis(\mathbf {G} (\neg R),z))$

was dem Rossersatz R entspricht. Dies ist ein Widerspruch, da R nach Annahme nicht beweisbar sein kann. Also ist der Rossersatz in einem konsistenten System nicht widerlegbar.

Genaue Formulierung und Beweisskizze des zweiten Unvollständigkeitssatzes

Der zweite Unvollständigkeitssatz besagt:

Jedes hinreichend mächtige konsistente System kann die eigene Konsistenz nicht beweisen.

Eine hinreichende Bedingung für „hinreichend mächtig“ ist, dass der Beweis des ersten Unvollständigkeitssatzes im System formalisiert werden kann. Dazu muss es eine Formel Bew(x) besitzen, die die Beweisbarkeit in diesem System ausdrückt. Zudem muss diese Formel den sogenannten Bernays-Löb-Axiomen genügen. Diese fordern, dass für alle Formeln F und H folgende Bedingungen gelten:

1. Wenn $T\vdash F$, dann $T\vdash Bew(\mathbf {G} (F))$
2. $T\vdash Bew(\mathbf {G} (F\rightarrow H))\rightarrow (Bew(\mathbf {G} (F))\rightarrow Bew(\mathbf {G} (H)))$
3. $T\vdash Bew(\mathbf {G} (F))\rightarrow Bew(\mathbf {G} (Bew(\mathbf {G} (F))))$

Dies ist zwar im System Q, für das sich der erste Unvollständigkeitssatz bereits zeigen lässt, noch nicht erfüllt, aber bereits in der Primitiv Rekursiven Arithmetik (PRA), und erst recht in stärkeren Theorien wie der Peano-Arithmetik und der Mengenlehre.

Mithilfe dieser Eigenschaften lässt sich nun wie folgt der erste Unvollständigkeitssatz formalisieren. Sei F die beim Beweis des ersten Satzes konstruierte Aussage mit der Bedeutung „Ich bin nicht beweisbar.“ Dann lassen sich folgende drei Aussagen ableiten:

• $T\vdash Bew(\mathbf {G} (F))\rightarrow Bew(\mathbf {G} (Bew(\mathbf {G} (F))))$ (nach Axiom 3)
• $T\vdash Bew(\mathbf {G} (Bew(\mathbf {G} (F))))\rightarrow Bew(\mathbf {G} (\neg F))$ (nach der Definition von F)
• $T\vdash Bew(\mathbf {G} (F))\rightarrow (Bew(\mathbf {G} (\neg F))\rightarrow Bew(\mathbf {G} (0=1))$ (nach Axiom 1 und 3)

Durch Kontraposition erhält man aus diesen drei Sätzen folgenden Satz, der dem ersten Unvollständigkeitssatz entspricht:

• $T\vdash \neg Bew(\mathbf {G} (0=1))\rightarrow \neg Bew(\mathbf {G} (F))$

Um einen Widerspruch zu erzeugen, nehme man nun an, dass T seine Konsistenz beweist, das heißt $T\vdash \neg Bew(\mathbf {G} (0=1))$. Damit gilt $T\vdash \neg Bew(\mathbf {G} (F))$, also $T\vdash F$. Nach Axiom 1 gilt $T\vdash Bew(\mathbf {G} (F))$. Andererseits erhält man aus $T\vdash \neg Bew(\mathbf {G} (0=1))\rightarrow \neg Bew(\mathbf {G} (F))$ und $T\vdash \neg Bew(\mathbf {G} (0=1))$ aber $T\vdash \neg Bew(\mathbf {G} (F))$.

Dann wäre aber T inkonsistent, da es sowohl F als auch $\neg F$ beweist. Also kann T, wenn es konsistent ist, die eigene Konsistenz nicht beweisen.

Alternativ lässt sich der zweite Unvollständigkeitssatz auch durch den Satz von Löb beweisen. Nach diesem gilt für ein System T, das die Bernays-Löb-Axiome erfüllt, die Aussage $T\vdash Bew(\mathbf {G} (P))\rightarrow P$ nur dann, wenn auch $T\vdash P$ gilt. Wenn nun T seine eigene Konsistenz beweist, gilt $T\vdash \neg Bew(\mathbf {G} \bot )$ und damit $T\vdash (Bew(\mathbf {G} \bot )\rightarrow \bot )$. Nach dem Satz von Löb gilt also $T\vdash \bot$, also ist T inkonsistent.

Relationship with computability

The incompleteness theorem is closely related to several results about undecidable sets in recursion theory.

Stephen Cole Kleene (1943) presented a proof of Gödel's incompleteness theorem using basic results of computability theory. One such result shows that the halting problem is unsolvable: there is no computer program that can correctly determine, given a program P as input, whether P eventually halts when run with some given input. Kleene showed that the existence of a complete effective theory of arithmetic with certain consistency properties would force the halting problem to be decidable, a contradiction. This method of proof has also been presented by Shoenfield (1967, p. 132); Charlesworth (1980); and Hopcroft and Ullman (1979).

Franzén (2005, p. 73) explains how Matiyasevich's solution to Hilbert's 10th problem can be used to obtain a proof to Gödel's first incompleteness theorem. Matiyasevich proved that there is no algorithm that, given a multivariate polynomial p(x₁, x₂,...,x_k) with integer coefficients, determines whether there is an integer solution to the equation p = 0. Because polynomials with integer coefficients, and integers themselves, are directly expressible in the language of arithmetic, if a multivariate integer polynomial equation p = 0 does have a solution in the integers then any sufficiently strong theory of arithmetic T will prove this. Moreover, if the theory T is ω-consistent, then it will never prove that some polynomial equation has a solution when in fact there is no solution in the integers. Thus, if T were complete and ω-consistent, it would be possible to determine algorithmically whether a polynomial equation has a solution by merely enumerating proofs of T until either "p has a solution" or "p has no solution" is found, in contradiction to Matiyasevich's theorem.

James Jones gives a concrete example of Diophantine equation (containing a parameter, say K) with a property that for every consistent effectively generated theory T there exists an integer value of parameter K such that the equation has no solutions over non-negative integers, but it cannot be proved in T. Moreover, for every such theory, the set of numbers with this property is an infinite, not recursively enumerable set. In principle, (at least one) such value of K can be effectively computed from the axioms of T.

Smorynski (1977, p. 842) shows how the existence of recursively inseparable sets can be used to prove the first incompleteness theorem. This proof is often extended to show that systems such as Peano arithmetic are essentially undecidable (see Kleene 1967, p. 274).

Chaitin's incompleteness theorem gives a different method of producing independent sentences, based on Kolmogorov complexity. Like the proof presented by Kleene that was mentioned above, Chaitin's theorem only applies to theories with the additional property that all their axioms are true in the standard model of the natural numbers. Gödel's incompleteness theorem is distinguished by its applicability to consistent theories that nonetheless include statements that are false in the standard model; these theories are known as ω-inconsistent.

sonst

In principle, proving a statement true or false can be shown to be equivalent to proving that the number matching the statement does or doesn't have a given property. Because the formal system is strong enough to support reasoning about numbers in general, it can support reasoning about numbers which represent formulae and statements as well. Crucially, because the system can support reasoning about properties of numbers, the results are equivalent to reasoning about provability of their equivalent statements.

The "truth" of the Gödel sentence

The proof of Gödel's incompleteness theorem just sketched is proof-theoretic (also called syntactic) in that it shows that if certain proofs exist (a proof of P(G(P)) or its negation) then they can be manipulated to produce a proof of a contradiction. This makes no appeal to whether P(G(P)) is "true", only to whether it is provable. Truth is a model-theoretic, or semantic, concept, and is not equivalent to provability except in special cases.

By analyzing the situation of the above proof in more detail, it is possible to obtain a conclusion about the truth of P(G(P)) in the standard model $\mathbb {N}$ of natural numbers. As just seen, q(n,G(P)) is provable for each natural number n, and is thus true in the model $\mathbb {N}$. Therefore, within this model,

P(G(P)) = $\forall y\,q(y,G(P))$

holds. This is what the statement "P(G(P)) is true" usually refers to—the sentence is true in the intended model. It is not true in every model, however: If it were, then by Gödel's completeness theorem it would be provable, which we have just seen is not the case.

Discussion and implications

The incompleteness results affect the philosophy of mathematics, particularly versions of formalism, which use a single system formal logic to define their principles. One can paraphrase the first theorem as saying the following:

An all-encompassing axiomatic system can never be found that is able to prove all mathematical truths, but no falsehoods.

On the other hand, from a strict formalist perspective this paraphrase would be considered meaningless because it presupposes that mathematical "truth" and "falsehood" are well-defined in an absolute sense, rather than relative to each formal system.

The following rephrasing of the second theorem is even more unsettling to the foundations of mathematics:

If an axiomatic system can be proven to be consistent from within itself, then it is inconsistent.

Therefore, to establish the consistency of a system S, one needs to use some other more powerful system T, but a proof in T is not completely convincing unless T's consistency has already been established without using S.

Theories such as Peano arithmetic, for which any computably enumerable consistent extension is incomplete, are called essentially undecidable or essentially incomplete.

This fact is sometimes thought to have severe consequences for the program of logicism proposed by Gottlob Frege and Bertrand Russell, which aimed to define the natural numbers in terms of logic (Hellman 1981, p. 451–468). Some (like Bob Hale and Crispin Wright) argue that it is not a problem for logicism because the incompleteness theorems apply equally to second order logic as they do to arithmetic. They argue that only those who believe that the natural numbers are to be defined in terms of first order logic have this problem.

Minds and machines

Authors including J. R. Lucas have debated what, if anything, Gödel's incompleteness theorems imply about human intelligence. Much of the debate centers on whether the human mind is equivalent to a Turing machine, or by the Church–Turing thesis, any finite machine at all. If it is, and if the machine is consistent, then Gödel's incompleteness theorems would apply to it.

Hilary Putnam (1960) suggested that while Gödel's theorems cannot be applied to humans, since they make mistakes and are therefore inconsistent, it may be applied to the human faculty of science or mathematics in general. Assuming that it is consistent, either its consistency cannot be proved or it cannot be represented by a Turing machine.

Avi Wigderson (2010) has proposed that the concept of mathematical "knowability" should be based on computational complexity rather than logical decidability. He writes that "when knowability is interpreted by modern standards, namely via computational complexity, the Gödel phenomena are very much with us."

Paraconsistent logic

Although Gödel's theorems are usually studied in the context of classical logic, they also have a role in the study of paraconsistent logic and of inherently contradictory statements (dialetheia). Graham Priest (1984, 2006) argues that replacing the notion of formal proof in Gödel's theorem with the usual notion of informal proof can be used to show that naive mathematics is inconsistent, and uses this as evidence for dialetheism. The cause of this inconsistency is the inclusion of a truth predicate for a theory within the language of the theory (Priest 2006:47). Stewart Shapiro (2002) gives a more mixed appraisal of the applications of Gödel's theorems to dialetheism. Carl Hewitt (2008) has proposed that (inconsistent) paraconsistent logics that prove their own Gödel sentences may have applications in software engineering.

Appeals to the incompleteness theorems in other fields

Appeals and analogies are sometimes made to the incompleteness theorems in support of arguments that go beyond mathematics and logic. Several authors have commented negatively on such extensions and interpretations, including Torkel Franzén (2005); Alan Sokal and Jean Bricmont (1999); and Ophelia Benson and Jeremy Stangroom (2006). Bricmont and Stangroom (2006, p. 10), for example, quote from Rebecca Goldstein's comments on the disparity between Gödel's avowed Platonism and the anti-realist uses to which his ideas are sometimes put. Sokal and Bricmont (1999, p. 187) criticize Régis Debray's invocation of the theorem in the context of sociology; Debray has defended this use as metaphorical (ibid.).

The role of self-reference

Torkel Franzén (2005, p. 46) observes:

Gödel's proof of the first incompleteness theorem and Rosser's strengthened version have given many the impression that the theorem can only be proved by constructing self-referential statements [...] or even that only strange self-referential statements are known to be undecidable in elementary arithmetic. To counteract such impressions, we need only introduce a different kind of proof of the first incompleteness theorem.

He then proposes the proofs based on Computability, or on information theory, as described earlier in this article, as examples of proofs that should "counteract such impressions".

History

Nachdem Gödel in seiner Doktorarbeit 1929 den Gödelschen Vollständigkeitssatz bewiesen hatte, wandte er sich einem zweiten Problem für seine Habilitation zu. Sein ursprüngliches Ziel war, eine positive Lösung zu Hilberts zweitem Problem zu finden (Dawson 1997, p. 63), das nach einem finiten Konsistenzbeweis für die Arithmetik fragt.

Zach, Richard (2003), "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program", Synthese (Berlin, New York: Springer-Verlag) 137 (1): 211–259, doi:10.1023/A:1026247421383, ISSN 0039-7857

Gödel war nicht der einzige, der am Problem der Konsistenz arbeitete. Ackermann hatte 1925 einen fehlerhaften Konsistenzbeweis für die Analysis veröffentlicht, in dem er Hilberts Methode der ε-Substitution anzuwenden versuchte. Von Neumann korrigierte 1927 diesen Beweis für Arithmetik ohne Induktion. 1928 teilte Ackermann Bernays einen neuen Beweis mit. Nachdem der Unvollständigkeitssatz zeigte, dass der Beweis fehlerhaft sein musste, zeigte von Neumann konkret, dass die verwendete Beweistechnik inkorrekt war. 1931 veröffentlichte Jacques Herbrand einen weiteren Konsistenzbeweis für die Arithmetik ohne Induktion.

Im Laufe seiner Arbeit entdeckte Gödel, dass, während ein Satz, der seine eigene Falschheit behauptet, zu einem Paradox führt, ein Satz, der seine eigene Unbeweisbarkeit behauptet, dies nicht tut. Gödel war sich auch des später von Tarski veröffentlichten Resultats über die Undefinierbarkeit von Wahrheit bewusst, veröffentlichte es aber nicht. Gödel announced his first incompleteness theorem to Carnap, Feigel and Waismann on August 26, 1930; all four would attend a key conference in Königsberg the following week.

Announcement

The 1930 Königsberg conference was a joint meeting of three academic societies, with many of the key logicians of the time in attendance. Carnap, Heyting, and von Neumann delivered one-hour addresses on the mathematical philosophies of logicism, intuitionism, and formalism, respectively (Dawson 1996, p. 69). The conference also included Hilbert's retirement address, as he was leaving his position at the University of Göttingen. Hilbert used the speech to argue his belief that all mathematical problems can be solved. He ended his address by saying,

"For the mathematician there is no Ignorabimus, and, in my opinion, not at all for natural science either. ... The true reason why [no one] has succeeded in finding an unsolvable problem is, in my opinion, that there is no unsolvable problem. In contrast to the foolish Ignoramibus, our credo avers: We must know. We shall know!"

This speech quickly became known as a summary of Hilbert's beliefs on mathematics (its final six words, "Wir müssen wissen. Wir werden wissen!", were used as Hilbert's epitaph in 1943). Although Gödel was likely in attendance for Hilbert's address, the two never met face to face (Dawson 1996, p. 72).

Gödel announced his first incompleteness theorem at a roundtable discussion session on the third day of the conference. The announcement drew little attention apart from that of von Neumann, who pulled Gödel aside for conversation. Later that year, working independently with knowledge of the first incompleteness theorem, von Neumann obtained a proof of the second incompleteness theorem, which he announced to Gödel in a letter dated November 20, 1930 (Dawson 1996, p. 70). Gödel had independently obtained the second incompleteness theorem and included it in his submitted manuscript, which was received by Monatshefte für Mathematik on November 17, 1930.

Gödel's paper was published in the Monatshefte in 1931 under the title Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I (On Formally Undecidable Propositions in Principia Mathematica and Related Systems I). As the title implies, Gödel originally planned to publish a second part of the paper; it was never written.

Generalisierung und Akzeptanz

Gödel gave a series of lectures on his theorems at Princeton in 1933–1934 to an audience that included Church, Kleene, and Rosser. By this time, Gödel had grasped that the key property his theorems required is that the theory must be effective (at the time, the term "general recursive" was used). Rosser bewies 1936, dass sich die Voraussetzung der ω-Konsistenz durch einfache Konsistenz ersetzen lässt, wenn der Gödelsatz entsprechend geändert wird. Alonzo Church und Alan Turing bewiesen 1936 unabhängig voneinander mithilfe ihrer neu entwickelten Berechenbarkeitsmodelle und aufbauend auf Gödels Arbeit die Unentscheidbarkeit der Prädikatenlogik, aus der sich der erste Unvollständigkeitssatz ebenfalls herleiten lässt.

Gentzen veröffentlichte 1936 einen Konsistenzbeweis für die volle erststufige Arithmetik mithilfe transfiniter Induktion. Hilbert akzeptierte diesen Beweis als „finit“, obwohl er nach Gödels Resultat nicht in der Arithmetik formalisiert werden kann.

Die Bedeutung des Unvollständigkeitssatzes für Hilberts Programm war schnell erkannt. Bernays veröffentlichte im zweiten Band von Grundlagen der Mathematik (1939) den ersten detaillierten Beweis des zweiten Unvollständigkeitssatzes, mit weiteren Resultaten von Ackermann über die Methode der ε-Substitution und Gentzens Konsistenzbeweis.

Kritik

Im September 1931 schrieb Ernst Zermelo Gödel, dass er eine wesentliche Lücke in Gödels Argument gefunden habe.. Gödel antwortete im Oktober mit einem zehnseitigen Brief, aber Zermelo veröffentlichte seine Kritik. Gödel entschied decided that to pursue the matter further was pointless, and Carnap agreed (Dawson:77). Zermelo konzentrierte sich in der Folge auf viel stärkere Logiken als Logik erster Stufe, mit denen er hoffte

Paul Finsler benutzte 1926 eine Version des Richard-Paradoxons, um eine Aussage zu konstruieren, die in einem informellen System, das er entwickelt hatte, unbeweisbar ist. Gödel kannte diese Arbeit nicht, als er den Unvollständigkeitssatz bewies (Collected Works Vol. IV., p. 9). Finsler schrieb Gödel 1931 über seine Arbeit, die er als ersten Beweis des Unvollständigkeitssatzes ansah. Finslers Methoden beruhten nicht auf einer Formalisierung der Beweisbarkeit. Gödel hielt Finslers Arbeit für fehlerhaft. Finsler argumentierte weiterhin für seine Philosophie der Mathematik, die Formalisierung scheute.

Wittgenstein and Gödel

Ludwig Wittgenstein schrieb einige Passagen über den Unvollständigkeitssatz, die 1953 posthum in seinen Philosophische Untersuchungen veröffentlicht wurden. Gödel was a member of the Vienna Circle during the period in which Wittgenstein's early ideal language philosophy and Tractatus Logico-Philosophicus dominated the circle's thinking. Writings in Gödel's Nachlass express the belief that Wittgenstein deliberately misread his ideas.

Multiple commentators have read Wittgenstein as misunderstanding Gödel (Rodych 2003), although Juliet Floyd and Hilary Putnam (2000), as well as Graham Priest (2004), have provided textual readings arguing that most commentary misunderstands Wittgenstein. On their release, Bernays, Dummett, and Kreisel wrote separate reviews on Wittgenstein's remarks, all of which were extremely negative (Berto 2009:208). The unanimity of this criticism caused Wittgenstein's remarks on the incompleteness theorems to have little impact on the logic community. In 1972, Gödel, stated: "Has Wittgenstein lost his mind? Does he mean it seriously?" (Wang 1996:197) And wrote to Karl Menger that Wittgenstein's comments demonstrate a willful misunderstanding of the incompleteness theorems writing:

"It is clear from the passages you cite that Wittgenstein did "not" understand [the first incompleteness theorem] (or pretended not to understand it). He interpreted it as a kind of logical paradox, while in fact is just the opposite, namely a mathematical theorem within an absolutely uncontroversial part of mathematics (finitary number theory or combinatorics)." (Wang 1996:197)

Since the publication of Wittgenstein's Nachlass in 2000, a series of papers in philosophy have sought to evaluate whether the original criticism of Wittgenstein's remarks was justified. Floyd and Putnam (2000) argue that Wittgenstein had a more complete understanding of the incompleteness theorem than was previously assumed. They are particularly concerned with the interpretation of a Gödel sentence for an ω-inconsistent theory as actually saying "I am not provable", since the theory has no models in which the provability predicate corresponds to actual provability. Rodych (2003) argues that their interpretation of Wittgenstein is not historically justified, while Bays (2004) argues against Floyd and Putnam's philosophical analysis of the provability predicate. Berto (2009) explores the relationship between Wittgenstein's writing and theories of paraconsistent logic.

Autoren

http://en.wikipedia.org/w/index.php?title=G%C3%B6del%27s_incompleteness_theorems&oldid=478418644

• 2012-02-23 12:43 (diff) CBM (Many of the other changes by this editor sounded good, but this one sounds worse to my ear. "at least one of that statement and its negation")
• 2012-02-23 09:15 (diff) 114.96.77.126 (anon) (/* Meaning of the first incompleteness theorem */)
• 2012-02-23 09:11 (diff) 114.96.77.126 (anon) (/* Meaning of the first incompleteness theorem */)
• 2012-02-23 09:00 (diff) 114.96.77.126 (anon) (/* Background */)
• 2012-02-14 12:26 (diff) (minor) CBM (Reverted edits by 87.249.121.115 (talk) to last version by 160.45.152.6)
• 2012-02-14 12:19 (diff) 87.249.121.115 (anon) (/* Background */)
• 2012-02-06 15:28 (diff) 160.45.152.6 (anon) (Adding new reference: A Concise Introduction to Mathematical Logic)
• 2012-01-25 16:08 (diff) (minor) Minsbot (bot) (r2.7.2) (Robot: Modifying en:he:משפטי האי-שלמות של גדל)
• 2012-01-25 15:22 (diff) (minor) Pasky (/* Examples of undecidable statements */ Chaitin's incompleteness theorem (link))
• 2012-01-22 22:39 (diff) (minor) Wvbailey (link "effective procedure")
• 2012-01-22 19:25 (diff) 67.122.210.96 (anon) (restore "but not universally" in lede per talk page)
• 2012-01-22 19:14 (diff) 67.122.210.96 (anon) (/* Formalized proofs */ m add first name for style consistency)
• 2012-01-22 16:52 (diff) David Eppstein (Undo — I think this rather misses the point and will cause only confusion)
• 2012-01-22 11:42 (diff) Vibritannia (/* First incompleteness theorem */ -- amplification of 'by reasoning outside the system' in the second paragraph)
• 2012-01-22 11:23 (diff) Vibritannia (/* First incompleteness theorem */ -- amplification of the third paragraph)
• 2012-01-22 11:07 (diff) 87.99.27.160 (anon) (/* Limitations of Gödel's theorems */)
• 2012-01-14 21:58 (diff) דניאל ב. (/* Relationship with computability */ the halting problem)
• 2012-01-14 18:47 (diff) (minor) AnomieBOT (bot) (Dating maintenance tags: {{Cn}})
• 2012-01-14 18:26 (diff) Ajoykt (Undid revision 470370278 by David Eppstein (talk)Out on Wikipedia, we look for reliable secondary sources, not serious primary work. Primary sources can be cherry-picked.)
• 2012-01-09 03:12 (diff) David Eppstein (Undo. It is not hard to find serious work on constrained theories of logic that are decidable, and the {{cn}} tag on a well-cited paragraph about the halting problem is pure tendentiousness.)
• 2012-01-09 02:55 (diff) Ajoykt (Please provide secondary sources for Hilbert's second being open. Primary sources can always be cherry-picked to push marginal viewpoints to the center.)
• 2012-01-09 02:54 (diff) Ajoykt (/* Relationship with computability */ The halting theorem proof is from Alan Turing.)
• 2012-01-09 02:47 (diff) Ajoykt (Hilbert's second isn't thought an open question; please cite if you want to say otherwise.)
• 2012-01-06 00:58 (diff) David Eppstein (Undid revision 469816887 by 49.245.146.98 (talk) I'm not convinced axiometry is a word, and some of these changes make the text incoherent)
• 2012-01-06 00:28 (diff) 49.245.146.98 (anon)
• 2011-12-21 21:36 (diff) CBM (Heading seems fine)
• 2011-12-21 21:21 (diff) Wavelength (removing “The” [1 instance]—en:MOS:HEAD: provisions in en:WP:MOS#Article titles—en:WP:VA/E)
• 2011-12-20 21:51 (diff) CBM ("canonically possible" has no meaning to me, same for several other changes in the last edit)
• 2011-12-20 17:29 (diff) (minor) Marktoiii0 (reduced wordiness and corrected split infinitives)
• 2011-12-14 02:20 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-14 02:19 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-14 02:18 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-14 02:17 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-14 02:16 (diff) Avaya1 (/* Wittgenstein and Gödel */ add)
• 2011-12-14 02:11 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-14 02:00 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-14 01:58 (diff) Avaya1 (Undid revision 465727087 by Trovatore (talk) will add sources in a minute)
• 2011-12-14 01:57 (diff) Avaya1 (Undid revision 465727184 This is accurate - actually the Nachlass supports stronger than this sentence. I will add sources)
• 2011-12-13 23:44 (diff) Trovatore (rv to last by .mau.)
• 2011-12-13 23:43 (diff) Trovatore (Undid revision 465726148 by Avaya1 (talk) "resentful" is speculative)
• 2011-12-13 23:37 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-13 23:34 (diff) Avaya1 (/* Wittgenstein and Gödel */)
• 2011-12-13 23:32 (diff) Avaya1 (/* Wittgenstein and Gödel */ willful)
• 2011-12-13 13:54 (diff) (minor) .mau. (/* External links */ updated link to Podnieks's book)
• 2011-12-12 19:51 (diff) David Eppstein (/* Relationship with computability */ remove wlink to dab page en:James Jones (disambiguation) per en:WP:WTAF)
• 2011-12-12 19:29 (diff) VladimirReshetnikov (/* Relationship with computability */ Removed explicit polynomial)
• 2011-12-12 14:36 (diff) (minor) CBM (Reverted edits by 65.213.94.246 (talk) to last version by VladimirReshetnikov)
• 2011-12-12 14:31 (diff) 65.213.94.246 (anon)
• 2011-12-09 00:41 (diff) VladimirReshetnikov (/* Relationship with computability */ Undecidable polynomial equation)
• 2011-11-29 23:43 (diff) (minor) RPHv (/* Proof sketch for the first theorem */)
• 2011-11-27 20:18 (diff) Trovatore (Undid revision 462783626 by 71.225.228.187 (talk) paradoxium?)
• 2011-11-27 20:00 (diff) 71.225.228.187 (anon)
• 2011-11-27 17:50 (diff) 66.229.252.203 (anon) (fixed typo by rewording)
• 2011-11-15 03:31 (diff) Mandarax (/* External links */Typo patrol, typos fixed: theorum → theorem using AWB (7852))
• 2011-11-14 07:04 (diff) (minor) Niceguyedc (WPCleaner (v1.09) Repaired link to disambiguation page - (You can help) - en:Diagonal argument)
• 2011-11-13 10:28 (diff) 110.33.172.241 (anon) (/* Second incompleteness theorem */ this should only be undirectional - there can be inconsistent theories without completeness statements.)
• 2011-11-12 01:22 (diff) CBM (/* Lede */ but not universally)
• 2011-11-12 01:18 (diff) CBM (/* Lede */ The lede is not the place for this sort of detail; it is discussed in more detail below. The summary gives the right impression about the overall status.)
• 2011-11-12 00:59 (diff) 65.27.96.82 (anon)
• 2011-11-12 00:59 (diff) 65.27.96.82 (anon)
• 2011-11-12 00:58 (diff) 65.27.96.82 (anon)
• 2011-11-08 08:47 (diff) Arthur Rubin (Reverted good faith edits by Negyek (talk): Little to do with the incompleteness theorem, actually. (TW))
• 2011-11-08 08:16 (diff) Negyek
• 2011-11-04 09:23 (diff) (minor) EmausBot (bot) (r2.6.4) (Robot: Modifying en:fr:Théorèmes d'incomplétude de Gödel)
• 2011-11-01 01:29 (diff) Wvbailey (Undid revision 458333812 by 81.43.212.56 (talk) I prefer earlier version, e.g. a formula is constructed, not a "procedure". If editor challenges revert, pls carry to talk page.)
• 2011-10-31 18:15 (diff) 81.43.212.56 (anon) (/* Proof sketch for the first theorem */)
• 2011-10-31 18:06 (diff) 81.43.212.56 (anon) (/* First incompleteness theorem */)
• 2011-10-23 20:38 (diff) Trovatore (Undid revision 457035273 by Dan Gluck (talk) too much detail for this article)
• 2011-10-23 20:20 (diff) Dan Gluck (/* Proof sketch for the second theorem */)
• 2011-10-21 04:21 (diff) (minor) ClueBot NG (bot) (Reverting possible vandalism by 50.37.100.98 to version by RDBury. False positive? Report it. Thanks, ClueBot NG. (668898) (Bot))
• 2011-10-21 04:21 (diff) 50.37.100.98 (anon)
• 2011-10-18 23:07 (diff) RDBury (More specific cat.)
• 2011-10-13 05:00 (diff) 174.25.153.132 (anon) (/* External links */)
• 2011-09-29 00:41 (diff) Trovatore (Undid revision 452967498 by 72.24.236.157 (talk) rm drive-by tag)
• 2011-09-29 00:39 (diff) 72.24.236.157 (anon)
• 2011-09-17 03:58 (diff) R.e.b. (/* See also */ Gödel's speed-up theorem)
• 2011-09-15 01:30 (diff) (minor) Valeria.depaiva (/* Articles by Gödel */ by the author gives the impression that Goedel did the translation.)
• 2011-09-13 04:45 (diff) (minor) LaaknorBot (bot) (Robot: Adding en:nn:Ufullstendigheitsteorema)
• 2011-08-30 23:00 (diff) (minor) Wvbailey (Some "anonymous" has a hair up their ass about this article, cf the talk page. I've fixed this particular, silly problem.)
• 2011-08-30 22:47 (diff) 98.224.222.241 (anon) (Undid revision 447424413 by 98.224.222.241 (talk))
• 2011-08-30 02:54 (diff) 98.224.222.241 (anon)
• 2011-08-30 02:52 (diff) 98.224.222.241 (anon)
• 2011-08-29 14:09 (diff) 128.214.20.122 (anon) (/* Wittgenstein and Gödel */)
• 2011-08-25 21:12 (diff) Trovatore (Undid revision 446665747 by 131.111.16.20 (talk) that's a en:WP:EGG -- a reader who sees "numbers" in blue is entitled to expect that it links to en:number)
• 2011-08-25 15:05 (diff) 131.111.16.20 (anon) (/* First incompleteness theorem */)
• 2011-08-19 12:30 (diff) CBM (Remove this. On one hand, it is not obvious that paradoxes "only appear" contradictotry. More importantly, the liar paradox is not the subject of this article, it is just an analogy here)
• 2011-08-19 11:25 (diff) 212.137.36.230 (anon) (/* Relation to the liar paradox */)
• 2011-08-09 19:55 (diff) (minor) CRGreathouse (wording)
• 2011-08-09 19:19 (diff) (minor) CBM (Reverted edits by 202.78.160.108 (talk) to last version by Wvbailey)
• 2011-08-09 18:13 (diff) 202.78.160.108 (anon)
• 2011-08-09 15:06 (diff) Wvbailey (remove vile we-word banner; see talk page)
• 2011-08-09 15:05 (diff) Wvbailey (/* Discussion and implications */ elimination of we-words)
• 2011-08-09 15:01 (diff) Wvbailey (/* Proof sketch for the second theorem */eliminate we-words)
• 2011-08-09 14:59 (diff) Wvbailey (/* Proof sketch for the first theorem */elimination of the we-word)
• 2011-08-08 18:14 (diff) CRGreathouse ({{inappropriate person}}; formatting: 14x HTML entity, 2x whitespace (using Advisor.js))
• 2011-08-01 04:55 (diff) 96.240.15.59 (anon) (/* First incompleteness theorem */)
• 2011-07-31 08:36 (diff) 94.159.213.102 (anon) (/* Construction of a statement about "provability" */)
• 2011-07-14 12:39 (diff) CBM (/* Meaning of the first incompleteness theorem */ copyedit)
• 2011-07-14 12:38 (diff) CBM (/* First incompleteness theorem */ copyedit paragraph)
• 2011-07-14 12:31 (diff) CBM (/* Implications for consistency proofs */ copyedit sentence, to remove "actually")
• 2011-07-12 18:26 (diff) CBM (/* Examples of undecidable statements */ "proven to be true" is a longwinded way of saying "proven")
• 2011-07-12 18:24 (diff) CBM (/* First incompleteness theorem */ "proved to be true" is just a longwinded way of saying "proved")
• 2011-07-12 01:29 (diff) CBM (/* Relationship with computability */ add note on Chaitin's theorem)
• 2011-07-04 11:28 (diff) (minor) Yobot (bot) (/* Proof sketch for the first theorem */en:WP:CHECKWIKI error 44|45|51|52|53|54|57|64|66|80|86|88|91|76 fixes + general fixes (BRFA 21) using AWB (7779))
• 2011-06-27 17:50 (diff) Trovatore (Undid revision 436532278 by 213.151.48.139 (talk) no, this is better; the two hypotheses imply the conclusion)
• 2011-06-27 17:28 (diff) 213.151.48.139 (anon) (/* Second incompleteness theorem */)
• 2011-06-12 21:44 (diff) 72.44.15.104 (anon)
• 2011-06-12 21:37 (diff) 72.44.15.104 (anon)
• 2011-06-09 21:33 (diff) (minor) Rhkramer (/* Arithmetization of syntax */ change 2-digit and 3-digit ASCII to decimal and octal, respectively--that's what they are--if you look up, for example, x in what was called 2-digit ASCII it will be 120, which is 3 digits)
• 2011-06-08 06:57 (diff) (minor) Tobias Bergemann (Undid revision 433017067 by 193.193.185.201 (talk))
• 2011-06-07 11:37 (diff) 193.193.185.201 (anon) (/* First incompleteness theorem */)
• 2011-06-03 02:34 (diff) CasualUser1729 (Fixed link to another Wikipedia article)
• 2011-06-02 14:14 (diff) (minor) AugPi (/* Paraconsistent logic */)
• 2011-06-02 14:12 (diff) (minor) AugPi (/* Paraconsistent logic */ sp)
• 2011-06-02 14:11 (diff) (minor) AugPi (/* Paraconsistent logic */ sp)
• 2011-05-17 16:08 (diff) 192.150.10.201 (anon)
• 2011-05-05 21:03 (diff) (minor) FT2 (/* Proof of independence */ tweak)
• 2011-05-05 21:02 (diff) FT2 (/* Proof of independence */ tweak)
• 2011-05-05 21:00 (diff) FT2 (/* Proof of independence */ clarify adding axioms)
• 2011-05-01 00:24 (diff) (minor) FT2 (/* Proof sketch for the first theorem */ tweak)
• 2011-05-01 00:22 (diff) FT2 (/* Proof sketch for the first theorem */ clarify argument)
• 2011-05-01 00:12 (diff) (minor) FT2 (/* Arithmetization of syntax */ move a sentence)
• 2011-05-01 00:11 (diff) (minor) FT2 (/* Proof sketch for the first theorem */ typo)
• 2011-05-01 00:10 (diff) (minor) FT2 (/* Proof sketch for the first theorem */ italic)
• 2011-05-01 00:09 (diff) FT2 (/* Proof sketch for the first theorem */ improve summary)
• 2011-04-30 23:32 (diff) (minor) FT2 (/* Arithmetization of syntax */ precision)
• 2011-04-30 23:22 (diff) FT2 (/* Proof sketch for the first theorem */ clarify part 2)
• 2011-04-30 23:19 (diff) (minor) FT2 (/* Arithmetization of syntax */ correction)
• 2011-04-30 23:18 (diff) FT2 (/* Arithmetization of syntax */ clarify more)
• 2011-04-30 23:10 (diff) FT2 (/* Proof sketch for the first theorem */ explain Godel numbering better)
• 2011-04-24 15:05 (diff) (minor) Shaun.mk
• 2011-04-24 12:45 (diff) 210.212.8.60 (anon) (/* Background */)
• 2011-04-11 20:31 (diff) CBM (The quote is directly out of the cited paper, which we even have a link to.)
• 2011-04-11 20:06 (diff) 89.242.137.68 (anon) (/* Minds and machines */)
• 2011-04-04 23:20 (diff) Arthur Rubin (Undid revision 422390994 by 86.161.84.65 (talk) accurate, but more confusing)
• 2011-04-04 21:38 (diff) 86.161.84.65 (anon) (Trivial fix in Criticism section from 'wrote Godel' to 'wrote to Godel')
• 2011-04-02 23:53 (diff) (minor) Yobot (bot) (/* Articles by others */en:WP:CHECKWIKI error 61 fixes + general fixes using AWB (7671))
• 2011-03-24 15:17 (diff) 66.117.145.231 (anon) (/* Second incompleteness theorem */)
• 2011-03-19 03:32 (diff) 115.78.73.229 (anon) (/* Background */)
• 2011-03-09 07:06 (diff) (minor) Valeria.depaiva (/* Articles by Gödel */)
• 2011-03-09 07:03 (diff) Valeria.depaiva (/* Articles by Gödel */ adding the most authoritative version German and English)
• 2011-03-06 07:33 (diff) 121.64.47.67 (anon) (/* Dission and implications */)
• 2011-03-06 07:31 (diff) 121.64.47.67 (anon) (/* Discussion and implications */)
• 2011-03-02 17:44 (diff) 82.26.0.138 (anon) (/* Wittgenstein and Gödel */)
• 2011-03-01 02:25 (diff) CBM (/* Wittgenstein and Gödel */ fix up references)
• 2011-03-01 01:33 (diff) 82.26.0.138 (anon) (/* Wittgenstein and Gödel */ clear up a paragraph in this section)
• 2011-03-01 01:26 (diff) 82.26.0.138 (anon) (/* Wittgenstein and Gödel */)
• 2011-02-26 15:18 (diff) 196.210.228.213 (anon) (/* Arithmetization of syntax */)
• 2011-02-26 15:17 (diff) 196.210.228.213 (anon) (/* Arithmetization of syntax */)
• 2011-02-23 21:41 (diff) 132.170.68.20 (anon) (/* Criticism */)
• 2011-02-23 17:00 (diff) (minor) Popopp (/* Appeals to the incompleteness theorems in other fields */ fix rdrct)
• 2011-02-18 00:02 (diff) CBM (Undid revision 414529452 by 171.66.74.205 (talk) - sockpuppet of banned editor)
• 2011-02-17 23:56 (diff) 171.66.74.205 (anon) (/* External links */ A proof of the incompleteness theorem that anyone can understand.)
• 2011-02-17 14:47 (diff) (minor) Herk1955 (/* External links */)
• 2011-01-22 18:47 (diff) CBM (/* First incompleteness theorem */ rephrase)
• 2011-01-22 15:30 (diff) CBM (/* First incompleteness theorem */ No need for footnote, I guess)
• 2011-01-22 15:29 (diff) CBM (/* First incompleteness theorem */ Clarify pronoun "it")
• 2011-01-20 11:37 (diff) (minor) AnomieBOT (bot) (Dating maintenance tags: {{Clarify}})
• 2011-01-20 11:17 (diff) Michael C Price (/* First incompleteness theorem */ pronoun ambiguity tagged for clarification)
• 2011-01-14 16:16 (diff) Arthur Rubin (Undid revision 407831733 by 134.93.128.12 (talk) seems to be about a different topic than the article en:Closure of Physics before the last set of edits)
• 2011-01-14 12:39 (diff) 134.93.128.12 (anon) (/* Discussion and implications */)
• 2011-01-04 17:00 (diff) (minor) CRGreathouse (Disambiguated: en:Hao Wang → en:Hao Wang (academic) using Dab solver)
• 2010-12-24 15:28 (diff) Wvbailey (Rejected the last change (by 77.126.207.101) and restored revision 401969600 by Arthur Rubin)
• 2010-12-24 15:26 (diff) 77.126.207.101 (anon) (/* Second incompleteness theorem */)
• 2010-12-12 16:02 (diff) (minor) Arthur Rubin (Reverted edits by 114.96.75.107 (talk) to last version by CBM)
• 2010-12-12 13:43 (diff) 114.96.75.107 (anon) (/* Limitations of Gödel's theorems */)
• 2010-12-02 21:05 (diff) CBM (/* Implications for consistency proofs */ Rm claim about Kriesel; it may be true, but it's not really important here)
• 2010-12-02 19:45 (diff) EmilJ (/* Second incompleteness theorem */ corrections)
• 2010-12-02 16:32 (diff) CBM (/* Second incompleteness theorem */ Add one more in other words)
• 2010-12-02 16:30 (diff) CBM (/* Second incompleteness theorem */ Copyedit the provability conditions, add sharps for Goedel numbers)
• 2010-11-28 21:41 (diff) Trovatore (Undid revision 399393941 by 76.254.235.105 (talk) not this again)
• 2010-11-28 21:40 (diff) 76.254.235.105 (anon) (standard reference Common sense for concurrency and inconsistency robustness using Direct Logic(TM) and the Actor Model)
• 2010-11-26 19:24 (diff) (minor) Gregbard (/* External links */Template:Logic using AWB)
• 2010-11-22 09:11 (diff) 69.111.192.233 (anon) (/* Articles by others */ fmt and add page number)
• 2010-11-22 09:10 (diff) 69.111.192.233 (anon) (/* Articles by others */ add Davis article which looks pretty good)
• 2010-11-08 21:51 (diff) CBM (It is neither unreferenced nor self-promotion. It is a reference to the literature for one of the topics of the paragraph.)
• 2010-11-08 21:38 (diff) Tnxman307 (/* Limitations of Gödel's theorems */ not sure what that was doing there - it was unreferenced (possibly self promotion?))
• 2010-11-07 20:25 (diff) (minor) David Eppstein (Reverted edits by 91.64.89.209 (talk) to last version by LilHelpa)
• 2010-11-07 20:21 (diff) 91.64.89.209 (anon) (/* First incompleteness theorem */)
• 2010-11-01 00:47 (diff) (minor) LilHelpa (General fixes and Typo fixing, typos fixed: Guiness → Guinness, of of → of (2) using AWB)
• 2010-10-21 08:14 (diff) 83.78.126.223 (anon) (/* Books about the theorems */ fix)
• 2010-10-02 02:02 (diff) (minor) CBM (Configured pending changes settings for en:Gödel's incompleteness theorems: Because the protection expired. Setting another expiration in 3 months. Should reevaluate at that time. [Accept: require "autoconfirmed" permission] (expires 02:02, 2)
• 2010-10-02 01:58 (diff) (minor) CBM (Configured pending changes settings for en:Gödel's incompleteness theorems: Somehow the pending changes was disabled without a log entry [Accept: require "autoconfirmed" permission])
• 2010-10-01 22:24 (diff) 136.152.180.157 (anon) (/* Discussion and implications */)
• 2010-09-20 17:45 (diff) Kozation (/* Relationship with computability */ corrrected "no" to "some given")
• 2010-09-17 22:32 (diff) (minor) Luckas-bot (bot) (robot Adding: en:no:Ufullstendighetsteoremet)
• 2010-09-09 01:00 (diff) CBM (/* Meaning of the first incompleteness theorem */ replace possible with "there are", shorter phrasing suggested by aleph4 on talk)
• 2010-09-08 11:26 (diff) CBM (/* Meaning of the first incompleteness theorem */ add link to true arithmetic)
• 2010-09-07 19:56 (diff) Trovatore (rvv)
• 2010-09-07 19:56 (diff) 202.78.163.27 (anon)
• 2010-09-07 19:55 (diff) 202.78.163.27 (anon)
• 2010-09-02 10:54 (diff) (minor) Citation bot 1 (bot) (Citations: [Pu184]Unified citation types. You can use this bot yourself. Report bugs here.)
• 2010-08-26 21:02 (diff) Trovatore (Undid revision 381111005 by 76.64.1.246 (talk) confuses two sorts of "undecidability")
• 2010-08-26 12:55 (diff) 76.64.1.246 (anon) (/* Relationship with computability */)
• 2010-08-23 05:25 (diff) (minor) David Eppstein (Reverted edits by 211.30.251.190 (talk) to last version by 88.104.161.156)
• 2010-08-23 05:22 (diff) 211.30.251.190 (anon)
• 2010-08-16 10:33 (diff) 88.104.161.156 (anon) (/* First incompleteness theorem */ - added important qualifications)
• 2010-08-16 00:28 (diff) CBM (/* Wittgenstein and Gödel */ add sentence on Berto 2009)
• 2010-08-16 00:24 (diff) CBM (/* Wittgenstein and Gödel */ make point of this paragraph more clear)
• 2010-08-16 00:03 (diff) CBM (/* First incompleteness theorem */ The meaning of "true" is explained in the footnote)
• 2010-08-15 23:58 (diff) (minor) Wvbailey (/* Meaning of the first incompleteness theorem */alternately: "are those who have this problem")
• 2010-08-15 11:14 (diff) CBM (/* First incompleteness theorem */ copyedit some, add nbsp, unlink duplicate link in statement)
• 2010-08-15 10:56 (diff) CBM (/* Background */ copyediting)
• 2010-08-15 09:24 (diff) The Rhymesmith (/* Wittgenstein and Gödel */)
• 2010-08-15 05:17 (diff) Tkuvho (/* First incompleteness theorem */)
• 2010-08-15 01:22 (diff) Wvbailey (/* Miscellaneous references */ add Wang 1996 reference)
• 2010-08-15 01:19 (diff) Wvbailey (/* Wittgenstein and Gödel */source of quote is Hao Wang 1996 "A Logical Journey: From Goedel to Philosophy", The MIT Press, Cambridge MA, ISBN 0-262-23189-1)
• 2010-08-14 18:30 (diff) CBM (Add Rodych 2003 bibliographic info, sort references some)
• 2010-08-14 18:12 (diff) CBM (Add bibliographic info for Floyd/Putnam 2000. Add inline cite for a fact tag.)
• 2010-08-14 18:07 (diff) CBM (/* Wittgenstein and Gödel */ Remove a quote - it was not clear what point Wittgenstein was making, and we don't want to take the space to try to explain it, even if that were possible)
• 2010-08-14 13:53 (diff) Wvbailey (/* Wittgenstein and Gödel */well written but needs citations to page and etc. Eliminate the nasty "cquote" formatting.)
• 2010-08-14 11:27 (diff) The Rhymesmith (/* Criticism */)
• 2010-08-14 11:27 (diff) The Rhymesmith (/* Criticism */)
• 2010-08-14 11:24 (diff) The Rhymesmith (/* Criticism */)
• 2010-08-14 11:16 (diff) The Rhymesmith (/* Criticism */)
• 2010-08-14 11:15 (diff) The Rhymesmith (/* Criticism */)
• 2010-08-12 22:08 (diff) Yousou (Undid revision 378611766 by 213.122.51.147 (talk))
• 2010-08-12 22:05 (diff) 213.122.51.147 (anon) (/* Proof sketch for the second theorem */)
• 2010-08-12 22:02 (diff) 213.122.51.147 (anon) (/* Miscellaneous references */)
• 2010-08-11 16:59 (diff) Wvbailey (/* External links */remove per discussion on talk page)
• 2010-08-11 09:22 (diff) 75.62.4.94 (anon) (Undid revision 378328047 by Twiceuponatime (talk) The edit summary is accurate, please check it.)
• 2010-08-11 08:27 (diff) Twiceuponatime (Undid revision 378325095 by 75.62.4.94 edit summary does not match actual edit)
• 2010-08-11 07:54 (diff) 75.62.4.94 (anon) (m fmt (move Wigderson citation to misc references section instead of using footnote))
• 2010-08-11 07:40 (diff) 75.62.4.94 (anon) (/* Minds and machines */ m fix punctuation of Wigderson quote)
• 2010-08-11 07:33 (diff) 75.62.4.94 (anon) (/* External links */ remote Hewitt video, see talk page and en:WP:EL. Not sure what to do about BBC video.)
• 2010-08-11 07:29 (diff) 75.62.4.94 (anon) (/* Discussion and implications */ add viewpoint of Avi Wigderson)
• 2010-08-11 07:18 (diff) 75.62.4.94 (anon) (/* Discussion and implications */ m wikilink essential undecidabillity as alternate terminology)
• 2010-08-10 00:36 (diff) 63.112.0.74 (anon) (/* External links */ Long videos from BBC (Malone) and Stanford (Hewitt))
• 2010-08-07 13:01 (diff) CBM (Undo previous edit. We don't usually put space before closing quotation marks.)
• 2010-08-07 12:57 (diff) 59.167.255.27 (anon) (/* First incompleteness theorem */)
• 2010-08-05 18:48 (diff) (minor) AvicAWB (rm template, soon to be deleted, see discussion here. using AWB)
• 2010-08-01 17:40 (diff) 64.165.100.82 (anon) (added references by Professor Berto)
• 2010-07-26 23:39 (diff) CBM (replace is with are)
• 2010-07-26 20:28 (diff) MarcelB612 (/* Limitations of Gödel's theorems */)
• 2010-07-16 17:39 (diff) (minor) Apokrif (/* Miscellaneous references */)
• 2010-07-14 20:21 (diff) Trovatore (/* Formalized proofs */ ... and there's only one Shankar in the refs, so we don't need a first name)
• 2010-07-14 20:19 (diff) Trovatore (/* Formalized proofs */ ...but we don't need the link repeated)
• 2010-07-14 20:17 (diff) 130.107.15.43 (anon) (/* Formalized proofs */)
• 2010-07-14 20:16 (diff) 130.107.15.43 (anon) (/* Formalized proofs */)
• 2010-07-11 12:21 (diff) AmirOnWiki (trying again to dispel a misinterpretation - now only quoting a source)
• 2010-07-08 23:48 (diff) (minor) Iamthedeus (/* See also */ undefinability not indefinability)
• 2010-07-06 23:17 (diff) (minor) Citation bot 1 (bot) (Citations: [Pu170]Tweaked: doi. You can use this bot yourself! Report bugs here.)
• 2010-07-03 18:28 (diff) Arthur Rubin (revert unsourced statements ABOUT the given reference. As he's living, it's also a BLP violation)
• 2010-07-03 17:49 (diff) (minor) AmirOnWiki (/* Miscellaneous references */)
• 2010-07-03 17:48 (diff) AmirOnWiki (/* Misinterpretations of the incompleteness theorems */)
• 2010-06-30 12:39 (diff) CBM (/* Books about the theorems */ add Lindstrom 1997 from talk page)
• 2010-06-30 12:31 (diff) (minor) CBM (Configured pending changes settings for en:Gödel's incompleteness theorems: Chronically semi-protected; lowering to pending changes as part of that trial [Accept: require "autoconfirmed" permission] (expires 12:31, 30 September 2010 (UTC)))
• 2010-06-30 12:31 (diff) (minor) CBM (Unprotected Gödel's incompleteness theorems: Chronically semi-protected; lowering to pending changes as part of that trial)
• 2010-06-30 12:30 (diff) CBM (Changing to "pending changes" protection)
• 2010-06-05 15:07 (diff) (minor) Jimpaz (/* Criticism */ quotation mark fix)
• 2010-06-03 20:35 (diff) Arthur Rubin (Undid revision 365861209 by 63.249.108.250 (talk) revert topic-banned editor. AGAIN.)
• 2010-06-03 17:59 (diff) Beeblebrox (adding {{pp-semi-protected|expiry={{subst:#time:F j, Y|+1 month}}}} (TW))
• 2010-06-03 17:58 (diff) (minor) Beeblebrox (Protected Gödel's incompleteness theorems: Semi-protection. using TW ([edit=autoconfirmed] (expires 17:58, 3 July 2010 (UTC)) [move=autoconfirmed] (expires 17:58, 3 July 2010 (UTC))))
• 2010-06-03 17:05 (diff) 63.249.108.250 (anon) (Undid revision 365859181 by Arthur Rubin (talk))
• 2010-06-03 16:51 (diff) Arthur Rubin (Undid revision 365854709 by 99.29.247.230 (talk) revert topic-banned Hewitt edit)
• 2010-06-03 16:22 (diff) 99.29.247.230 (anon) (Undid revision 365853770 by Arthur Rubin (talk))
• 2010-06-03 16:15 (diff) Arthur Rubin (Undid revision 365853268 by 99.29.247.230 (talk) reverted topic-banned Hewitt edit.)
• 2010-06-03 16:12 (diff) 99.29.247.230 (anon) (restored edit)
• 2010-06-03 07:59 (diff) Arthur Rubin (Undid revision 365766916 by 64.9.242.94 (talk) revert edit by banned editor)
• 2010-06-03 03:57 (diff) 64.9.242.94 (anon) (Undid revision 365765269 by Gavia immer (talk))
• 2010-06-03 03:42 (diff) Gavia immer (Reverted 1 edit by 64.9.242.94; Consensus is not to plump Hewitt this way. (TW))
• 2010-06-03 03:40 (diff) 64.9.242.94 (anon) (Undid revision 365739463 by Arthur Rubin (talk))
• 2010-06-03 00:32 (diff) (minor) Arthur Rubin (Reverted edits by 17.244.68.54 (talk) to last version by Wvbailey)
• 2010-06-03 00:23 (diff) 17.244.68.54 (anon) (Undid revision 365736241 by Wvbailey (talk))
• 2010-06-03 00:10 (diff) Wvbailey (Undid revision 365719917 by 171.66.50.25 (talk) Hewitt's student's edits -- over-the-top wording has little to do w/ GODOEL'S theorems)
• 2010-06-02 22:19 (diff) 171.66.50.25 (anon) (Undid revision 365710748 by Trovatore (talk))
• 2010-06-02 21:20 (diff) Trovatore (rv)
• 2010-06-02 21:16 (diff) 171.66.50.25 (anon) (edit dispappeared again)
• 2010-06-02 21:02 (diff) Trovatore (of course it "disappeared")
• 2010-06-02 21:01 (diff) 171.66.50.25 (anon) (edit disappeared)
• 2010-06-02 20:56 (diff) Trovatore (not this again)
• 2010-06-02 20:52 (diff) 171.66.50.25 (anon) (better reference)
• 2010-05-27 20:12 (diff) 69.228.170.24 (anon) (/* Miscellaneous references */ link preprint of Zach article)
• 2010-05-26 07:47 (diff) 69.228.170.24 (anon) (Add Zach 2003 reference about epsilon calculus, mainly because it's available online)
• 2010-05-26 07:25 (diff) 69.228.170.24 (anon) (/* Articles by others */ remove Feferman 1984 reference per talk page. The article doesn't currently refer to it.)
• 2010-05-23 20:06 (diff) SunCreator (TypoFix and general fixes of B-class articles using AWB)
• 2010-05-19 04:57 (diff) 158.144.65.86 (anon) (/* Criticism */)
• 2010-05-14 03:56 (diff) 67.248.22.159 (anon) (oe/ö)
• 2010-05-09 23:35 (diff) CBM (/* Paraconsistent logic */ We have a published paper; no need for an unpublished one in addition)
• 2010-05-09 23:34 (diff) CBM (/* Miscellaneous references */ Rm unpublished Hwitt paper, leaving the other, published, one)
• 2010-05-09 12:16 (diff) CBM (Undid revision 361066068 by Joseph Solis in Australia (talk))
• 2010-05-09 11:06 (diff) (minor) Joseph Solis in Australia (/* Notes */ Change the font size)
• 2010-05-05 10:37 (diff) CBM (Goedel's incompleteness theorems are not part of computational complexity theory)
• 2010-05-05 10:29 (diff) Bijuro
• 2010-05-03 12:22 (diff) CBM (/* Criticism */ spelling (after major edit of this section))
• 2010-05-03 12:15 (diff) CBM (/* Criticism */ Significant edit)
• 2010-05-03 06:01 (diff) Trovatore (/* History */ Gavia immer: I'm fairly sure "falsehood" is the usual word here. If you're still not convinced let me know and we can look into it further.)
• 2010-05-03 00:12 (diff) Wvbailey (/* Criticism */I pulled my verison in, edited the quotes, but kept CBM's version as hidden text)
• 2010-05-02 17:11 (diff) CBM (/* History */ c/e)
• 2010-05-02 12:19 (diff) CBM (/* History */ copyedit and add some references)
• 2010-05-02 12:12 (diff) CBM (/* Miscellaneous references */ + Zach 2006)
• 2010-05-02 03:38 (diff) Gavia immer (/* History */ falseness?)
• 2010-05-02 03:24 (diff) CBM (/* History */ falsehood)
• 2010-05-02 03:23 (diff) CBM (/* History */ Use "habilitation", the meaning is OK and it is easier to read and spell correctly)
• 2010-05-02 03:19 (diff) CBM (/* History */ small copyedits)
• 2010-05-02 03:09 (diff) CBM (/* History */ correct year)
• 2010-05-02 01:25 (diff) CBM (A start at a history section)
• 2010-04-30 03:56 (diff) CBM (Revert to version without extra paragraph on "direct logic")
• 2010-04-30 03:32 (diff) (minor) Abecedare (Protected Gödel's incompleteness theorems: per en:Wikipedia:Requests_for_arbitration/Carl_Hewitt and recent resurrection of promotional IP edits ([edit=autoconfirmed] (expires 03:32, 14 May 2010 (UTC)) [move=autoconfirmed] (expires 03:32, 14 May 2010 (U)
• 2010-04-30 03:27 (diff) (minor) Gavia immer (/* Other Logics */ tyop)
• 2010-04-30 03:08 (diff) 17.244.70.240 (anon) (Changing the section title helps a little)
• 2010-04-30 02:04 (diff) CBM (Perhaps you prefer this section title?)
• 2010-04-30 01:56 (diff) 17.244.70.240 (anon) (Wikipedia hates Hewitt. But that's not a good reason for inaccuracies in articles.)
• 2010-04-30 01:21 (diff) 69.228.170.24 (anon) (revert to CBM's version with the dialetheism section)
• 2010-04-30 01:07 (diff) 69.228.170.24 (anon) (Section removed per talkpage discussion. It's not a matter of accuracy, it's undue weight in the article en:WP:UNDUE. Please stop re-inserting it.)
• 2010-04-30 00:52 (diff) 68.65.169.180 (anon) (This version is more accurate than previous version. So someone should fix the bugs and not just revert.)
• 2010-04-30 00:44 (diff) 69.228.170.24 (anon) (/* Internet information reasoning */ remove section about fringe topic per talk page.)
• 2010-04-29 23:47 (diff) 68.65.169.140 (anon) (improved paragraph)
• 2010-04-29 21:50 (diff) CBM (/* Miscellaneous references */ non-functional link)
• 2010-04-29 21:50 (diff) CBM (/* Miscellaneous references */ title correction)
• 2010-04-29 21:43 (diff) Trovatore (please stop pushing the Hewitt stuff)
• 2010-04-29 21:42 (diff) 17.226.15.239 (anon) (disappeared again so I put a comment on discussion paage)
• 2010-04-29 21:36 (diff) CBM (No reason I can see to emphasize Hewitt's work to that degree)
• 2010-04-29 21:21 (diff) 17.226.15.239 (anon) (improvements disappeared again)
• 2010-04-29 21:05 (diff) Trovatore (rv to last by Trovatore)
• 2010-04-29 20:33 (diff) 17.244.70.240 (anon) (improvements disappeared?)
• 2010-04-29 19:07 (diff) Trovatore (rv to last by Arthur Rubin)
• 2010-04-29 16:44 (diff) 71.198.220.76 (anon) (corrected title)
• 2010-04-29 16:42 (diff) 71.198.220.76 (anon) (Internet information reasoning)
• 2010-04-25 07:54 (diff) (minor) Arthur Rubin (Reverted edits by 67.186.133.62 (talk) to last version by CBM)
• 2010-04-24 20:53 (diff) 67.186.133.62 (anon) (/* Second incompleteness theorem */)
• 2010-04-24 11:42 (diff) CBM (/* Discussion and implications */ rm paragraph under discussion on talk page, and rm stuff that duplicates other material in the article)
• 2010-04-20 16:43 (diff) CBM (/* Dialethism */ c/e)
• 2010-04-20 14:22 (diff) CBM (/* Dialethism */ correct year in Shapiro reference)
• 2010-04-20 14:22 (diff) CBM (/* Miscellaneous references */ Add Priest (1984, 2006) and Shapiro (2002))
• 2010-04-20 14:17 (diff) CBM (/* Appeals to the incompleteness theorems in other fields */ expand section on dialethism)
• 2010-04-14 10:59 (diff) (minor) RjwilmsiBot (bot) (/* Articles by others */fixing page range dashes using AWB)
• 2010-04-13 05:32 (diff) (minor) Ytcracker (/* Original statements */)
• 2010-04-08 20:50 (diff) (minor) Morgaladh (/* Appeals to the incompleteness theorems in other fields */)
• 2010-04-08 18:01 (diff) (minor) Długosz (/* Arithmetization of syntax */ multiplication sign instead of computer-language asterisk)
• 2010-04-08 16:22 (diff) (minor) Długosz (/* Meaning of the first incompleteness theorem */ dashes)
• 2010-04-07 21:33 (diff) CBM (/* References */ This article uses parenthetical referencing. If you don't read an article to determine the referencing style, please don't place tags on it)
• 2010-04-07 19:04 (diff) Jrtayloriv (/* References */)
• 2010-04-04 05:19 (diff) H.ehsaan (/* First incompleteness theorem */)
• 2010-04-03 23:54 (diff) (minor) Illythr (Reverted edits by 99.22.51.202 to last revision by ClueBot (HG))
• 2010-04-03 23:54 (diff) 99.22.51.202 (anon)
• 2010-04-03 23:52 (diff) (minor) ClueBot (bot) (Reverting possible vandalism by 99.22.51.202 to version by Hairy Dude. False positive? Report it. Thanks, ClueBot. (583489) (Bot))
• 2010-04-03 23:52 (diff) 99.22.51.202 (anon)
• 2010-03-30 08:31 (diff) Hairy Dude (don't put quotations in italics)
• 2010-03-26 16:54 (diff) Noaqiyeum (/* Limitations of Gödel's theorems */)
• 2010-03-23 03:01 (diff) 66.127.52.47 (anon) (/* Original statement */ m fix singular/plural and referent of "his")
• 2010-03-19 09:07 (diff) 66.127.52.47 (anon) (remove original statements of theorems, they are in incomprehensible notation. see talkpage)
• 2010-03-07 07:00 (diff) (minor) CRGreathouse (Disambiguated: en:ordinal → en:Ordinal number using Dab solver)
• 2010-03-07 06:32 (diff) (minor) CRGreathouse (spacing, links in See also and elsewhere)
• 2010-03-03 17:45 (diff) (minor) SolarMcPanel
• 2010-02-15 20:26 (diff) SarekOfVulcan (rv apparent COATRACK)
• 2010-02-15 20:25 (diff) (minor) SarekOfVulcan (Protected Gödel's incompleteness theorems: per en:Wikipedia:Requests for arbitration/Carl Hewitt#Post-case clarification ([edit=autoconfirmed] (expires 20:25, 1 March 2010 (UTC)) [move=autoconfirmed] (expires 20:25, 1 March 2010 (UTC))))
• 2010-02-15 13:46 (diff) 98.210.236.39 (anon) (/* Miscellaneous references */ repaired link)
• 2010-02-15 11:55 (diff) 98.210.236.39 (anon) (Undid revision 344172169 by 66.127.55.192 (talk))
• 2010-02-15 08:08 (diff) 66.127.55.192 (anon) (/* Extensions of Gödel's original result */ remove en:WP:COATRACK xref to article now redirected to here)
• 2010-02-14 23:13 (diff) 99.29.247.230 (anon) (/* Extensions of Gödel's original result */ Contemporary incompleteness theorems)
• 2010-02-12 09:09 (diff) (minor) Tobias Bergemann (/* Limitations of Gödel's theorems */ Typo ("Frankel" → "Fraenkel"))
• 2010-02-11 00:37 (diff) CBM (Undid revision 343255236 by 171.66.107.218 (talk) - the tone of this is completely unencyclopedic)
• 2010-02-11 00:25 (diff) 171.66.107.218 (anon) (Incompleteness in Logic for the Internet Age (from talk page))
• 2010-02-10 20:18 (diff) 66.127.55.192 (anon) (/* Appeals to the incompleteness theorems in other fields */ tweak "possible"->"proposed")
• 2010-02-10 18:51 (diff) 66.127.55.192 (anon) (/* Appeals to the incompleteness theorems in other fields */ tweak paraconsistency again)
• 2010-02-10 07:07 (diff) 66.127.55.192 (anon) (/* Appeals to the incompleteness theorems in other fields */ expand slightly on Hewitt work)
• 2010-02-10 06:25 (diff) 66.127.55.192 (anon) (shorten Hewitt paraconsistency stuff and move to more appropriate section)
• 2010-02-10 04:51 (diff) 66.127.55.192 (anon) (/* Limitations of Gödel's theorems */ wikilink true arithmetic)
• 2010-02-10 04:50 (diff) 66.127.55.192 (anon) (/* Limitations of Gödel's theorems */ restore Willard citation)
• 2010-02-10 04:33 (diff) 66.127.55.192 (anon) (/* Limitations of Gödel's theorems */ self-verifying m)
• 2010-02-10 04:31 (diff) 66.127.55.192 (anon) (/* Limitations of Gödel's theorems */ gloss/link self-verifying theories)
• 2010-02-10 03:15 (diff) 66.127.55.192 (anon) (revert to CBM's most recent version)
• 2010-02-10 03:01 (diff) 66.127.55.192 (anon) (cite Kleene in lede since the statement is pasted directly)
• 2010-02-10 03:00 (diff) 66.127.55.192 (anon) (wikilink "theory")
• 2010-02-10 02:59 (diff) 66.127.55.192 (anon) (use Kleene's terminology with a slight gloss)
• 2010-02-10 02:54 (diff) CBM (slight copyedit of the lede)
• 2010-02-10 02:51 (diff) 66.127.55.192 (anon) (specify and gloss "effective procedure", the theorems are not about computer programs)
• 2010-02-10 02:49 (diff) 66.127.55.192 (anon) (attempt to simplify exposition)
• 2010-02-10 02:16 (diff) 70.231.251.220 (anon) (/* Extensions of Gödel's original result */ fixing inaccuracies per talk page)
• 2010-02-09 15:12 (diff) (minor) Arthur Rubin (Reverted edits by Likebox (talk) to last version by CBM)
• 2010-02-09 12:40 (diff) (minor) Likebox (sufficiently powerful is needed for second theorem, and clarify sentence)
• 2010-02-09 12:22 (diff) Likebox (The added assumptions are not necessary--- the theorem is stated carefully)
• 2010-02-09 12:12 (diff) CBM (/* Lede */ rearrange and add description of second. copyedit.)
• 2010-02-09 12:04 (diff) CBM (I'm not really sure what the point of this short paragraph re Feferman was; Sigma^0_1 is weaker than arithmetical, which we use higher up; and no literature pointer makes it hard to fix; removing)
• 2010-02-09 12:00 (diff) CBM (/* Extensions of Gödel's original result */ try to merge changes from 98.xxx from yesterday)
• 2010-02-09 09:12 (diff) Arthur Rubin (Undid revision 342806948 by 98.210.236.129 (talk) reduced accuracy, actually)
• 2010-02-08 23:38 (diff) 98.210.236.129 (anon) (increased accuracy of description)
• 2010-02-08 16:19 (diff) CBM (Trim back some - I think that a brief pointer belongs here, but it seems to be growing and growing)
• 2010-02-08 15:08 (diff) 98.210.236.129 (anon) (clarification)
• 2010-02-08 03:23 (diff) 166.205.137.151 (anon) (/* Extensions of Gödel's original result */)
• 2010-02-08 03:15 (diff) 166.205.137.151 (anon) (/* Extensions of Gödel's original result */)
• 2010-02-08 03:10 (diff) 166.205.137.151 (anon) (/* Extensions of Gödel's original result */)
• 2010-02-08 03:06 (diff) 166.205.137.151 (anon) (/* Miscellaneous references */)
• 2010-02-07 22:43 (diff) CBM (Once again condense Hewitt refs)
• 2010-02-07 22:42 (diff) CBM (/* Miscellaneous references */ Re-insert Hewitt refs (why did they disappear?))
• 2010-02-07 22:33 (diff) 98.210.236.129 (anon) (See published article)
• 2010-02-07 21:50 (diff) (minor) Arthur Rubin (Reverted edits by 63.249.99.129 (talk) to last version by Arthur Rubin)
• 2010-02-07 21:46 (diff) 63.249.99.129 (anon) (/* Proof via Self-refutation */)
• 2010-02-07 21:46 (diff) 63.249.99.129 (anon) (Undid revision 342562763 by Arthur Rubin (talk))
• 2010-02-07 21:44 (diff) Arthur Rubin (Undid revision 342562569 by 63.249.99.129 (talk) rm Hewett weirdness)
• 2010-02-07 21:43 (diff) 63.249.99.129 (anon) (Undid revision 342243022 by 66.127.55.192 (talk))
• 2010-02-06 05:32 (diff) 66.127.55.192 (anon) (/* Proof via Self-refutation */ rm hewitt weirdness)
• 2010-02-06 03:03 (diff) 209.131.62.144 (anon) (/* Proof via Self-refutation */ fixed typo)
• 2010-02-06 02:58 (diff) 209.131.62.144 (anon) (from discussion page)
• 2010-02-06 01:33 (diff) Likebox (/* Proof via Self-refutation */ There is no new idea here)
• 2010-02-06 01:06 (diff) 65.106.72.229 (anon) (Proof via Self-refutation)
• 2010-01-30 09:02 (diff) Gandalf61 (Undid revision 340769459 by IsleLaMotte (talk) rv book spam)
• 2010-01-29 19:33 (diff) IsleLaMotte
• 2010-01-26 13:35 (diff) Fredeaker (/* External links */)
• 2010-01-26 01:44 (diff) CBM (Move "formalized proofs" subsection under "proof")
• 2010-01-09 17:27 (diff) (minor) Razimantv (disambig)
• 2010-01-05 23:25 (diff) (minor) VolkovBot (bot) (robot Modifying: en:ru:Теорема Гёделя о неполноте)
• 2010-01-02 22:14 (diff) AshtonBenson
• 2009-12-28 14:11 (diff) CBM (/* Articles by others */ Add Willard 2001 (see previous edit). The van in Van H. is ignored for alphabetizing.)
• 2009-12-28 14:07 (diff) CBM (/* Limitations of Gödel's theorems */ I do think it is worth mentioning Willard's work; adding a proper reference next)
• 2009-12-28 10:58 (diff) Tedickey (rv unusable link)
• 2009-12-28 09:11 (diff) (minor) AshtonBenson (/* Limitations of Gödel's theorems */)
• 2009-12-22 20:04 (diff) (minor) Rjwilmsi (/* References */Typo fixing, typos fixed: Guiness → Guinness using en:Project:AWB)
• 2009-12-15 08:06 (diff) Trovatore (please don't replace redirects by pipes. see en:WP:NOTBROKEN)
• 2009-12-15 06:58 (diff) (minor) Mark Renier (Redirect bypass from en:Berry's paradox to en:Berry paradox using popups)
• 2009-12-04 12:19 (diff) CBM (/* See also */ logicism already linked in article)
• 2009-12-04 08:37 (diff) Tkuvho (/* See also */)
• 2009-12-04 01:29 (diff) Trovatore (challenged perhaps, but still widely held. alternative views can certainly be discussed in the article)
• 2009-12-04 01:27 (diff) Likebox (this was a near universal belief, but is challenged today within the very mainstream reverse mathematics)
• 2009-12-03 19:45 (diff) Trovatore (hmm, not bad, but "theorems" is confusing here (the statements don't have a proof in the theory under study). Also restore present tense.)
• 2009-12-03 18:50 (diff) Likebox (replace recursive by computable, and simplify language)
• 2009-12-03 02:32 (diff) Gregbard (/* Examples of undecidable statements */en:truth value using en:Project:AWB)
• 2009-12-01 12:05 (diff) CBM (/* Lede */ rm cleanup tag; query still on talk page)
• 2009-11-27 19:01 (diff) CBM (/* Lede */ This article uses parenthetical inline references and informative footnotes, a style permitted by the MOS)
• 2009-11-26 00:55 (diff) 193.136.173.42 (anon) (Undid revision 327960997 by 193.136.173.42 (talk))
• 2009-11-26 00:48 (diff) 193.136.173.42 (anon)
• 2009-11-25 22:05 (diff) Stan the fisher (I'm putting in the cleanup and in-line citations tags mainly because the article has two different citation standards (parenthetical and footnote) and the references section is really messy.)
• 2009-11-20 08:00 (diff) 88.218.158.182 (anon) (/* Minds and machines */)
• 2009-11-16 11:01 (diff) Fictionalist (/* Meaning of the first incompleteness theorem */)
• 2009-11-16 11:01 (diff) Fictionalist (/* Meaning of the first incompleteness theorem */)
• 2009-11-15 19:59 (diff) Trovatore (I'm not sure what the point of previous edit was -- it *looks* like mostly removing whitespace for some reason. Reverting to avoid checking everything.)
• 2009-11-15 18:06 (diff) 91.55.196.93 (anon)
• 2009-11-11 00:20 (diff) (minor) Srnec (can't > cannot)
• 2009-11-09 00:11 (diff) (minor) Gregbard (Quick-adding category Metatheorems (using HotCat))
• 2009-11-08 21:31 (diff) Trovatore (restoring gentler opening sentence -- see talk)
• 2009-11-08 01:40 (diff) Gregbard (/* External links */Category:Metatheorems using AWB)
• 2009-11-06 16:50 (diff) Philosofool (Undid revision 324263371 by Þjóðólfr (talk) The previous version was better.)
• 2009-11-06 12:07 (diff) Þjóðólfr (Reorder - Description first)
• 2009-11-04 23:35 (diff) Trovatore (/* Appeals to the incompleteness theorems in other fields */ the sentence is in present tense; the shift to past tense is jarring unless the intent is that this no longer happens, which I doubt)
• 2009-11-04 23:33 (diff) Frungi (/* Appeals to the incompleteness theorems in other fields */)
• 2009-11-03 11:51 (diff) CBM (/* Lede */ skip dab page)
• 2009-11-01 02:01 (diff) (minor) Standardfact (udl)
• 2009-10-31 23:53 (diff) (minor) Frungi (theorys → theories)
• 2009-10-31 05:01 (diff) 69.228.171.150 (anon) (/* Formalized proofs */ got confused with a different Boyer-Moore prover. see http://eom.springer.de/b/b120410.htm)
• 2009-10-30 23:02 (diff) Arthur Rubin (disambiguate en:formal theory)
• 2009-10-30 23:01 (diff) Arthur Rubin (replace en:formal system by en:formal theory in the lede, add "effectively generated")
• 2009-10-30 22:41 (diff) Philosofool (added statement of theorem to the introduction)
• 2009-10-30 22:30 (diff) 70.171.199.139 (anon) (clean up prose of intro.)
• 2009-10-30 19:04 (diff) Wvbailey (The theorems are applicable to a specific type of axiomatic system, not "mathematics" globally)
• 2009-10-30 18:53 (diff) (minor) Baccyak4H (xtra word)
• 2009-10-30 17:07 (diff) Philosofool (Stated basic result in the introduction, something that the article should do.)
• 2009-10-24 16:53 (diff) 69.228.171.150 (anon) (/* Formalized proofs */ m clarify citations)
• 2009-10-24 16:50 (diff) 69.228.171.150 (anon) (/* Articles by others */ rm citation of Shankar article, which may not be the right one anyway. O'Connor cites Shankar's book (which appears in the book section) instead.)
• 2009-10-24 15:17 (diff) 69.228.171.150 (anon) (formalizations)
• 2009-10-22 10:00 (diff) Tkuvho (/* Articles by others */)
• 2009-10-19 12:51 (diff) CBM2 (/* Relationship with computability */ + Shoenfield 1967)
• 2009-10-19 12:49 (diff) CBM2 (/* Miscellaneous references */ + Shoenfield 1967)
• 2009-10-19 05:23 (diff) (minor) Arthur Rubin (Reverted 1 edit by Likebox identified as vandalism to last revision by CBM. (TW))
• 2009-10-18 18:37 (diff) Likebox (I know you're following this--- please help. I am sick of arguing about this.)
• 2009-10-15 02:41 (diff) CBM (Reverting "modern proof" again, still as inappropriate as it was in 2007)
• 2009-10-15 02:27 (diff) Likebox (/* Modern version of Gödel's proof */ extend per trovatore suggestion)
• 2009-10-15 02:26 (diff) Likebox (Undid revision 319940413 by Arthur Rubin (talk))
• 2009-10-15 02:18 (diff) Arthur Rubin (Undid revision 319938676 by Likebox (talk) revert nonsense. AGAIN)
• 2009-10-15 02:05 (diff) Likebox (Undid revision 319938483 by CBM (talk))
• 2009-10-15 02:04 (diff) CBM (Removing "modern proof" which has same problems as it did in 2007. See talk page and archives)
• 2009-10-15 00:12 (diff) (minor) Likebox (/* Modern version of Gödel's Proof */ WP style+ minor error)
• 2009-10-15 00:08 (diff) (minor) Likebox (/* Modern version of Gödel's Proof */ effective->computable (easier to understand term))
• 2009-10-15 00:07 (diff) (minor) Likebox (/* Modern version of Gödel's Proof */ forgot an "effective")
• 2009-10-15 00:04 (diff) (minor) Likebox (/* Modern version of Gödel's Proof */ move a paragraph, minor tweaks)
• 2009-10-14 23:47 (diff) Likebox (/* Modern version of Godel's Proof */ links, umlauts)
• 2009-10-14 23:04 (diff) Likebox (/* Proof sketch for the first theorem */ modern proof.)
• 2009-10-14 16:01 (diff) (minor) SieBot (bot) (robot Modifying: en:pt:Teorema da incompletude de Gödel)
• 2009-10-12 18:00 (diff) 66.245.43.17 (anon) (/* Arithmetization of syntax */ Inserted "the" ("fleshing out the proof"))
• 2009-09-30 03:04 (diff) CBM (/* Second incompleteness theorem */ rm a sentence that is slighly dubious)
• 2009-09-20 03:36 (diff) (minor) CBM (Reverted edits by 67.86.5.25 (talk) to last version by CBM)
• 2009-09-20 03:34 (diff) 67.86.5.25 (anon) (/* Diagonalization */)
• 2009-09-18 03:53 (diff) CBM (Undid revision 314625535 by Gregbard (talk))
• 2009-09-18 00:00 (diff) Gregbard (/* Background */Formal language, Replaced: en:formal language → formal language, using AWB)
• 2009-09-09 19:40 (diff) CBM2 (/* Meaning of the first incompleteness theorem */ this is not a reference, it is just a link; to do justice to the topic requires more space than can be afforded to a single reference)
• 2009-09-09 19:36 (diff) 76.252.185.93 (anon) (citation needed: not that I disagree, but I would really like to see who and why)
• 2009-08-24 01:06 (diff) 79.74.49.49 (anon) (/* Meaning of the first incompleteness theorem */)
• 2009-08-23 12:35 (diff) 114.76.44.0 (anon) (/* Translations, during his lifetime, of Gödel’s paper into English */ Added umlaut to Gödel's name.)
• 2009-08-21 00:16 (diff) Trovatore (Standard usage is "if" in definitions, not "if and only if" -- this is not a sentence in the propositional calculus; it's more like an assignment. Other changes not bad, but not greatly helpful.)
• 2009-08-21 00:08 (diff) Aunin (/* Background */)
• 2009-08-05 03:11 (diff) CBM (/* First incompleteness theorem */ again, the choice of numbering is not the issue)
• 2009-08-05 03:03 (diff) CBM (/* First incompleteness theorem */ there are more fundamental reasons for the non-uniqueness, even if a unique coding is fixed)
• 2009-08-04 18:21 (diff) Vibritannia (/* First incompleteness theorem */ explain adding G won't complete T)
• 2009-08-04 18:17 (diff) Vibritannia (/* First incompleteness theorem */ explain adding G won't complete T)
• 2009-08-04 18:07 (diff) Vibritannia (/* First incompleteness theorem */ explain why infinitely many Gödel sentences)
• 2009-08-04 18:04 (diff) Vibritannia (/* First incompleteness theorem */ explain why infinitely many Gödel sentences)
• 2009-07-31 19:24 (diff) CBM (/* First incompleteness theorem */ copyedit second parenthetical)
• 2009-07-31 17:51 (diff) Vibritannia (/* First incompleteness theorem */ tweaks to make less likely any paradoxical impression)
• 2009-07-31 17:43 (diff) 90.218.229.117 (anon) (/* First incompleteness theorem */ tweaks to make less likely any paradoxical impression)
• 2009-07-28 01:38 (diff) CBM (Please remain calm. Undid revision 304592871 by 92.39.205.210 (talk))
• 2009-07-28 01:35 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */)
• 2009-07-27 12:04 (diff) CBM (/* Arithmetization of syntax */ Note that Bew(y) is an abbreviation for a very long formula)
• 2009-07-26 19:05 (diff) Trovatore (Undid revision 304275873 by Vibritannia (talk) rm personal essay)
• 2009-07-26 13:38 (diff) CBM (/* Appeals to the incompleteness theorems in other fields */ link Goldstein)
• 2009-07-26 11:06 (diff) Vibritannia (Undid revision 304271744 by Trovatore (talk) Mike, content over style, I believe. Please make your objection specific.)
• 2009-07-26 10:26 (diff) Trovatore (rm personal essay)
• 2009-07-26 08:35 (diff) Vibritannia (Undid revision 303933959 by Chalst (talk) Charles, point conceded but utility before beauty, I believe.)
• 2009-07-26 00:08 (diff) CBM (/* Appeals to the incompleteness theorems in other fields */ too many tos to listen to)
• 2009-07-25 21:40 (diff) CBM (/* Appeals to the incompleteness theorems in other fields */ no need for polemical "humanist intellectuals")
• 2009-07-25 21:35 (diff) CBM (/* Postmodernism and continental philosophy */ better section title (please improve it further))
• 2009-07-25 21:33 (diff) CBM (/* Postmodernism and continental philosophy */ Move Debray sentence to end, make reference more clear. The reference refers to "sociology" not "politics")
• 2009-07-25 21:29 (diff) CBM (/* Miscellaneous References */ add Sokal/Bricmont 1999 and Stangroom/Benson 2006)
• 2009-07-25 21:26 (diff) CBM (/* Postmodernism and continental philosophy */ add more explicit references, and try to make the tone more neutral)
• 2009-07-25 21:13 (diff) CBM (/* Theories of everything and physics */ rm. Perhaps this could be discussed briefly in the preceding section, but Jaki's essay seems to be self-published only (realviewbooks.com))
• 2009-07-25 20:00 (diff) (minor) Trovatore (/* First incompleteness theorem */ close quote in footnote)
• 2009-07-25 12:47 (diff) CBM (/* First incompleteness theorem */ need year in reference)
• 2009-07-25 12:46 (diff) CBM (/* First incompleteness theorem */ replace prose description with quote from Smoryński)
• 2009-07-25 12:36 (diff) CBM (Remving refimprove tag, see en:Talk:Gödel's_incompleteness_theorems#reference_style.2C_removing_refimprove_tag)
• 2009-07-25 12:32 (diff) CBM (/* First incompleteness theorem */ rephrased; you misread "implied")
• 2009-07-25 10:20 (diff) 92.39.205.210 (anon) (The notes here are used like references and there are no proper references. It is a mess and not Wikipedia standard format.)
• 2009-07-25 10:14 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */ State the exact page in in Franzen from which the text "to say GT is true simply means that, in fact, no number with that property exists" comes from.)
• 2009-07-25 10:10 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */ It's either true or it isn't. You can't have implied truth. Please clarity or remove the word implied.)
• 2009-07-25 09:59 (diff) MPeterHenry
• 2009-07-24 13:50 (diff) Chalst (Undid revision 303928928 by Vibritannia: sorry, but this content makes no attempt to integrate itself with what we have.)
• 2009-07-24 13:13 (diff) Vibritannia (/* New section: How to understand incompleteness */)
• 2009-07-20 13:07 (diff) CBM (/* First incompleteness theorem */ ref)
• 2009-07-20 13:05 (diff) CBM (/* Miscellaneous References */ add Kleene 1967, format Goldstein 2005)
• 2009-07-20 10:09 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */)
• 2009-07-20 10:06 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */ State your references(s) for this complete definition. Do not remove this tag until done.)
• 2009-07-17 12:16 (diff) (minor) SmackBot (bot) (/* First incompleteness theorem */Date maintenance tags and general fixes)
• 2009-07-16 17:41 (diff) Trovatore (take it to talk)
• 2009-07-16 10:44 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */ "true" used here plus your ref [1] is extremely unclear to the reader. Do not remove the clarify tag again until you have clarified in the article.)
• 2009-07-16 09:07 (diff) Trovatore (...last edit summary should have said "see e.g. Franzen". If you want to discuss, bring up on talk)
• 2009-07-16 09:05 (diff) Trovatore (it's true, period. see e.g.)
• 2009-07-16 09:03 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */Theorem VI doesn't use the word true. The definition of "true" is not agreed by experts. The statement is unprovable, nothing more. Very unclear why true is put here.)
• 2009-07-15 23:03 (diff) Trovatore ("true" has its natural meaning here -- it means what it intuitively means in natural language. The footnote is only to clear up a possible quibble.)
• 2009-07-15 22:38 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */ Despite the reference explanation it will still be completely unclear to the most readers what the meaning of true is in this context)
• 2009-07-15 16:27 (diff) (minor) SmackBot (bot) (Date maintenance tags and general fixes)
• 2009-07-13 20:41 (diff) 92.39.205.210 (anon) (/* Implications for consistency proofs */ revert this to what it was since I can't be sure. Add clarify tag.)
• 2009-07-13 20:26 (diff) 92.39.205.210 (anon) (/* Implications for consistency proofs */ put in link)
• 2009-07-13 20:21 (diff) 92.39.205.210 (anon) (/* Implications for consistency proofs */ try and clarify very twisted sentence.)
• 2009-07-13 19:51 (diff) 92.39.205.210 (anon) (/* First incompleteness theorem */ Tidy up the roughly speaking part. Too rough I think.)
• 2009-07-06 22:00 (diff) (minor) Obersachsebot (bot) (robot Modifying: en:es:Teoremas de incompletitud de Gödel)
• 2009-07-06 07:48 (diff) Trovatore (rv to last by Trovatore -- addition is too chatty for an encyclopedia)
• 2009-07-05 23:02 (diff) 66.127.54.65 (anon) (/* Second incompleteness theorem */)
• 2009-07-05 23:01 (diff) 66.127.54.65 (anon) (/* Second incompleteness theorem */)
• 2009-07-05 23:00 (diff) 66.127.54.65 (anon) (/* Second incompleteness theorem */)
• 2009-07-05 22:59 (diff) 66.127.54.65 (anon) (/* Second incompleteness theorem */)
• 2009-07-05 22:58 (diff) 66.127.54.65 (anon) (/* Second incompleteness theorem */)
• 2009-07-05 20:10 (diff) Trovatore (partial rv; "proved to be true" might be useful once but repetition annoying. more seriously, truth v provability issue.)
• 2009-07-05 19:52 (diff) 66.127.54.65 (anon) (/* First incompleteness theorem */)
• 2009-07-05 15:25 (diff) Ruud Koot (/* Extensions of Gödel's original result */ spam)
• 2009-07-05 15:22 (diff) Ruud Koot (/* Articles by others */ spam)
• 2009-06-30 02:36 (diff) CBM (/* Meaning of the first incompleteness theorem */ for references, see http://en.wikipedia.org/wiki/Hilbert%27s_second_problem#Modern_viewpoints_on_the_status_of_the_problem - this is just a summary)
• 2009-06-29 21:29 (diff) Paul August (/* Articles by others */ update year and add ISBN)
• 2009-06-29 21:21 (diff) (minor) Paul August (/* Articles by others */ fmt fix)
• 2009-06-29 11:27 (diff) 68.101.130.214 (anon) (/* Meaning of the first incompleteness theorem */)
• 2009-06-09 04:16 (diff) 115.194.181.58 (anon) (/* Second incompleteness theorem */ an to a)
• 2009-06-03 21:35 (diff) (minor) Gregbard (Undid revision 294230031 by Gregbard (talk))
• 2009-06-03 19:27 (diff) Gregbard (Removing backlinks to Consistency because ""; using TW)
• 2009-05-20 12:21 (diff) (minor) Ad88110 (/* Background */ another link)
• 2009-05-20 12:16 (diff) (minor) Ad88110 (/* Background */ direct links + link "contradictory", "maximal set")
• 2009-05-20 02:02 (diff) Trovatore (rv poss test edit)
• 2009-05-20 01:58 (diff) 24.184.94.170 (anon)
• 2009-05-19 13:16 (diff) (minor) D6 (bot) (fix ISBN syntax (Wikipedia Check Wikipedia check #69; fmt)
• 2009-05-17 18:58 (diff) 91.110.44.82 (anon) (/* First incompleteness theorem */)
• 2009-05-17 18:57 (diff) 91.110.44.82 (anon) (/* First incompleteness theorem */)
• 2009-05-17 15:19 (diff) CBM (/* Second incompleteness theorem */ copyedit, split a subsection out)
• 2009-05-17 15:04 (diff) CBM (/* Meaning of the first incompleteness theorem */ copyedit again)
• 2009-05-15 13:59 (diff) (minor) Citation bot (bot) (Citation maintenance. [Pu]Formatted: doi. You can use this bot yourself! Please report any bugs.)
• 2009-05-13 21:33 (diff) (minor) Wvbailey (/* Meaning of the first incompleteness theorem */make verb plural)
• 2009-05-13 19:00 (diff) CBM (/* Meaning of the first incompleteness theorem */ copyedit last para)
• 2009-05-13 04:04 (diff) (minor) Wtmitchell (Reverted edits by 65.93.84.104 to last revision by Trovatore (HG))
• 2009-05-13 04:03 (diff) 65.93.84.104 (anon) (/* First incompleteness theorem */)
• 2009-05-13 02:53 (diff) Trovatore (Undid revision 289437284 by Vibritannia (talk) unsourced personal essay)
• 2009-05-12 12:26 (diff) LoveMonkey (/* Miscellaneous References */)
• 2009-05-12 10:34 (diff) Vibritannia (/* New subsection: Illumination provided by Principia Mathematica */)
• 2009-05-09 03:30 (diff) (minor) SmackBot (bot) (Date maintenance tags and general fixes)
• 2009-05-08 15:16 (diff) CBM (/* Limitations of Gödel's theorems */ copyedit, en dash)
• 2009-05-08 15:13 (diff) CBM (/* Second incompleteness theorem */ copyedit and uniformize math. also en dashes.)
• 2009-05-08 14:56 (diff) CBM (/* First incompleteness theorem */ c/e and uniformize mathematics)
• 2009-05-08 14:48 (diff) CBM (/* Background */ copyedit last para)
• 2009-05-08 14:46 (diff) CBM (/* Background */ for example cannot be pluralized)
• 2009-05-08 14:46 (diff) CBM (/* Background */ actually this is already included lower in this section)
• 2009-05-08 14:45 (diff) CBM (/* Background */ clarify)
• 2009-05-08 07:41 (diff) (minor) Finell (/* Extensions of Gödel's original result */ Italic for book title)
• 2009-05-08 05:08 (diff) Finell (/* Background */ Comform definition of theory to en:Theory (mathematical logic), which is more precise; add {Clarify} tag)
• 2009-05-05 01:00 (diff) (minor) SieBot (bot) (robot Modifying: en:el:Θεωρήματα μη-πληρότητας του Γκέντελ)
• 2009-05-02 06:01 (diff) (minor) Sptzimas (Added Greek version of the article.)
• 2009-04-30 17:52 (diff) Waldir (/* External links */ +{{computable knowledge}})
• 2009-04-25 19:00 (diff) Trovatore (we have an article on en:Gödel's ontological proof. It's an interesting subject but has zero to do with incompleteness.)
• 2009-04-25 11:37 (diff) FeydHuxtable (new section, on Implications for the existence of God , which Goedel believed was one of the most important results of his work!)
• 2009-04-08 18:59 (diff) (minor) S2000magician (minor grammar)
• 2009-04-07 13:54 (diff) False vacuum (/* Minds and machines */ correct punctuation of en:Church–Turing thesis, eliminating redirect)
• 2009-04-07 13:47 (diff) False vacuum (/* Limitations of Gödel's theorems */ "all true statements about naturals" --> "all true statements about natural numbers")
• 2009-04-07 13:23 (diff) False vacuum (/* Background */ Italicised "effectively generated" the first time it appears)
• 2009-04-01 10:21 (diff) (minor) TXiKiBoT (bot) (robot Adding: en:scn:Tiurema d'incumplitizza di Gödel)
• 2009-03-20 04:56 (diff) (minor) TravisAF (Reverted edits by 72.130.45.134 to last revision by Charles Moss (HG))
• 2009-03-20 04:55 (diff) 72.130.45.134 (anon) (/* Limitations of Gödel's theorems */)
• 2009-03-05 07:00 (diff) Charles Moss (/* First incompleteness theorem */ (only in intro) changed italics to math (hooray semantics); added such where necessary)
• 2009-02-21 02:31 (diff) (minor) Nallimbot (bot) (robot Modifying: en:fi:Gödelin epätäydellisyyslause)
• 2009-02-19 13:14 (diff) (minor) Quaeler (Reverted 1 edit by MACherian; Sigh. using TW)
• 2009-02-19 12:34 (diff) MACherian (On Gödel’s Conjecture: ‘Not (proved or disproved)’ does not exhaust all reference to ‘proved’, or ‘disproved’.)
• 2009-02-14 22:46 (diff) (minor) Darkicebot (bot) (robot Removing: en:da:Gödels ufuldstændighedsteorem)
• 2009-02-12 03:23 (diff) CBM (/* Lede */ The added sentence doesn't match the rest of the lede, and doesn't really make sense)
• 2009-02-11 17:57 (diff) Baccyak4H (/* First incompleteness theorem */ clarify)
• 2009-02-11 17:55 (diff) Baccyak4H (/* First incompleteness theorem */ tighten prose)
• 2009-02-11 17:50 (diff) Baccyak4H (bold rephrasing of simple formulation)
• 2009-02-11 17:48 (diff) (minor) Baccyak4H (sp)
• 2009-02-11 15:39 (diff) Scouto2 (added a basic translation of it into normal language)
• 2009-02-06 03:25 (diff) (minor) Harttwood47 (comma correction)
• 2009-02-05 20:43 (diff) (minor) Broadbot (bot) (robot Adding: en:da:Gödels ufuldstændighedsteorem)
• 2009-01-30 13:03 (diff) ReluctantPhilosopher (Undid revision 267394200 by ReluctantPhilosopher (talk) Never mind)
• 2009-01-30 13:02 (diff) ReluctantPhilosopher (/* Relation to the liar paradox */ changed and wikilinked)
• 2009-01-28 16:34 (diff) (minor) Muro Bot (bot) (robot Adding: en:simple:Gödel's incompleteness theorems)
• 2009-01-19 00:57 (diff) CBM (Undid revision 264881118 by SmackBot (talk) With the use of Harvard references there is no issue with ibid.)
• 2009-01-18 15:35 (diff) (minor) SmackBot (bot) (tag)
• 2009-01-14 23:00 (diff) 81.102.130.73 (anon) (/* Postmodernism and continental philosophy */)
• 2009-01-14 23:00 (diff) 81.102.130.73 (anon) (/* Postmodernism and continental philosophy */)
• 2009-01-02 01:38 (diff) 67.169.48.85 (anon) (proofs and generalizations are in expanded version at ArXiv)
• 2009-01-01 05:22 (diff) (minor) Cydebot (bot) (Robot - Removing category No-go theorems per CFD at en:Wikipedia:Categories for discussion/Log/2008 December 22.)
• 2008-12-22 20:14 (diff) (minor) Infovarius (Quick-adding category "No-go theorems" (using HotCat))
• 2008-12-07 22:20 (diff) Hans Adler (undo misguided pedantry; according to MWDEU both "proved" and "proven" can be used interchangeably; people who distinguish use "proved" when it's not an attributive adjective)
• 2008-12-07 21:57 (diff) 66.62.165.3 (anon) (proved --> proven)
• 2008-11-22 19:29 (diff) Trovatore (rv; "provable" is correct)
• 2008-11-22 18:53 (diff) 88.25.161.226 (anon) (/* Relation to the liar paradox */)
• 2008-11-22 18:06 (diff) (minor) TaBOT-zerem (bot) (robot Modifying: en:nov:Teoreme de Gödel)
• 2008-11-21 11:58 (diff) Hakeem.gadi (/* External links */)
• 2008-11-10 17:19 (diff) (minor) Turkeyphant (/* Discussion and implications */)
• 2008-11-08 19:03 (diff) Meand (/* First incompleteness theorem */ remove uncited POV)
• 2008-11-08 12:58 (diff) CBM (The word "and" is required here, the theorem was discovered independently by Goedel and Tarski)
• 2008-11-08 01:31 (diff) 160.39.226.141 (anon) (/* Relation to the liar paradox */)
• 2008-11-07 00:54 (diff) 24.10.68.143 (anon) (/* Background */)
• 2008-11-06 22:33 (diff) Trovatore (no, not an appropriate category)
• 2008-11-06 22:31 (diff) Psyoptix
• 2008-11-05 21:28 (diff) (minor) LilHelpa (/* Articles by others */ spelling: mathemaic -> mathematic)
• 2008-10-20 21:42 (diff) Hans Adler (/* See also */ I don't think the uncertainly principle is related, except perhaps in postmodernist writings)
• 2008-10-20 19:53 (diff) LoveMonkey (/* See also */)
• 2008-10-20 19:52 (diff) LoveMonkey (/* See also */)
• 2008-10-10 13:17 (diff) (minor) Vishnava (Reverted edits by 66.203.37.240 to last version by Hans Adler (HG))
• 2008-10-10 13:14 (diff) 66.203.37.240 (anon)
• 2008-10-10 11:19 (diff) Hans Adler (/* Meaning of the first incompleteness theorem */ clarify a sentence)
• 2008-10-10 03:35 (diff) CBM (/* Examples of undecidable statements */ rm para about P = NP. This is not known to be independent of anything, and so no strong reason to include it here. It seems extremely tangential to me)
• 2008-10-09 22:54 (diff) CBM (/* Meaning of the first incompleteness theorem */ incomplete in the sense of being incomplete)
• 2008-10-09 22:50 (diff) (minor) 9258fahsflkh917fas (Undid revision 244242634 by Declan Davis (talk))
• 2008-10-09 22:49 (diff) 9258fahsflkh917fas (/* Relation to the liar paradox */ added 's)
• 2008-10-09 22:44 (diff) 9258fahsflkh917fas (/* Meaning of the first incompleteness theorem */ Swapped the order of two sentances without editing the sentences.)
• 2008-10-09 22:43 (diff) 9258fahsflkh917fas (Undid revision 244241419 by Declan Davis (talk))
• 2008-10-09 22:43 (diff) 9258fahsflkh917fas (/* Meaning of the first incompleteness theorem */ Swapped two sentences: reads better now.)
• 2008-10-05 19:36 (diff) (minor) SmackBot (bot) (fix defaultsort)
• 2008-10-02 00:12 (diff) 65.110.26.214 (anon) (/* Background */)
• 2008-09-29 11:03 (diff) 81.187.252.174 (anon)
• 2008-09-26 14:06 (diff) CBM (/* Relation to the liar paradox */ bad pronoun)
• 2008-09-26 14:05 (diff) CBM (/* Meaning of the first incompleteness theorem */ copyedit third para - rm 'you', clarify a couple things)
• 2008-09-26 13:59 (diff) CBM (/* Background */ examples of effectively generated theories: PA and ZFC)
• 2008-09-26 13:56 (diff) CBM (/* Background */ rewrite second para; it was not making the key ideas clear)
• 2008-09-25 22:06 (diff) Giftlite (Undid revision 241001164 by 81.0.198.161 (talk))
• 2008-09-25 22:04 (diff) 81.0.198.161 (anon) (/* Relation to the liar paradox */)
• 2008-09-25 20:50 (diff) CBM (/* Arithmetization of syntax */ slight rephrasing of first para)
• 2008-09-25 20:46 (diff) CBM (/* First incompleteness theorem */ copyedit top section a little)
• 2008-09-25 15:21 (diff) CBM (/* Relationship with computability */ rework - include more topics, focus less on proof)
• 2008-09-25 13:55 (diff) Zero sharp (Undid revision 240814780 by Likebox (talk) Wrong.)
• 2008-09-25 02:49 (diff) Likebox (Undid revision 240756910 by CBM (talk) No consensus yet (sorry))
• 2008-09-25 00:19 (diff) CBM (/* Extensions of Gödel's original result */ Rosser's trick - made an article on it, linking it in)
• 2008-09-24 21:32 (diff) CBM (Return to previous version on "relationship with computability". This was long-discussed and didn't have any agreement a while back; nothing has changed since then)
• 2008-09-24 20:55 (diff) Likebox (/* Relationship with computability */ computational proof)
• 2008-09-20 00:15 (diff) (minor) Beland (/* Meaning of the first incompleteness theorem */ fix the use of the second grammatical person)
• 2008-09-14 17:55 (diff) CBM (No need for nonstandard reference formatting here; plain references are fine)
• 2008-09-14 14:36 (diff) (minor) Gioto (/* References */)
• 2008-09-14 14:35 (diff) (minor) Gioto (/* Notes */)
• 2008-09-04 21:51 (diff) Francis Davey (rv unexplained deletion of material)
• 2008-09-04 16:30 (diff) 128.183.56.73 (anon)
• 2008-08-28 21:23 (diff) 70.181.171.241 (anon) (/* First incompleteness theorem */)
• 2008-08-27 13:29 (diff) (minor) Thoreaulylazy (/* First incompleteness theorem */ conjugation)
• 2008-08-27 10:06 (diff) Ht686rg90 (/* Relation to the liar paradox */ link)
• 2008-08-25 17:44 (diff) CBM (reword sentence)
• 2008-08-25 16:48 (diff) 18.42.6.105 (anon) (/* Meaning of the first incompleteness theorem */)
• 2008-08-25 06:28 (diff) 24.18.248.54 (anon)
• 2008-08-25 02:57 (diff) 75.62.4.102 (anon) (/* Examples of undecidable statements */ a little more cleanup, link ZFC list, add 1 more example. Actually this list is itself getting overlong and should be moved to a separate article?)
• 2008-08-24 17:02 (diff) CBM (/* Relation to the liar paradox */ copyedit)
• 2008-08-21 20:50 (diff) (minor) CBM (/* First incompleteness theorem */ Diacritic in Smorński)
• 2008-08-21 20:48 (diff) (minor) CBM (Diacritic in Franzén)
• 2008-08-21 19:51 (diff) CBM (/* Articles by others */ Kikuchi and tanaka 2004, Smoryński 1977)
• 2008-08-21 19:46 (diff) CBM (/* First incompleteness theorem */ Improve footnote ?)
• 2008-08-21 16:09 (diff) CBM (/* First incompleteness theorem */ split this section into two, adding "background". I think this makes it easer to follow the discussion about the theorem itself in the lower parts)
• 2008-08-21 15:23 (diff) CBM (/* Extensions of Gödel's original result */ add explanatory sentence)
• 2008-08-20 17:34 (diff) CBM (/* Relationship with computability */ change footnote to inline reference)
• 2008-08-20 17:34 (diff) CBM (/* Miscellaneous References */ Hopcroft and Ullman 1979)
• 2008-08-20 17:04 (diff) (minor) Paul August (/* First incompleteness theorem */ move comma)
• 2008-08-20 16:45 (diff) CBM (/* Articles by others */ Add Hewitt 2008 and Feferman 1984)
• 2008-08-20 16:42 (diff) CBM (/* Extensions of Gödel's original result */ Insert short section on Hewitt - see talk page)
• 2008-08-20 16:34 (diff) CBM (/* Proof via Berry's paradox */ better word)
• 2008-08-20 16:34 (diff) CBM (/* Articles by others */ improve Boolos reference)
• 2008-08-20 16:31 (diff) CBM (/* Proof sketch for the first theorem */ Trim Boolos section as promised on talk page)
• 2008-08-20 10:15 (diff) 75.62.4.102 (anon) (/* Examples of undecidable statements */ rearrange slightly and add graph minors.)
• 2008-08-19 19:54 (diff) (minor) SmackBot (bot) (Date the maintenance tags and general fixes)
• 2008-08-18 14:33 (diff) CBM (/* Relation to the liar paradox */ c/e)
• 2008-08-18 14:31 (diff) CBM (/* First incompleteness theorem */ relation to the liar paradox)
• 2008-08-18 14:23 (diff) CBM (/* First incompleteness theorem */ rearrange)
• 2008-08-18 14:17 (diff) CBM (/* Examples of undecidable statements */ c/e)
• 2008-08-18 14:11 (diff) CBM (/* Meaning of the first incompleteness theorem */ rm paragraph on semidecidability of provable statements - this is not particularly a consquence of Goedel's theorem, it's just the halting problem)
• 2008-08-18 14:06 (diff) CBM (Move section on interpretation, see talk page)
• 2008-08-18 13:59 (diff) CBM (/* Limitations of Gödel's theorems */ transposed)
• 2008-08-18 13:58 (diff) CBM (/* Examples of undecidable statements */ link text was confusing me)
• 2008-08-18 13:56 (diff) CBM (Rearrange footnotes)
• 2008-08-18 13:53 (diff) CBM (/* References */ moving "in-text references" to notes; this article uses parenthetical citation, with expository footnotes)
• 2008-08-18 13:52 (diff) CBM (/* See also */ rm some that I am sure are mentioned higher up)
• 2008-08-18 13:51 (diff) CBM (/* Articles by others */ Hellman (moved from footnote))
• 2008-08-18 13:49 (diff) CBM (/* Meaning of Gödel's theorems */ change footnote to parenthetical citation)
• 2008-08-18 13:48 (diff) CBM (/* Limitations of Gödel's theorems */ principle of explosion)
• 2008-08-18 13:47 (diff) CBM (/* Limitations of Gödel's theorems */ copyedit)
• 2008-08-18 13:41 (diff) CBM (/* Examples of undecidable statements */ remove things not related to unecidability in the proof theory sense; in particular Matiyasevich's work was not related to Goedel's theorem)
• 2008-08-18 13:32 (diff) CBM (/* Second incompleteness theorem */ slight copyedit - this section needs more work)
• 2008-08-18 13:26 (diff) CBM (/* First incompleteness theorem */ copyedit, tone near end)
• 2008-08-18 13:20 (diff) CBM (/* Extensions of Gödel's original result */ copyedit para on Rosser)
• 2008-08-18 13:18 (diff) CBM (/* Proof of independence */ rm second mention of Rosser - discussed in detail above)
• 2008-08-18 13:15 (diff) CBM (/* Relationship with computability */ use full name for Kleene - this is the first mention of him)
• 2008-08-18 13:15 (diff) CBM (/* Relationship with computability */ copyedit)
• 2008-08-18 12:51 (diff) CBM (/* Relationship with computability */ No need for Kleene footnote)
• 2008-08-18 12:49 (diff) CBM (/* First incompleteness theorem */ rearrange first theorem)
• 2008-08-18 12:48 (diff) CBM (/* First incompleteness theorem */ rearrange statement of 1st theorem)
• 2008-08-18 11:32 (diff) (minor) Graham87 (moved en:Goedels Incompleteness Theorem to en:Gödel's incompleteness theorems over redirect: revert)
• 2008-08-18 11:28 (diff) (minor) Graham87 (moved en:Gödel's incompleteness theorems to en:Goedels Incompleteness Theorem: history merge)
• 2008-08-18 03:13 (diff) Zero sharp (moved section 'implications' to the end; plz see rationale on Talk)
• 2008-08-18 03:07 (diff) 71.128.152.149 (anon) (An anecdote on one man's flighty imagination is hardly relevant to mathematical proof)
• 2008-08-17 22:21 (diff) Blue Tie (The article does not support this conclusion)
• 2008-08-17 02:33 (diff) 76.197.56.242 (anon) (/* Extensions of Gödel's original result */ remove Hewitt paraconsistency stuff, see talk)
• 2008-08-17 00:44 (diff) Trovatore (/* Examples of undecidable statements */ this is not much of a "connection", and invites confusion--let's keep it clear that the two meanings are simply different)
• 2008-08-14 22:16 (diff) 98.210.238.83 (anon) (/* Extensions of Gödel's original result */)
• 2008-08-02 23:32 (diff) CBM (/* External links */ remove Myers site - suggested on talk page some time ago)
• 2008-08-01 09:06 (diff) (minor) OKBot (bot) (robot Modifying: en:tr:Gödel'in eksiklik teoremi)
• 2008-07-29 06:52 (diff) Trovatore (the two formulations are easily equivalent. If you have an argument as to why one is better here than the other, please bring it up on talk)
• 2008-07-29 04:12 (diff) Bender2k14 (/* Relationship with computability */ The definition of the Halting problem was incorrect)
• 2008-07-27 01:43 (diff) Trovatore (I rarely *remove* commas, but this one makes no sense)
• 2008-07-27 01:36 (diff) 128.125.133.184 (anon)
• 2008-07-26 22:24 (diff) Trovatore (I think the point is that Sokal and Bricmont *did* work together; this sentence structure elegantly indicates that)
• 2008-07-26 20:43 (diff) Exiledone (/* Postmodernism and continental philosophy */)
• 2008-07-23 18:15 (diff) 208.96.18.13 (anon)
• 2008-07-23 08:16 (diff) Gakrivas (/* First incompleteness theorem */ computably -> recursively)
• 2008-07-23 03:39 (diff) Trovatore (/* Postmodernism and continental philosophy */ oxford comma (here it's *clearly* essential, unless Bouveresse and Stangroom worked together))
• 2008-07-22 23:28 (diff) Exiledone (/* Postmodernism and continental philosophy */)
• 2008-07-22 20:54 (diff) CBM (/* Books about the theorems */ add mathscinet links to many)
• 2008-07-21 21:12 (diff) Quaeler (/* External links */ cleaning edits per discussion page to-do)
• 2008-07-21 21:09 (diff) (minor) Quaeler (Reverted 1 edit by 194.46.122.161 identified as vandalism to last revision by Quaeler. using TW)
• 2008-07-21 21:00 (diff) 194.46.122.161 (anon) (Entered Book reference and External link reference)
• 2008-07-21 14:47 (diff) (minor) Quaeler (Reverted 2 edits by Third Merlin to last revision by Selfworm; Blog, shilling for promotion, (and urls return a 404). using TW)
• 2008-07-21 14:39 (diff) Third Merlin
• 2008-07-21 14:36 (diff) (minor) Third Merlin
• 2008-07-11 00:22 (diff) (minor) Selfworm (/* See also */ Added Chaitin's incompleteness theorem)
• 2008-07-05 17:27 (diff) (minor) EjsBot (robot Modifying: en:fa:قضایای ناتمامیت گودل)
• 2008-07-02 20:43 (diff) (minor) AlnoktaBOT (bot) (robot Modifying: en:ar:مبرهنة عدم الاكتمال لغودل, en:fa:قضایای ناتمامیت گدل)
• 2008-06-28 15:46 (diff) 121.108.45.16 (anon)
• 2008-06-26 00:07 (diff) CBM (/* Extensions of Gödel's original result */ add paragraph on Hewitt's work from talk page)
• 2008-06-23 20:28 (diff) Trovatore (/* See also */ hmm--not sure this should really be here as it's probably linked from the article itself, but that's probably true of a lot of the others. In any case we can spell it right.)
• 2008-06-23 20:26 (diff) (minor) Byates5637
• 2008-06-23 00:55 (diff) 211.121.168.82 (anon) (/* Second incompleteness theorem */)
• 2008-06-23 00:54 (diff) 211.121.168.82 (anon) (/* Second incompleteness theorem */)
• 2008-06-22 23:14 (diff) Trovatore (/* Inconsistency as a Consequence of Gödel's Argument */ this whole section just doesn't make much sense -- please explain what you're talking about on talk page)
• 2008-06-20 19:38 (diff) 76.126.127.3 (anon) (/* Inconsistency as a Consequence of Gödel's Argument */ clarification)
• 2008-06-20 17:59 (diff) 98.210.240.252 (anon) (/* Inconsistency as a Consequence of Gödel's Argument */ typo)
• 2008-06-20 17:52 (diff) 98.210.240.252 (anon) (/* Inconsistency as a Consequence of Gödel's Argument */ refereence names)
• 2008-06-17 09:26 (diff) 98.210.237.43 (anon) (/* Inconsistency as a Consequence of Gödel's Argument */ links)
• 2008-06-17 03:56 (diff) 67.169.9.178 (anon) (Inconsistency as a Consequence of Gödel's Argument)
• 2008-06-10 10:34 (diff) 85.81.48.124 (anon) (/* Theories of everything and physics */)
• 2008-05-30 07:50 (diff) (minor) Quaeler (Reverted 1 edit by 4.243.5.34 identified as vandalism to last revision by 203.158.32.143. using TW)
• 2008-05-30 06:49 (diff) 4.243.5.34 (anon) (/* Minds and machines */)
• 2008-05-24 01:30 (diff) 203.158.32.143 (anon)
• 2008-05-22 19:12 (diff) 208.255.43.156 (anon) (/* First incompleteness theorem */)
• 2008-05-20 12:44 (diff) (minor) Admiral Norton (/* See also */)
• 2008-05-19 20:44 (diff) (minor) ClueBot (bot) (Reverting possible vandalism by 75.147.142.9 to version by Quaeler. False positive? Report it. Thanks, en:User:ClueBot. (384141) (Bot))
• 2008-05-19 20:44 (diff) 75.147.142.9 (anon)
• 2008-05-16 16:03 (diff) (minor) Quaeler (Reverted 1 edit by Vibritannia to last revision by Paul August; This is what the talk-arguments page is for - not the article. using TW)
• 2008-05-16 14:42 (diff) Vibritannia (/* External links */ - added one)
• 2008-05-10 22:03 (diff) (minor) Paul August (Reverted edits by 87.194.49.123 (talk) to last version by 83.131.72.152)
• 2008-05-10 21:23 (diff) 87.194.49.123 (anon) (/* First incompleteness theorem */)
• 2008-05-02 09:56 (diff) 83.131.72.152 (anon) (/* External links */ +hr)
• 2008-04-30 01:29 (diff) 24.21.61.173 (anon) (/* Relationship with computability */)
• 2008-04-21 18:32 (diff) (minor) ClueBot (bot) (Reverting possible vandalism by 190.50.104.67 to version by DDSaeger. False positive? Report it. Thanks, en:User:ClueBot. (331923) (Bot))
• 2008-04-21 18:31 (diff) 190.50.104.67 (anon)
• 2008-03-31 19:06 (diff) (minor) DDSaeger (Capitalization.)
• 2008-03-30 18:25 (diff) CBM (/* First incompleteness theorem */ better link target)
• 2008-03-30 18:22 (diff) (minor) Wikidsoup (/* First incompleteness theorem */ add internal link)
• 2008-03-25 02:00 (diff) (minor) Jason.grossman (/* First incompleteness theorem */ Changed "computably enumurable" to "recursively enumerable" to match the statement of the Second Incompleteness Theorem. (The two phrases mean the same thing.))
• 2008-03-22 00:03 (diff) 123.255.61.246 (anon) (/* Boolos's short proof */ Reformat last paragraph as bullet list; clarify how Boolos altered Berry's paradox)
• 2008-03-20 22:32 (diff) (minor) Michael Hardy
• 2008-03-20 12:00 (diff) CBM (Please don't remove links to JStor)
• 2008-03-20 08:20 (diff) Palnot (/* Articles by others */ add Zach)
• 2008-03-19 03:05 (diff) (minor) Karl Dickman (/* Discussion and implications */ rm linebreak)
• 2008-03-16 05:43 (diff) (minor) Mpholmes (corrected spelling error and one instance of bad grammar)
• 2008-03-15 10:18 (diff) Hans Adler (Undid revision 198356799 by 202.82.33.202 (talk). Depending on how you parse this, sentence is either trivial or false.)
• 2008-03-15 05:27 (diff) 202.82.33.202 (anon) (/* First incompleteness theorem was not completely stated */)
• 2008-03-09 05:29 (diff) 202.46.137.77 (anon)
• 2008-03-09 04:50 (diff) 76.99.49.91 (anon)
• 2008-03-06 12:13 (diff) CBM (/* First incompleteness theorem */ copyedit last paragraph in top section)
• 2008-03-06 07:11 (diff) JoeBruno (/* First incompleteness theorem */ Clarification.)
• 2008-03-03 07:35 (diff) Brick Thrower (/* Relationship with computability */ // link in Kleene in opening sentence of this section (first reference))
• 2008-03-01 04:02 (diff) 74.222.220.126 (anon) (/* Proof sketch for the first theorem */ minor edit, added the word it)
• 2008-02-29 16:59 (diff) Wvbailey (/* Original statement of Gödel’s Theorem XI */ replace changed wording with CBM's wording)
• 2008-02-29 16:12 (diff) Xamce (/* Original statement of Gödel’s Theorem XI */)
• 2008-02-29 15:00 (diff) Pavel Jelínek (Expanded the section about limitations)
• 2008-02-22 04:08 (diff) CBM (Undo ; this is an archaic usage, not related to propositional logic.)
• 2008-02-22 03:56 (diff) (minor) Gregbard (propositional formula using AWB)
• 2008-02-08 12:36 (diff) Khalid hassani (/* Postmodernism and continental philosophy */ wikilink)
• 2008-02-07 19:49 (diff) (minor) Gregbard (deductive system using AWB)
• 2008-02-05 01:38 (diff) Trovatore (the Goedel theorems are FOL-specific -- I'm not familiar with the system of PM in detail but I think it works fine in FOL, even if that's not the original presentation. OW pls discuss on talk page.)
• 2008-02-04 23:22 (diff) 66.218.45.10 (anon) (/* Meaning of Gödel's theorems */ Principia Mathematica isn't first-order!)
• 2008-01-28 20:46 (diff) (minor) MagnusW (ö)
• 2008-01-28 14:03 (diff) 87.114.143.101 (anon) (/* Discussion and implications */ removed repeat phrase)
• 2008-01-25 11:01 (diff) Peterdjones (/* Discussion and implications */ GIT not inimical to all versions of formalism)
• 2008-01-23 14:26 (diff) 71.197.53.83 (anon)
• 2008-01-23 14:25 (diff) 71.197.53.83 (anon)
• 2008-01-16 21:01 (diff) CBM (/* Meaning of Gödel's theorems */ rephrase a little, Presburger arithmetic)
• 2008-01-16 18:42 (diff) Gene Nygaard (disamb)
• 2008-01-16 17:47 (diff) CBM (/* Meaning of Gödel's theorems */ add reference)
• 2008-01-16 17:43 (diff) CBM (/* Meaning of Gödel's theorems */ this is just a rephrasing of the statement of the theorem higher above. The other citation request is valid, and I'll look into that)
• 2008-01-16 17:37 (diff) Grover cleveland (/* Meaning of Gödel's theorems */ citation needed here: what about Pressburger arithmetic -- does that not also "define the natural numbers"?)
• 2008-01-16 17:35 (diff) Grover cleveland (copyedit)
• 2008-01-16 17:34 (diff) Grover cleveland (/* Meaning of Gödel's theorems */ clafiry)
• 2008-01-16 17:34 (diff) Grover cleveland (/* Original statement of Gödel’s Theorem XI */ copyedit)
• 2008-01-16 09:46 (diff) (minor) TicketMan (Spelling: discription ==> description. You can help!)
• 2008-01-15 23:49 (diff) (minor) Gregbard (duplicate category using AWB)
• 2008-01-14 16:08 (diff) (minor) Gregbard (metalogic using AWB)
• 2008-01-12 18:53 (diff) CBM (I see no need for an image of Godel on this article; please justify it on the talk page rather tha ocntinuing to unilaterally add it. Will comment on talk.)
• 2008-01-12 18:07 (diff) 86.40.246.81 (anon)
• 2008-01-10 18:13 (diff) (minor) Tamalet (/* Examples of undecidable statements */)
• 2008-01-09 14:16 (diff) 124.170.127.251 (anon) (/* Books about the theorems */)
• 2008-01-09 13:51 (diff) 124.170.127.251 (anon) (/* Books about the theorems */)
• 2008-01-05 05:36 (diff) (minor) Andycjp (/* See also */link included in main text)
• 2007-12-29 15:19 (diff) CBM (Removing image of Goedel. That would be appropriate for a biographical article, but not for an article about a theorem. This is not a grade-school text with pictures of each person mentioned)
• 2007-12-29 09:28 (diff) 72.193.109.144 (anon)
• 2007-12-28 17:57 (diff) (minor) Warut (clean up , typos fixed: Chruch → Church using AWB)
• 2007-12-21 00:00 (diff) (minor) MalafayaBot (bot) (robot Modifying: en:he:משפטי האי שלמות של גדל)
• 2007-12-10 14:11 (diff) (minor) Hans Adler (/* See also */ update link)
• 2007-12-10 09:17 (diff) Kwertii (/* See also */ Munchhausen-Trilemma -)
• 2007-12-06 05:00 (diff) 132.181.160.42 (anon) (/* Boolos's short proof */ bring together both mentions of times and less than.)
• 2007-12-06 02:36 (diff) 132.181.160.42 (anon) (/* External links */ add link to SEP)
• 2007-12-06 02:30 (diff) 132.181.160.42 (anon) (/* Boolos's short proof */ Berry's paradox innocent of infinity, proof intuitionistically sound, Fx "names" n)
• 2007-12-05 01:31 (diff) Trovatore (sorry, what do you mean by "prove the statement is consistent"? The point is that if the system proves the system is consistent, then the system is inconsistent.)
• 2007-12-05 00:35 (diff) (minor) Liyang (/* Meaning of Gödel's theorems */ anaphora disambiguation)
• 2007-12-04 05:01 (diff) 132.181.160.42 (anon) (/* Boolos's short proof */ make specific how little arithmetic the proof requires; shift to present tense)
• 2007-12-03 19:00 (diff) Trovatore (/* Boolos's short proof */ "iff" is a blackboard abbreviation not appropriate in an encyclopedia article. Wikilink unnecessary.)
• 2007-12-03 05:08 (diff) 132.181.160.42 (anon) (/* Boolos's short proof */ greatly expand the details of the discussion here)
• 2007-12-01 21:06 (diff) Wvbailey (/* Relationship with computability */ a proof sketch can be found in Hopcroft and Ullman 1979 p,354 and 371, also Minsky 1967. Hide Hopcroft-Ullman sketch. Refer readers to tag systems and P.C.P.)
• 2007-12-01 16:52 (diff) (minor) Ksnortum (/* Second incompleteness theorem */)
• 2007-12-01 16:46 (diff) (minor) Ksnortum (/* Second incompleteness theorem */)
• 2007-12-01 16:41 (diff) (minor) Ksnortum (/* Extensions of Gödel's original result */)
• 2007-11-26 10:09 (diff) Hans Adler (reverting distorting change by Simplifier. "single most" is in common use for stressing that it is not just "one of the most"; see e.g. http://dictionary.reference.com/browse/single)
• 2007-11-26 06:16 (diff) (minor) Simplifier (/* First incompleteness theorem */ copy-edit: superlative cannot be qualified)
• 2007-11-25 01:13 (diff) Eliko (adding back the link of Robinson arithmetic)
• 2007-11-25 01:08 (diff) Eliko (Robinson's arithmetic is irrelevant here)
• 2007-11-21 23:11 (diff) (minor) Wvbailey (/* References */ this section reappears above, and can be eliminated)
• 2007-11-21 20:24 (diff) Eliko (additional links)
• 2007-11-17 01:10 (diff) (minor) Matthew Kornya (/* Proof sketch for the second theorem */)
• 2007-11-16 17:44 (diff) Hairy Dude (/* Arithmetization of syntax */ "beweisbar" shouldn't really be capitalised)
• 2007-11-16 17:38 (diff) (minor) Hairy Dude (/* Arithmetization of syntax */ tweak)
• 2007-11-16 17:37 (diff) Hairy Dude (/* Arithmetization of syntax */ ASCII is just an example - make the analogy more precise)
• 2007-11-16 17:01 (diff) (minor) Hairy Dude (/* Meaning of Gödel's theorems */ spacing)
• 2007-11-15 15:31 (diff) CBM (After consulting Charlesworth paper, move the reference up here)
• 2007-11-15 15:07 (diff) 75.62.4.229 (anon) (cite the computer proof, hopefully this is enough.)
• 2007-11-15 10:42 (diff) (minor) CaptinJohn (Added note on the consequence for physics (Theory of everything) to complement that page.)
• 2007-11-14 21:11 (diff) (minor) CBM (/* Arithmetization of syntax */ copyedit)
• 2007-11-14 19:48 (diff) 75.62.4.229 (anon) (/* Arithmetization of syntax */ etymology)
• 2007-11-13 05:39 (diff) 134.10.176.84 (anon) (/* Second incompleteness theorem */)
• 2007-11-13 05:29 (diff) 132.181.160.42 (anon) (/* Boolos's short proof */ style edits)
• 2007-11-10 14:24 (diff) 212.105.18.129 (anon) (/* Examples of undecidable statements */)
• 2007-11-08 13:53 (diff) CBM (/* Relationship with computability */ copyedit - no need for completeness theorem to enumerate proofs (a lingering issue not removed in the rewrite))
• 2007-11-07 22:43 (diff) 132.181.160.42 (anon) (/* See also */)
• 2007-11-07 22:37 (diff) 132.181.160.42 (anon) (/* Proof sketch for the first theorem */ add years to Boolos and Rosser references)
• 2007-11-07 22:36 (diff) 132.181.160.42 (anon) (/* Articles by others */ no need to elaborate on content of Boolos (1998))
• 2007-11-07 22:34 (diff) 132.181.160.42 (anon) (/* Proof of independence */ Add section on Boolos proof)
• 2007-11-07 03:11 (diff) 132.181.160.42 (anon) (/* See also */ add link to Proof sketch)
• 2007-11-06 13:38 (diff) CBM (/* Relationship with computability */ remove second person)
• 2007-11-06 13:12 (diff) CBM (/* Computational Proof */ retitle (this is not a proof) and change ref to Kleene 1943)
• 2007-11-06 13:11 (diff) CBM (/* Articles by others */ add Kleene 1943)
• 2007-11-06 13:07 (diff) CBM (/* Computational Proof */ edit to reflect reference to Kleene 1943)
• 2007-11-06 12:54 (diff) CBM (Undoing changes by Likebox, will edit some more)
• 2007-11-06 06:52 (diff) Likebox (/* Computational Proof */)
• 2007-11-06 06:23 (diff) Likebox (Undid revision 169489112 by Trovatore (talk) Sorry Trov. you're completely wrong on this)
• 2007-11-05 23:56 (diff) Trovatore (rv to last by Carl -- see talk page)
• 2007-11-05 23:50 (diff) Likebox (Undid revision 169486075 by CBM (talk))
• 2007-11-05 23:41 (diff) CBM (/* Computational Proof */ copyedited but not removed)
• 2007-11-05 23:16 (diff) (minor) Likebox (/* Modern Proof */ minor reword)
• 2007-11-05 22:59 (diff) Likebox (Undid revision 169457210 by David Eppstein (talk))
• 2007-11-05 22:01 (diff) (minor) Pokipsy76 (/* Books about the theorems */ +link)
• 2007-11-05 21:20 (diff) David Eppstein (Undo per talk page. Written in such a way as to sound like original research, badly integrated into article, and incorrectly presents itself as a proof when it isn't one.)
• 2007-11-05 20:57 (diff) Likebox (/* Relationship with undecidable problems */ replaced vague stuff with precise proof. Please discuss before deleting.)
• 2007-11-02 03:42 (diff) CBM (/* Relationship with undecidable problems */ point out that an explicit program gan be given (this is what this section was formerly proving))
• 2007-11-02 03:12 (diff) CBM (/* Relationship with undecidable problems */ second typo in rewrite)
• 2007-11-02 03:11 (diff) CBM (/* Relationship with undecidable problems */ copyedit rewrite)
• 2007-11-02 03:08 (diff) CBM (/* Algorithmic Point of View */ rewrite to remove unneded parts and make it clear what's going on)
• 2007-11-02 02:34 (diff) DFRussia (Undid revision 168639981 by David Eppstein (talk) - please refer to talk page before doing random undoes)
• 2007-11-02 01:35 (diff) David Eppstein (Rv to 12:47, 1 November 2007 CBM. This is fluff that only peripherally relates to the incompleteness theorems and seriously unbalances the article.)
• 2007-11-01 23:40 (diff) Likebox (/* Algorithmic Point of View */ noted that CS is Godel)
• 2007-11-01 23:31 (diff) (minor) Likebox (/* Modern Proof */ retitle)
• 2007-11-01 21:30 (diff) 128.84.241.146 (anon) (/* Proof sketch for the first theorem */ reinserted modern proof.)
• 2007-11-01 19:47 (diff) CBM (/* Proof sketch for the second theorem */ expand)
• 2007-11-01 19:39 (diff) CBM (/* Diagonalization */ exmaple in English)
• 2007-11-01 19:35 (diff) CeilingCrash (/* Examples of undecidable statements */ OK, i think i really really did the ref properly now *sticks head in bucket Schreiber ✉ 16:18, 23. Feb. 2012 (CET))
• 2007-11-01 19:34 (diff) CeilingCrash (/* Examples of undecidable statements */ I think I got it this time. Can anyone recommend a good Wiki-editor-program ? Schreiber ✉ 16:18, 23. Feb. 2012 (CET))
• 2007-11-01 19:32 (diff) CeilingCrash (/* Examples of undecidable statements */ er, trying to fix in-text reference Schreiber ✉ 16:18, 23. Feb. 2012 (CET))
• 2007-11-01 19:30 (diff) CBM (/* Arithmetization of syntax */ not needed hypothesis - Bew is defined from the system, so if the system proves something, there is by def a Godel number of the proof)
• 2007-11-01 19:29 (diff) CeilingCrash (/* Examples of undecidable statements */ Added in-text reference Schreiber ✉ 16:18, 23. Feb. 2012 (CET))
• 2007-11-01 19:21 (diff) CeilingCrash (/* Examples of undecidable statements */ Polished addition of Hilbert's 10th problem with links, need to add ref Schreiber ✉ 16:18, 23. Feb. 2012 (CET))
• 2007-11-01 19:19 (diff) (minor) CBM (/* Examples of undecidable statements */ typo)
• 2007-11-01 19:18 (diff) CBM (/* Examples of undecidable statements */ copyedit hilbert's 10th)
• 2007-11-01 19:11 (diff) CeilingCrash (/* Examples of undecidable statements */ Added Hilbert's Tenth Problem to examples)
• 2007-11-01 19:11 (diff) CBM (/* Proof of independence */ because)
• 2007-11-01 19:07 (diff) CBM (/* Proof sketch for the first theorem */ rephrase some to emphasize diagonality)
• 2007-11-01 18:38 (diff) CBM (/* Proof sketch for the first theorem */ onlyneed to link to a concept once in a section (consistent, Godel number, ω-consistent))
• 2007-11-01 13:14 (diff) CBM (/* Modern Proof */ remove again, will leave commenton talk page)
• 2007-11-01 11:52 (diff) DFRussia (Undid revision 168469173 by CeilingCrash (talk) - Discuss first on talk page, for such a major cut)
• 2007-11-01 07:55 (diff) CeilingCrash (Removed "Modern Proof". The Church-Turing theorem came 5 years after Godel's, they adapt G'd technique. To assume CT as a lemma is to assume G (and mis-attribute it) Schreiber ✉ 16:18, 23. Feb. 2012 (CET))
• 2007-10-27 23:05 (diff) (minor) MalafayaBot (bot) (robot Adding: en:nov:Teoreme de Godel Modifying: en:fa:قضایای ناتمامیت گودل)
• 2007-10-26 20:09 (diff) Likebox (/* Modern Proof */)
• 2007-10-26 20:08 (diff) Likebox (/* External links */)
• 2007-10-26 20:06 (diff) Likebox (/* Modern Proof */ added necessary cite)
• 2007-10-19 12:22 (diff) 62.216.204.108 (anon) (/* Examples of undecidable statements */ o umlaut)
• 2007-10-19 11:46 (diff) 62.216.204.108 (anon) (/* Modern Proof */ linkfix)
• 2007-10-18 04:40 (diff) Zero sharp (/* Extensions of Gödel's original result */ if it's not omega-consistent then what?)
• 2007-10-18 01:26 (diff) (minor) Likebox (/* Modern Proof */ added link)
• 2007-10-16 14:18 (diff) (minor) Utcursch (Reverted edits by 204.9.144.54 (talk) to last version by 204.112.128.156)
• 2007-10-16 13:15 (diff) 204.9.144.54 (anon)
• 2007-10-16 13:14 (diff) 204.9.144.54 (anon)
• 2007-10-13 01:03 (diff) 204.112.128.156 (anon) (/* Theories of everything and physics */)
• 2007-10-13 01:01 (diff) 204.112.128.156 (anon) (/* Theories of everything and physics */)
• 2007-10-13 00:59 (diff) 204.112.128.156 (anon) (/* Theories of everything and physics */)
• 2007-10-12 19:40 (diff) (minor) Likebox (/* Modern Proof */ reword false claim.)
• 2007-10-12 04:56 (diff) (minor) Likebox (/* Modern Proof */)
• 2007-10-12 04:17 (diff) 216.7.9.34 (anon) (/* Modern Proof */ minor stuff)
• 2007-10-12 04:10 (diff) 216.7.9.34 (anon) (/* Modern Proof */ Rosserize)
• 2007-10-11 22:49 (diff) Wvbailey (/* Articles by others */ add Rosser 1939 and show these are both in The Undecidable)
• 2007-10-11 20:08 (diff) Trovatore (Likebox, I would prefer that you took this a little slower. At this pace there isn't time for others to evaluate your work and respond. Could you make a proposed-revisions page?)
• 2007-10-11 20:04 (diff) Likebox (/* Theories of everything and physics */ crit. of Hawking)
• 2007-10-11 20:01 (diff) Likebox (/* Discussion and implications */ added necessary refs to Hilbert.)
• 2007-10-11 19:31 (diff) (minor) Likebox (/* Decision Problems */ fixed numbering)
• 2007-10-11 19:20 (diff) Likebox (/* Decision Problems */ removed ugly bolded text)
• 2007-10-11 19:16 (diff) Likebox (/* Examples of undecidable statements */)
• 2007-10-11 16:31 (diff) Crisófilax (The results DO NOT require the Gödel Theorem)
• 2007-10-11 16:27 (diff) Likebox (/* Examples of undecidable statements */ replaced "do not" with "do".)
• 2007-10-11 15:04 (diff) (minor) DragonflySixtyseven (Reverted edits by Ademh (talk) to last version by CBM)
• 2007-10-11 13:33 (diff) Ademh (/* Proof sketch for the second theorem */)
• 2007-10-11 11:25 (diff) CBM (Removing erroneous essay again)
• 2007-10-11 08:00 (diff) Ademh (i put up a discussion and no one answered it -so the entry is back)
• 2007-10-10 23:59 (diff) (minor) Likebox (/* Modern Proof */ reword)
• 2007-10-10 23:35 (diff) Likebox (/* Modern Proof */)
• 2007-10-10 23:31 (diff) Likebox (/* Modern Proof */ second incompleteness theorem)
• 2007-10-10 23:15 (diff) Likebox (/* Examples of undecidable statements */ added short modern proof)
• 2007-10-09 17:26 (diff) (minor) CRGreathouse (unicode, linking)
• 2007-10-09 14:25 (diff) Wvbailey (Undid revision 163329515 by Ademh (talk) Please go to talk page and address the problem there. This is a revert war.)
• 2007-10-09 14:08 (diff) Ademh (replacing attempt to censor research in the public interest)
• 2007-10-09 13:46 (diff) Wvbailey (/* Paradox in Godels incompleteness theorem that invalidates it */ try again to move "censored view" to talk page)
• 2007-10-09 13:34 (diff) Ademh (replaceing censored view)
• 2007-10-09 13:30 (diff) CBM (Remove lengthy comments that are confused about the application to various formal systems)
• 2007-10-09 09:31 (diff) Ademh (/* Proof sketch for the second theorem */)
• 2007-10-07 20:38 (diff) (minor) Kborer (/* Original statement of Gödel’s Theorem XI */ Godel -> Gödel)
• 2007-10-02 23:42 (diff) Pol098 (/* Theories of everything and physics */ will ==> can)
• 2007-10-02 23:22 (diff) (minor) Pol098
• 2007-09-29 11:41 (diff) Blaisorblade (/* First incompleteness theorem */ Improve explaination of what "true" means - please check)
• 2007-09-14 13:44 (diff) 168.170.197.140 (anon)
• 2007-09-14 13:44 (diff) 168.170.197.140 (anon)
• 2007-09-13 21:01 (diff) Wvbailey (/* Translations, during his lifetime, of Gödel’s paper into English */add a 4th version which is actually his rather famous lectures to the IAS in Princeton during 1934)
• 2007-09-13 15:51 (diff) Trovatore (hmm, let's start with 0, otherwise those who include 0 in natural numbers may read the statement as something false)
• 2007-09-13 05:08 (diff) 203.206.223.208 (anon) (/* Meaning of Gödel's theorems */)
• 2007-09-12 12:48 (diff) Juustensson (Correcting typo Widerspuchfreiheit -> Widerspruchfreiheit)
• 2007-09-10 20:08 (diff) Trovatore (/* Criticism of Godel's theorem */ rm crank section)
• 2007-09-10 20:03 (diff) 220.238.202.11 (anon) (/* Criticism of Godel's theorem */)
• 2007-09-10 18:12 (diff) Merzul (/* Theories of everything and physics */ this was slightly over-simplified...)
• 2007-09-10 17:57 (diff) Merzul (/* References */ inconsistent ref styles being used here, but at least they should be shown.)
• 2007-09-10 12:13 (diff) CBM (Move external link to that section)
• 2007-09-10 12:03 (diff) Libett (/* Limitations of Gödel's theorems */)
• 2007-09-09 20:36 (diff) 86.141.75.237 (anon) (/* Theories of Everything and Physics */ tidy up recent badly written edit)
• 2007-09-09 20:09 (diff) NBeale (/* Discussion and implications */ Theories of Everything and Physics)
• 2007-08-22 14:36 (diff) 38.119.244.46 (anon) (/* Limitations of Gödel's theorems */)
• 2007-08-19 01:48 (diff) 71.238.109.97 (anon) (/* Translations, during his lifetime, of Gödel’s paper into English */)
• 2007-08-15 20:35 (diff) Wvbailey (/* Books about the theorems */ add Dawson)
• 2007-08-15 20:30 (diff) Wvbailey (/* Articles by Gödel */ remove van Heijenoort (he is listed below). Add comment re Hirzel Martin (suspect tr)
• 2007-08-15 20:26 (diff) Wvbailey (/* Translations of Gödel’s paper into English */make it clear that Godel saw these translations and commented on all of them)
• 2007-08-15 20:21 (diff) Wvbailey (/* Articles by Gödel */ add the three translations with cautionary guidance to would-be editors)
• 2007-08-15 19:16 (diff) Wvbailey (/* Second incompleteness theorem */add the original statement of Theorem XI as translated in van Heijenoort, with translations of the abbreviations)
• 2007-08-15 18:20 (diff) Wvbailey (/* First incompleteness theorem */ add translation of abbreviations)
• 2007-08-15 17:44 (diff) Wvbailey (/* First incompleteness theorem */Fussy Godel would wantthe translation precisely right and made clear that the reader will encounter "Theorem VI" in the original)
• 2007-07-20 11:10 (diff) (minor) OKBot (bot) (robot Adding: en:fa:قضایای عدم تمامیت گدل)
• 2007-07-16 12:36 (diff) Dan Gluck (/* See also */)
• 2007-07-13 17:30 (diff) (minor) SieBot (bot) (robot Modifying: en:es:Teoremas de la incompletitud de Gödel, en:uk:Теореми Геделя про неповноту)
• 2007-07-08 19:20 (diff) Trovatore (sorry, I misinterpreted. Readding Carl's change, put in commas, move footnotes)
• 2007-07-08 19:16 (diff) Trovatore (/* First incompleteness theorem */ useful commas (avoid the reading "true...in the theory"))
• 2007-07-08 19:15 (diff) Trovatore (no, I don't like that change -- I think we need to say off the bat that it's true, and then discuss possible objections)
• 2007-07-08 17:40 (diff) CBM (/* First incompleteness theorem */ rephrase slightly)
• 2007-07-03 12:54 (diff) Guruparan18 (/* Books about the theorems */ Link fixed)
• 2007-06-29 16:53 (diff) 151.142.237.194 (anon) (/* Proof sketch for the first theorem */)
• 2007-06-28 03:17 (diff) 71.113.227.141 (anon) (Undid revision 141092926 by 211.31.106.202 (talk))
• 2007-06-28 02:53 (diff) 211.31.106.202 (anon)
• 2007-06-26 11:58 (diff) Anchor Link Bot (Notifying of internal link to section Second incompleteness theorem from en:Mathematics)
• 2007-06-11 20:53 (diff) (minor) Davebuehler (/* External links */)
• 2007-06-10 19:54 (diff) (minor) D14C050 (Removed unnecessary newlines)
• 2007-05-24 18:45 (diff) 148.87.1.171 (anon) (/* Extensions of Gödel's original result */)
• 2007-05-24 18:44 (diff) 148.87.1.171 (anon) (/* Extensions of Gödel's original result */)
• 2007-05-16 11:05 (diff) Peterdjones (/* Postmodernism and continental philosophy */ gr.)
• 2007-05-16 10:55 (diff) JRSpriggs (/* Postmodernism and continental philosophy */ try to fix the grammar of the first sentence in another way)
• 2007-05-16 09:26 (diff) 143.167.74.60 (anon) (/* Postmodernism and continental philosophy */)
• 2007-05-08 08:51 (diff) (minor) SieBot (bot) (robot Modifying: en:sv:Gödels ofullständighetssats)
• 2007-05-04 19:27 (diff) 86.131.194.92 (anon) (/* Limitations of Gödel's theorems */)
• 2007-05-04 19:26 (diff) 86.131.194.92 (anon) (/* Limitations of Gödel's theorems */)
• 2007-05-03 09:07 (diff) JRSpriggs (Undid revision 127896274 by 67.171.67.153 (talk)notation of change is not consistent with other text)
• 2007-05-03 07:02 (diff) 67.171.67.153 (anon) (/* Second incompleteness theorem */)
• 2007-04-29 22:20 (diff) 71.169.150.172 (anon) (en:Hilbert's program already links to en:David Hilbert. link it once. Hilbert is linked later.)
• 2007-04-26 19:40 (diff) 145.116.236.110 (anon) (/* Books about the theorems */ Doug Hofstadter's new book has a more accessible discussion of the themes in GEB, including Gödel's theorem.)
• 2007-04-26 01:46 (diff) Trovatore (/* See also */ rm a couple irrelevant links)
• 2007-04-26 01:44 (diff) (minor) Zchenyu (/* See also */)
• 2007-04-24 06:54 (diff) 58.107.159.155 (anon)
• 2007-04-15 04:30 (diff) (minor) Quux0r (/* First incompleteness theorem */ minor clarifications)
• 2007-04-14 11:53 (diff) 74.117.47.205 (anon) (moved ref because it was breaking the formatting...)
• 2007-04-13 02:56 (diff) 71.244.214.129 (anon)
• 2007-04-09 00:19 (diff) 67.126.143.230 (anon) (/* Meaning of Gödel's theorems */)
• 2007-04-07 10:46 (diff) JRSpriggs (/* Discussion and implications */ rephrase it again to make it hypothetical)
• 2007-04-07 07:21 (diff) Sgutkind (/* Discussion and implications */ Clarified hypothetical language)
• 2007-04-04 11:14 (diff) JRSpriggs (/* Second incompleteness theorem */)
• 2007-04-04 11:13 (diff) JRSpriggs (/* First incompleteness theorem */ spelling)
• 2007-04-04 07:10 (diff) 67.173.250.17 (anon) (/* First incompleteness theorem */)
• 2007-04-04 07:08 (diff) 67.173.250.17 (anon) (/* Second incompleteness theorem */)
• 2007-04-04 03:49 (diff) 69.114.149.244 (anon)
• 2007-04-01 21:07 (diff) Zero sharp (/* See also */ I don't.)
• 2007-04-01 09:35 (diff) AndySimpson (/* See also */ I think it fits)
• 2007-03-31 16:55 (diff) Peterdjones (/* Limitations of Gödel's theorems */ +ref)
• 2007-03-29 03:31 (diff) 70.23.64.82 (anon) (Removed cranky link with its POV commentary)
• 2007-03-27 13:59 (diff) (minor) SpuriousQ (/* First incompleteness theorem */ cap)
• 2007-03-27 05:39 (diff) 74.134.249.199 (anon) (/* First incompleteness theorem */)
• 2007-03-23 18:13 (diff) Nbhatla (/* Second incompleteness theorem */)
• 2007-03-20 23:07 (diff) 203.200.95.130 (anon) (/* Limitations of Gödel's theorems */)
• 2007-03-20 23:07 (diff) 203.200.95.130 (anon) (/* Limitations of Gödel's theorems */)
• 2007-03-14 08:28 (diff) (minor) Thijs!bot (bot) (robot Modifying: en:pt:Teorema da Incompletude de Gödel)
• 2007-03-08 23:15 (diff) 128.230.144.125 (anon)
• 2007-03-08 08:17 (diff) 202.36.179.65 (anon) (/* Books about the theorems */ add Smullyan (1994))
• 2007-03-08 03:11 (diff) Latulla (/* Proof sketch for the first theorem */ unlinked section title added Main instead)
• 2007-03-05 05:21 (diff) 143.44.53.240 (anon) (/* Proof sketch for the first theorem */)
• 2007-03-05 05:17 (diff) 143.44.53.240 (anon) (/* Proof sketch for the first theorem */)
• 2007-03-02 19:19 (diff) CBM (I think this is a good example. ←Undid revision 112128024 by 207.171.180.101 (talk))
• 2007-03-02 18:41 (diff) 207.171.180.101 (anon) (/* Meaning of Gödel's theorems */)
• 2007-03-02 06:56 (diff) 205.237.161.22 (anon) (/* Discussion and implications */)
• 2007-03-01 22:47 (diff) Trovatore ("the fact that this is also" makes no sense; please re-read the sentence)
• 2007-03-01 22:45 (diff) 140.247.29.68 (anon) (/* Discussion and implications */)
• 2007-02-28 20:36 (diff) (minor) Chobot (bot) (robot Adding: en:ca:Teorema d'incompletesa de Gödel)
• 2007-02-24 14:42 (diff) CBM (/* Extensions of Gödel's original result */ small copyedit)
• 2007-02-24 10:02 (diff) JRSpriggs (/* Proof sketch for the first theorem */ spelling; pointer)
• 2007-02-24 09:55 (diff) JRSpriggs (/* Examples of undecidable statements */ spelling)
• 2007-02-24 03:16 (diff) (minor) SpuriousQ (rv, grammar)
• 2007-02-24 02:30 (diff) 74.139.209.44 (anon) (/* Discussion and implications */)
• 2007-02-24 00:49 (diff) Cacycle (/* Books about the theorems */ rm link to Wacko site http://www.transplexity.org)
• 2007-02-23 16:57 (diff) CBM (/* Limitations of Gödel's theorems */ remove sentence that is now in lede)
• 2007-02-23 13:30 (diff) CBM (/* See also */ remove two more that are included in the article)
• 2007-02-23 13:29 (diff) CBM (/* Lede */ wikilink en:Hilbert's second problem)
• 2007-02-23 13:23 (diff) CBM (/* See also */ remove some that are already included in the article. more could be integrated.)
• 2007-02-23 13:21 (diff) CBM (/* Examples of undecidable statements */ copedit, wikilink. en:computability theory is a dabpage that should be used for general links to the subject rather than en:recursion theory)
• 2007-02-23 08:35 (diff) JRSpriggs (/* First incompleteness theorem */ spelling)
• 2007-02-23 00:34 (diff) CBM (/* Footnotes */ add one on notation)
• 2007-02-23 00:33 (diff) CBM (/* First incompleteness theorem */ copyedit)
• 2007-02-23 00:15 (diff) CBM (/* Articles by others */ + Putnam 1960)
• 2007-02-23 00:15 (diff) CBM (/* Minds and machines */ add year to Putnam, resolve vague "some")
• 2007-02-23 00:12 (diff) CBM (/* Lede */ copyedit second para and try to resolve vague "some claim")
• 2007-02-21 06:28 (diff) (minor) David.Monniaux (/* Proof sketch for the first theorem */ missing 'of')
• 2007-02-20 08:44 (diff) 202.36.179.65 (anon) (/* External links */ add Myers)
• 2007-02-06 19:39 (diff) (minor) GTBacchus (Reverted edits by Lifeisfun0007 (talk) to last version by Trovatore)
• 2007-02-06 19:39 (diff) Lifeisfun0007
• 2007-02-06 19:30 (diff) Trovatore (rvv)
• 2007-02-06 19:29 (diff) Lifeisfun0007
• 2007-01-28 10:48 (diff) (minor) Thijs!bot (bot) (robot Modifying: en:ru:Теоремы Гёделя о неполноте)
• 2007-01-27 14:59 (diff) Dan Gluck (/* Discussion and implications */)
• 2007-01-27 14:51 (diff) Dan Gluck (/* Limitations of Gödel's theorems */)
• 2007-01-27 14:48 (diff) Dan Gluck (/* Proof sketch for the first theorem */)
• 2007-01-27 14:42 (diff) (minor) Dan Gluck (/* Meaning of Gödel's theorems */)
• 2007-01-27 14:21 (diff) (minor) Dan Gluck (/* Minds and machines */)
• 2007-01-27 14:17 (diff) Dan Gluck (/* Minds and machines */)
• 2007-01-27 14:05 (diff) (minor) Dan Gluck (/* Proof sketch for the first theorem */)
• 2007-01-27 14:02 (diff) Dan Gluck (/* Proof sketch for the first theorem */)
• 2007-01-27 12:23 (diff) (minor) Dan Gluck (/* Proof sketch for the first theorem */)
• 2007-01-27 03:51 (diff) CBM (/* External links */ remove POV annotation)
• 2007-01-27 02:08 (diff) (minor) Geremia (Removed broken hyperlink)
• 2007-01-26 21:43 (diff) Dan Gluck (/* Proof sketch for the first theorem */)
• 2007-01-26 19:36 (diff) Trovatore (/* Gödel's theorem */ remove section header. The name "Gödel's theorem" doesn't pick out first incompleteness from his other theorems.)
• 2007-01-26 13:29 (diff) CBM (/* Intro */ for arithmetic, comment on talk)
• 2007-01-26 07:23 (diff) Trovatore (don't agree with all of the intro rewrite. see talk.)
• 2007-01-26 06:29 (diff) 132.181.160.42 (anon) (rewrite intro; Limitations)
• 2007-01-26 06:09 (diff) 132.181.160.42 (anon) (/* External links */ restore umlauts)
• 2007-01-26 04:46 (diff) 132.181.160.42 (anon) (/* Articles by others */ mention peano axioms)
• 2007-01-26 04:44 (diff) 132.181.160.42 (anon) (/* See also */ add Tarski's theorem)
• 2007-01-26 04:42 (diff) 132.181.160.42 (anon) (/* Articles by others */ mention primitive recursive functions)
• 2007-01-26 04:40 (diff) 132.181.160.42 (anon) (/* Articles by others */ describe Boolos)
• 2007-01-26 04:36 (diff) 132.181.160.42 (anon) (/* External links */ reformat; move Podnieks here)
• 2007-01-26 04:24 (diff) 132.181.160.42 (anon) (/* References */ reformat; add Boolos)
• 2007-01-25 20:50 (diff) 212.200.215.77 (anon)
• 2007-01-25 02:54 (diff) Trovatore (/* Gödel's theorem */ link to article on paper)
• 2007-01-24 18:59 (diff) (minor) Trovatore (oops, editing goof -- removed the wrong cats. Fixing.)
• 2007-01-24 18:41 (diff) Trovatore (The article is not about any sort of publication. If you want to write an article on Gödel's famous paper, the cats would be appropriate there.)
• 2007-01-24 13:57 (diff) APH (en:Category: Important publication in logic)
• 2007-01-23 19:40 (diff) (minor) Husond (Reverted edits by 207.165.117.3 (talk) to last version by Husond)
• 2007-01-23 19:39 (diff) 207.165.117.3 (anon) (/* First incompleteness theorem */)
• 2007-01-23 19:15 (diff) (minor) Husond (Reverted edits by 207.165.117.3 (talk) to last version by Husond)
• 2007-01-23 19:15 (diff) 207.165.117.3 (anon) (/* Gödel's theorem */)
• 2007-01-23 19:14 (diff) (minor) Husond (Reverted 1 edits by 207.165.117.3 (talk) to last revision (102208195) by Kid A using VP2)
• 2007-01-23 19:13 (diff) 207.165.117.3 (anon) (/* Gödel's theorem */)
• 2007-01-21 13:36 (diff) Kid A (en:Gödel sentence redirects to this article)
• 2007-01-17 09:12 (diff) JRSpriggs (revert to SpuriousQ's version. The publication is the first one listed in the References.)
• 2007-01-17 01:46 (diff) Mon4 (/* External links */ -cat: not a publication)
• 2007-01-17 01:26 (diff) SpuriousQ (/* Scientific articles */ moving out references that had to do with minds and machines)
• 2007-01-17 01:13 (diff) SpuriousQ (/* Minds and machines */ merged to en:Mechanism (philosophy))
• 2007-01-17 01:05 (diff) SpuriousQ (rv see proof right below it)
• 2007-01-16 21:09 (diff) Lou2261 (/* The theorem had an incorrect if and only if statement implying that if a system was inconsistent, then it must include a statement of its own inconsistency. This isn't the theorem. Schreiber ✉ 16:18, 23. Feb. 2012 (CET) */)
• 2007-01-16 15:06 (diff) 82.46.16.220 (anon) (/* Discussion and implications */)
• 2007-01-15 05:42 (diff) JRSpriggs (/* See also */ point to Hilbert's second problem)
• 2007-01-14 11:18 (diff) APH (en:Category: Important publication in mathematics)
• 2007-01-13 04:49 (diff) (minor) Ruakh (/* Examples of undecidable statements */ clean up last edit)
• 2007-01-13 04:18 (diff) CBM (/* Examples of undecidable statements */ this is the liar paradox, not Russell's paradox (set of all sets?))
• 2007-01-12 18:08 (diff) Ruakh (/* Discussion and implications */ partial rv: rm highly debatable claim (how do we define "prove"?))
• 2007-01-12 16:30 (diff) 82.46.16.220 (anon) (/* Discussion and implications */)
• 2007-01-12 16:29 (diff) 82.46.16.220 (anon) (/* Discussion and implications */)
• 2007-01-12 16:28 (diff) 82.46.16.220 (anon) (/* Discussion and implications */)
• 2007-01-12 16:23 (diff) 82.46.16.220 (anon) (/* Examples of undecidable statements */)
• 2007-01-12 16:22 (diff) 82.46.16.220 (anon) (/* Examples of undecidable statements */)
• 2007-01-12 16:15 (diff) 82.46.16.220 (anon) (/* Examples of undecidable statements */)
• 2007-01-12 16:12 (diff) 82.46.16.220 (anon) (/* Meaning of Gödel's theorems */)
• 2007-01-12 16:10 (diff) 82.46.16.220 (anon) (/* Meaning of Gödel's theorems */)
• 2007-01-12 16:09 (diff) 82.46.16.220 (anon) (/* Meaning of Gödel's theorems */)
• 2007-01-12 15:56 (diff) 82.46.16.220 (anon) (/* Minds and machines */)
• 2007-01-11 23:41 (diff) (minor) Ruakh (s/ω/ω/g;)
• 2007-01-11 12:39 (diff) CBM (/* Gödel's theorem */ copyedit. Main change: Godel's original statement is already the one listed above; fix final paragraph)
• 2007-01-11 12:22 (diff) CBM (/* Discussion and implications */ copyedit)
• 2007-01-09 02:51 (diff) Trovatore (rv)
• 2007-01-09 02:38 (diff) Germanium
• 2007-01-08 19:05 (diff) Ruakh (/* See also */ rm redlink and link to article about seemingly irrelevant webcomic)
• 2007-01-08 18:57 (diff) Sacramentis (/* Books */)
• 2007-01-08 00:23 (diff) Nilfanion (revert to last version before hist merge)
• 2007-01-08 00:21 (diff) (minor) Nilfanion (moved en:Goedel's incompleteness theorem to en:Gödel's incompleteness theorems: hist-merging)
• 2007-01-06 12:51 (diff) CBM (/* Proof sketch for the first theorem */ move comment by Biedermann to en:Talk:Gödel's incompleteness theorems/Arguments#Comment by Biedermann)
• 2007-01-06 10:44 (diff) Biedermann (/* Proof sketch for the first theorem */)
• 2007-01-06 07:53 (diff) JRSpriggs (revert my last two edits. I was trying to over-simplify.)
• 2007-01-06 07:48 (diff) JRSpriggs (/* First incompleteness theorem */ left out best part)
• 2007-01-06 07:44 (diff) JRSpriggs (/* First incompleteness theorem */ add another wording)
• 2007-01-06 07:37 (diff) JRSpriggs (Undo revision 98771035 by Timwi (talk)is more convenient to see whether it is ps or pdf ahead of time)
• 2007-01-06 06:45 (diff) Ruakh (/* Proof sketch for the first theorem */ fix up a bit, in response to comment on talk-page)
• 2007-01-06 00:58 (diff) (minor) Timwi (/* Footnotes */)
• 2007-01-06 00:56 (diff) (minor) Timwi (/* Minds and machines */ so?)
• 2007-01-05 03:16 (diff) (minor) CBM (/* Intro */ remove unecessary comma)
• 2007-01-04 23:04 (diff) (minor) Steel (Reverted edits by Germanium (talk) to last version by Trovatore)
• 2007-01-04 22:55 (diff) Germanium (rv, someone please block Trovatore)
• 2007-01-04 22:50 (diff) Trovatore (rv; someone please block this guy)
• 2007-01-04 22:48 (diff) 68.114.185.27 (anon) (no long explanation?)
• 2007-01-04 22:38 (diff) Trovatore (rv)
• 2007-01-04 22:35 (diff) Germanium (remove CMummert, crankish)
• 2007-01-04 22:32 (diff) CBM (/* Godel's Incompleteness Theorem and the en:Theory of Everything */ remove this section (crankish))
• 2007-01-04 22:16 (diff) (minor) Chris the speller (Correcting spelling: truely->truly)
• 2007-01-04 22:10 (diff) Germanium (rv, please see en:WP:OR)
• 2007-01-04 22:00 (diff) (minor) SpuriousQ (rv, please see en:WP:OR)
• 2007-01-04 21:53 (diff) Germanium (see also)
• 2007-01-04 21:52 (diff) Germanium (/* Proof sketch for the second theorem */)
• 2007-01-04 21:51 (diff) Germanium
• 2007-01-04 21:20 (diff) SpuriousQ (rv, please see en:WP:OR)
• 2007-01-04 21:17 (diff) 68.114.185.27 (anon) (/* Godel's Incompleteness Theorem and what it implies for the en:Theory of Everything */)
• 2007-01-04 21:11 (diff) 68.114.185.27 (anon) (/* Godel's Incompleteness Theorem and what it implies for the en:Theory of Everything */)
• 2007-01-04 21:11 (diff) 68.114.185.27 (anon) (/* See also */)
• 2007-01-04 21:09 (diff) 68.114.185.27 (anon) (/* Godel's Incompleteness Theorem and what it implies for the en:Theory of Everything */)
• 2007-01-04 21:07 (diff) 68.114.185.27 (anon) (/* Godel's Incompleteness Theorem and what it implies for the en:Theory of Everything */)
• 2007-01-04 21:02 (diff) 68.114.185.27 (anon)
• 2007-01-04 21:01 (diff) 68.114.185.27 (anon)
• 2007-01-04 20:59 (diff) 68.114.185.27 (anon)
• 2007-01-04 20:10 (diff) (minor) SpuriousQ (not Putnam, Lucas)
• 2007-01-04 20:00 (diff) 88.111.12.248 (anon) (/* Minds and machines */)
• 2007-01-03 10:45 (diff) JRSpriggs (/* First incompleteness theorem */ pointer to better article for "infinite set")
• 2007-01-03 06:15 (diff) 71.193.11.55 (anon) (/* First incompleteness theorem */)
• 2007-01-02 22:51 (diff) Nick (clean up using AWB)
• 2006-12-28 00:56 (diff) 82.6.103.159 (anon) (/* Books */)
• 2006-12-27 06:33 (diff) JRSpriggs (revert to 200.18.7.18's version. The system does not have to be complete for proving consistency to be inconsistent.)
• 2006-12-27 02:07 (diff) 168.253.132.134 (anon) (/* Meaning of Gödel's theorems */)
• 2006-12-27 02:03 (diff) 168.253.132.134 (anon) (/* Meaning of Gödel's theorems */)
• 2006-12-18 19:47 (diff) 200.18.7.18 (anon) (/* External links */)
• 2006-12-18 19:46 (diff) 200.18.7.18 (anon) (/* External links */)
• 2006-12-14 15:52 (diff) Dreftymac (wikify)
• 2006-12-04 00:33 (diff) (minor) David Eppstein (fix missorting)
• 2006-12-03 22:41 (diff) 66.217.179.50 (anon) (Paul August, you never responded to me on Talk with reason for reversal, so am restoring this link.)
• 2006-12-03 16:00 (diff) Gene Nygaard (fix missorting)
• 2006-12-01 03:47 (diff) DavidCBryant (/* First incompleteness theorem */ I hate the passive voice. And truth is timeless.)
• 2006-12-01 03:23 (diff) (minor) DavidCBryant (Changed past tense "was" to present tense "is'. Hilbert is dead, but his program still exists. And truth is timeless.)
• 2006-11-28 01:50 (diff) CBM (expanded lead. One sentence is not enough lead for an important article. More expansion and clarification in the lead would be fine with me)
• 2006-11-28 01:49 (diff) CBM (expanded lead. One sentence is not enough of a lead for an important article. I added a few summary sentences, but any additions to it would be fine with me)
• 2006-11-28 01:34 (diff) 83.67.216.72 (anon) (Added link to Goodstein's theorem - an unboring demonstration of what this theroem says)
• 2006-11-27 08:44 (diff) JRSpriggs (revert removal of section header and formal statement of theorem)
• 2006-11-27 00:56 (diff) SpuriousQ (/* First incompleteness theorem */ you can't understand godel's statement without reading the paper, doesn't belong at this point in the article if at all)
• 2006-11-26 07:01 (diff) 69.106.225.92 (anon) (/* First incompleteness theorem */ minor edit)
• 2006-11-24 04:45 (diff) (minor) Ruakh (/* Discussion and implications */ emdashify)
• 2006-11-24 04:24 (diff) 72.129.216.191 (anon) ("Limitations" of formal systems, rather than "Limits" because, while both words refer to the same concept, "limits" also refers to the mathematical definition of a limit.)
• 2006-11-16 03:03 (diff) (minor) Paul August (Reverted edits by 66.217.176.189 (talk) to last version by Ruakh)
• 2006-11-16 01:58 (diff) 66.217.176.189 (anon) (/* External links */)
• 2006-11-15 22:15 (diff) (minor) Ruakh (/* Meaning of Gödel's theorems */ emdashify)
• 2006-11-15 22:09 (diff) (minor) Ruakh (/* First incompleteness theorem */ punct fix per en:WP:MOS)
• 2006-11-15 01:14 (diff) Trovatore (This article is too long as it is, and the new material does not appear to be tightly focused on the theorems themselves (might go better in some phil-of-math article). Please discuss on talk.)
• 2006-11-15 00:50 (diff) 134.226.1.229 (anon) (/* Limitations of Gödel's theorems */)
• 2006-11-15 00:44 (diff) 134.226.1.229 (anon) (/* Limitations of Gödel's theorems */)
• 2006-11-10 23:20 (diff) (minor) JabberWok (/* First incompleteness theorem */ rm space)
• 2006-10-31 21:59 (diff) (minor) Lance Williams (/* First incompleteness theorem */)
• 2006-10-28 04:35 (diff) Ootachi (no need to link to QED; replaced with end-of-proof symbol)
• 2006-10-26 18:39 (diff) (minor) Paul August (Reverted edits by 155.198.196.151 (talk) to last version by 24.255.110.6)
• 2006-10-26 13:57 (diff) 155.198.196.151 (anon) (/* Proof sketch for the second theorem */)
• 2006-10-16 21:22 (diff) 24.255.110.6 (anon)
• 2006-09-29 17:27 (diff) (minor) CBM (revert anonymous vandalism)
• 2006-09-29 17:22 (diff) 128.187.0.164 (anon)
• 2006-09-27 19:56 (diff) 83.71.57.206 (anon) (/* Limitations of Gödel's theorems */)
• 2006-09-10 12:14 (diff) JRSpriggs (/* Gödel's theorem */ try to clarify omega consistency)
• 2006-09-10 10:26 (diff) Nicolaennio (/* Gödel's theorem */)
• 2006-09-05 20:39 (diff) Trovatore (Let's be a little serious, people. Also see en:WP:POINT.)
• 2006-09-05 20:12 (diff) K95 (No one can prove that this article doesn't belong in this new category)
• 2006-08-29 23:24 (diff) (minor) Michael Hardy
• 2006-08-28 21:00 (diff) Hairy Dude (rm subjective "celebrated" and add link to en:theorem)
• 2006-08-28 18:55 (diff) Trovatore (rv; "an infinite" is correct English)
• 2006-08-28 18:51 (diff) 84.248.199.61 (anon)
• 2006-08-23 16:20 (diff) 192.75.48.150 (anon) (/* Second incompleteness theorem */ en:primitive recursive arithmetic)
• 2006-08-23 13:16 (diff) 85.178.34.242 (anon) (/* First incompleteness theorem */)
• 2006-08-21 18:54 (diff) Trovatore (rv -- that *is* maybe one way to prove the theorem, but the theorem doesn't *depend* on undefinability. As for the set-theoretic paradoxes, that's a red herring.)
• 2006-08-21 18:39 (diff) 71.139.24.187 (anon) (/* Gödel's Theorem */)
• 2006-08-21 00:06 (diff) 132.181.160.42 (anon) (/* See also */)
• 2006-08-21 00:04 (diff) 132.181.160.42 (anon) (/* First incompleteness theorem */ extensive clarifications to paras 2,3,4)
• 2006-08-20 00:01 (diff) 71.56.59.97 (anon) (/* First incompleteness theorem */)
• 2006-08-15 19:50 (diff) Trovatore (rv unclear passage; please explain on talk page just what you mean)
• 2006-08-15 19:48 (diff) 63.164.145.198 (anon) (/* Limitations of Gödel's theorems */)
• 2006-08-15 17:22 (diff) (minor) Sopoforic (/* Books */)
• 2006-08-09 16:21 (diff) 209.129.85.4 (anon) (/* First incompleteness theorem */)
• 2006-08-08 00:43 (diff) Renosecond (/* Examples of undecidable statements */)
• 2006-08-06 05:12 (diff) 71.204.151.66 (anon) (/* Limitations of Gödel's theorems */)
• 2006-08-03 11:54 (diff) 202.36.179.65 (anon) (/* Books */ reformat)
• 2006-08-03 11:46 (diff) 202.36.179.65 (anon) (/* Scientific articles */ reformat)
• 2006-07-30 11:19 (diff) Clickheretologin (/* First incompleteness theorem */)
• 2006-07-27 00:10 (diff) 64.231.251.94 (anon) (/* Meaning of Gödel's theorems */)
• 2006-07-25 23:55 (diff) Giftlite (/* Examples of undecidable statements */ -link)
• 2006-07-25 09:47 (diff) JRSpriggs (/* See also */)
• 2006-07-24 15:14 (diff) 84.40.138.111 (anon) (/* External links */)
• 2006-07-24 02:18 (diff) CBM (/* Misconceptions about Gödel's theorems */ change to limitations; make shorter and (hopefully) less misleading. see talk)
• 2006-07-20 19:11 (diff) Qwertyus
• 2006-07-19 20:54 (diff) SpuriousQ (/* Minds and machines */ rm confusing/redundant sentence)
• 2006-07-18 12:06 (diff) (minor) Lousyd
• 2006-07-16 15:07 (diff) (minor) CBM (/* Examples of undecidable statements */ edit link)
• 2006-07-10 05:16 (diff) (minor) YurikBot (robot Adding: en:ka:გოდელის არასრულობის თეორემები)
• 2006-07-09 14:32 (diff) 67.160.85.110 (anon) (/* External links */)
• 2006-07-08 08:20 (diff) (minor) Joegoodbud (/* Minds and machines */)
• 2006-07-06 20:07 (diff) Lethe (revert: Gödel actually proved these celebrated theorems)
• 2006-07-06 20:01 (diff) (minor) Anetode (lead phrasing)
• 2006-06-30 15:19 (diff) Francis Davey ("theory contains" is grammatically correct English, there is no subjunctive here)
• 2006-06-30 10:42 (diff) (minor) Wfructose (correcting subjunctive Schreiber ✉ 16:18, 23. Feb. 2012 (CET))
• 2006-06-24 18:15 (diff) 131.130.1.135 (anon) (/* First incompleteness theorem */ consistency in commas -- they are there for a reason, you see)
• 2006-06-20 20:39 (diff) 151.203.26.46 (anon) (/* Minds and machines */ grammar: "that" to "the")
• 2006-06-19 23:44 (diff) (minor) Lambiam (/* Examples of undecidable statements */ fix redlink)
• 2006-06-19 02:21 (diff) (minor) SaxTeacher (/* Examples of undecidable statements */)
• 2006-06-18 23:30 (diff) 129.15.107.132 (anon) (/* First incompleteness theorem */)
• 2006-06-17 15:58 (diff) (minor) Mets501 (clean up using AWB)
• 2006-06-15 22:40 (diff) (minor) Qwertyus (/* First incompleteness theorem */)
• 2006-06-15 11:21 (diff) The Anome (/* External links */ en:Category:Epistemology)
• 2006-06-11 06:34 (diff) (minor) Marudubshinki (Robot: converting/fixing HTML)
• 2006-06-05 11:58 (diff) (minor) Kostmo (/* Minds and machines */ -- made into a subsection of "Implications and Discussion")
• 2006-06-02 06:42 (diff) 203.199.80.68 (anon)
• 2006-06-02 06:42 (diff) 203.199.80.68 (anon)
• 2006-05-23 08:20 (diff) (minor) Mandelum (/* See also */ GEB add, no discription yet)
• 2006-05-21 23:01 (diff) Paul August (/* See also */ This article has nothing to do with en:temporal logic)
• 2006-05-21 22:38 (diff) (minor) Pce3@ij.net (/* See also */)
• 2006-05-18 03:08 (diff) (minor) Kwertii (/* Gödel's Theorem */ link Principia mathematica)
• 2006-05-14 22:44 (diff) Trovatore (rvv)
• 2006-05-14 22:42 (diff) 83.135.51.53 (anon)
• 2006-05-14 22:41 (diff) Trovatore (rvv)
• 2006-05-14 22:40 (diff) 83.135.51.53 (anon)
• 2006-05-14 22:34 (diff) Trovatore (rv unexplained removal of interlang links to Turkish and Thai articles)
• 2006-05-14 22:30 (diff) 83.135.51.53 (anon)
• 2006-05-13 04:51 (diff) RoyArne (/* Scientific articles */)
• 2006-05-13 04:50 (diff) RoyArne (/* Scientific articles */)
• 2006-05-04 01:02 (diff) Trovatore (rv)
• 2006-05-03 23:29 (diff) 209.216.92.232 (anon)
• 2006-05-03 10:07 (diff) Aleph4 (revert. Gödel's theorem has nothing to to with discrete or continuous time. truth of arithmetical sentences does not change with time.)
• 2006-05-03 09:03 (diff) 209.216.92.232 (anon)
• 2006-05-01 23:48 (diff) Paul August (revert apparent copyvio)
• 2006-05-01 23:28 (diff) 209.216.92.232 (anon)
• 2006-04-25 20:11 (diff) 84.42.176.62 (anon) (/* External links */ +cs)
• 2006-04-24 09:52 (diff) (minor) Tosha (/* External links */)
• 2006-04-24 09:51 (diff) (minor) Tosha (/* External links */)
• 2006-04-23 18:49 (diff) (minor) Bkell (/* Gödel's Theorem */ non-breaking spaces)
• 2006-04-23 11:37 (diff) 161.200.92.241 (anon)
• 2006-04-21 14:58 (diff) (minor) Dmharvey (rv speculation about crack dealers)
• 2006-04-21 14:55 (diff) 65.117.145.6 (anon) (/* Misconceptions about Gödel's theorems */)
• 2006-04-15 05:53 (diff) Keenan Pepper (If you don't like it, improve it yourself. That's how Wikipedia works.)
• 2006-04-15 05:03 (diff) 87.69.53.57 (anon) (/* Proof sketch for the first theorem */)
• 2006-04-06 13:22 (diff) ASKingquestions (Cleaned up the rough proof)
• 2006-04-03 05:39 (diff) 69.61.72.80 (anon) (/* Second incompleteness theorem */ added omitted word)
• 2006-03-22 07:14 (diff) 138.16.7.239 (anon) (/* Meaning of Gödel's theorems */)
• 2006-03-22 06:54 (diff) (minor) YurikBot (robot Adding: en:sk:Gödelova veta o neúplnosti Modifying: en:nl:Onvolledigheidsstellingen van Gödel)
• 2006-03-21 19:11 (diff) (minor) Elroch (Changed two instances of "recursively enumerable" to the more evocative "computably enumerable" to avoid using two terms for same concept in the article)
• 2006-03-20 21:25 (diff) R.e.b. (/* Examples of undecidable statements */ links)
• 2006-03-17 05:17 (diff) R.e.b. (revert to last version by Keenan Pepper)
• 2006-03-17 01:59 (diff) Diegueins
• 2006-03-17 01:55 (diff) Diegueins
• 2006-03-12 19:27 (diff) (minor) Keenan Pepper (/* Meaning of Gödel's theorems */ use wiki syntax instead of html tag)
• 2006-03-12 18:22 (diff) (minor) MathMartin (/* Meaning of Gödel's theorems */ typo, link)
• 2006-03-12 18:08 (diff) Trovatore (/* Meaning of Gödel's theorems */ reword two paragraphs to address Dmharvey's concern (see talk))
• 2006-03-12 17:39 (diff) Trovatore (/* Meaning of Gödel's theorems */ one minor fix an a paragraph that has other problems)
• 2006-03-10 23:50 (diff) Trovatore (no, he didn't "go on to prove" that; it's inherent in the statement of the theorem)
• 2006-03-10 21:19 (diff) 88.104.57.185 (anon) (/* Gödel's Theorem */)
• 2006-02-28 19:37 (diff) Trovatore (fx dbl rd)
• 2006-02-28 19:34 (diff) (minor) Trovatore (moved en:Gödel's incompleteness theorem to en:Gödel's incompleteness theorems: The article is about two theorems.)
• 2006-02-20 18:56 (diff) 216.165.49.100 (anon) (Changed 'utilize' to the less pretentious 'use.')
• 2006-02-15 04:34 (diff) Trovatore (/* Second incompleteness theorem */ lk en:Gentzen's consistency proof)
• 2006-02-15 04:30 (diff) Trovatore (/* Gentzen's theorem */ remove whole section; now at en:Gentzen's consistency proof)
• 2006-02-15 04:01 (diff) (minor) Trovatore (/* First incompleteness theorem */ forgot the pipe)
• 2006-02-15 04:00 (diff) Trovatore (/* First incompleteness theorem */ make c.e. statement more precise)
• 2006-02-15 03:59 (diff) Trovatore (/* First incompleteness theorem */ remove convention of closure under logical consequence. Add note about theory being c.e.)
• 2006-02-14 16:43 (diff) 160.45.24.166 (anon) (/* Gödel's Theorem */)
• 2006-02-14 05:58 (diff) (minor) Dogcow (/* Gödel's Theorem */ yeah, it's a redlink, but it'd be nice to know wtf omega consistency is (hint hint).)
• 2006-02-11 17:34 (diff) 195.56.16.55 (anon) (/* External links */)
• 2006-02-11 17:24 (diff) 195.56.16.55 (anon) (/* Books */)
• 2006-02-11 17:22 (diff) 195.56.16.55 (anon)
• 2006-02-09 14:41 (diff) (minor) SimonP ({{GA}} belongs on talk page)
• 2006-02-08 22:28 (diff) John wesley
• 2006-02-05 23:26 (diff) 24.27.11.184 (anon) (/* Proof sketch for the first theorem */)
• 2006-02-03 02:18 (diff) 128.6.205.106 (anon) (/* External links */)
• 2006-02-02 14:39 (diff) (minor) Chobot (bot) (robot Modifying: he)
• 2006-02-01 19:25 (diff) 129.130.10.129 (anon) (/* Meaning of Gödel's theorems */)
• 2006-02-01 15:14 (diff) (minor) Trifon Triantafillidis (/* External links */ Link removed)
• 2006-02-01 10:53 (diff) 82.153.99.24 (anon) (/* External links */)
• 2006-02-01 08:40 (diff) 192.154.64.244 (anon) (/* Second incompleteness theorem */)
• 2006-02-01 08:38 (diff) 192.154.64.244 (anon) (/* Second incompleteness theorem */)
• 2006-01-24 23:45 (diff) 83.67.89.248 (anon) (/* Minds and machines */)
• 2006-01-24 20:01 (diff) Trovatore (null edit -- previous edit summary incorrect. Entscheidungsproblem is about deciding validities of FOL, not arithmetical statements.)
• 2006-01-24 19:58 (diff) 129.173.65.181 (anon) (The entscheidungsproblem asks for a method for mechanically deciding statements of arithmetic. Of course, Turing doesn't give one- he shows that none exists!)
• 2006-01-16 20:48 (diff) Trovatore (Gödel did not use anything called "typographic number theory"; that sounds like a phrase invented by Hofstadter)
• 2006-01-16 18:07 (diff) Evildictaitor (/* Gödel's Theorem */)
• 2006-01-16 17:12 (diff) (minor) Trifon Triantafillidis (/* Meaning of Gödel's theorems */ Restating)
• 2006-01-16 16:39 (diff) Evildictaitor (axioms are not "discovered" - Gödel proved that the system is inherently inconsistent.)
• 2006-01-13 22:14 (diff) Keenan Pepper (rm redundancy and unhelpful example)
• 2006-01-13 22:11 (diff) (minor) Keenan Pepper (Please use correct wiki markup!)
• 2006-01-13 19:18 (diff) 88.104.48.8 (anon) (/* First incompleteness theorem */)
• 2006-01-13 19:17 (diff) 88.104.48.8 (anon) (/* Misconceptions about Gödel's theorems */)
• 2006-01-10 01:00 (diff) 69.249.40.134 (anon) (/* Minds and machines */)
• 2006-01-10 00:58 (diff) 69.249.40.134 (anon) (/* Minds and machines */)
• 2006-01-07 00:43 (diff) Irving Anellis (/* Scientific articles */)
• 2006-01-07 00:43 (diff) (minor) Irving Anellis (/* Scientific articles */)
• 2006-01-07 00:40 (diff) (minor) Irving Anellis (/* Scientific articles */)
• 2006-01-06 15:27 (diff) 202.68.145.230 (anon) (/* Examples of undecidable statements */ simplified the syntax)
• 2006-01-05 22:48 (diff) Paul August (Trov: Personally I like this style of footnotes better, feel free to change it back if you like what was there before better.)
• 2006-01-05 22:47 (diff) (minor) Bevo (wikify)
• 2006-01-05 22:45 (diff) Paul August (Trov: Personally I like this style of footnotes better, feel free to change it back if you like what was there before better.)
• 2006-01-05 22:27 (diff) (minor) Trovatore (/* Footnotes */ I guess footnotes are supposed to be introduced with # rather than *)
• 2006-01-05 22:13 (diff) Trovatore (/* Footnotes */ whoops--order of quantifiers)
• 2006-01-05 22:08 (diff) Trovatore (/* Footnotes */ explain G_T)
• 2006-01-05 22:07 (diff) (minor) Trovatore (/* Footnotes */ italics again --3rd time charm?)
• 2006-01-05 22:04 (diff) (minor) Trovatore (/* Footnotes */ fx italics again)
• 2006-01-05 22:04 (diff) (minor) Trovatore (/* Footnotes */ fix italics)
• 2006-01-05 22:02 (diff) Trovatore (footnote about truth of Gödel sentence)
• 2006-01-03 19:34 (diff) Pakaran (/* Examples of undecidable statements */)
• 2006-01-01 20:35 (diff) 85.210.29.77 (anon) (fixed vandalism)
• 2006-01-01 19:49 (diff) 85.210.29.77 (anon)
• 2005-12-31 06:15 (diff) Trovatore (Nope, "valid" is about arguments. The Goedel sentence of a consistent theory is a proposition, not an argument, and it's true.)
• 2005-12-31 06:13 (diff) Gazpacho (clarify "true")
• 2005-12-31 06:07 (diff) Trovatore (rv anon -- the Goedel sentence of a consistent theory is true, though the theory doesn't prove it.)
• 2005-12-31 06:05 (diff) 67.70.46.147 (anon) (/* First incompleteness theorem */ Statements not provable from the theory should not be treated as a priori either true or false -- they're simply not decided by the theory.)
• 2005-12-26 10:43 (diff) (minor) GrinBot (bot) (robot Modifying: es)
• 2005-12-17 23:14 (diff) (minor) Khalid hassani (/* First incompleteness theorem */ wikify)
• 2005-12-14 15:36 (diff) RCSB (/* Books */)
• 2005-12-14 15:26 (diff) RCSB (/* First incompleteness theorem */ removed POV and user signature from article text)
• 2005-12-14 10:44 (diff) Biedermann
• 2005-12-12 22:10 (diff) 65.122.111.67 (anon) (/* First incompleteness theorem */)
• 2005-12-10 16:50 (diff) (minor) Bergsten (/* Second incompleteness theorem */ Bad link repair (You can help!))
• 2005-12-10 14:21 (diff) Revived (revert to previous version.)
• 2005-12-10 12:26 (diff) Biedermann (/* First incompleteness theorem */)
• 2005-12-04 07:22 (diff) (minor) Antandrus (rv--provability, not probability)
• 2005-12-04 07:19 (diff) 201.141.62.200 (anon) (/* Second incompleteness theorem */)
• 2005-11-28 16:38 (diff) 85.157.107.170 (anon)
• 2005-11-24 14:51 (diff) (minor) Chobot (bot) (robot Adding: ko)
• 2005-11-24 07:03 (diff) VKokielov (/* First incompleteness theorem */)
• 2005-11-23 10:40 (diff) Jdthood (Revert unnecessary change. Read the text carefully!)
• 2005-11-22 20:34 (diff) (minor) KSmrq (/* First incompleteness theorem */ typo)
• 2005-11-22 00:18 (diff) 161.24.74.27 (anon) (/* First incompleteness theorem */)
• 2005-11-21 18:27 (diff) Jdthood (/* First incompleteness theorem */)
• 2005-11-19 08:38 (diff) (minor) GrinBot (bot) (robot Adding: pl)
• 2005-11-14 22:24 (diff) SpuriousQ (there is already a proof sketch in a later section)
• 2005-11-14 18:54 (diff) Jdthood (/* Gentzen's theorem */)
• 2005-11-14 18:46 (diff) Jdthood (/* First incompleteness theorem */)
• 2005-11-14 18:43 (diff) Jdthood (/* First incompleteness theorem */)
• 2005-11-14 18:34 (diff) Jdthood (/* First incompleteness theorem */)
• 2005-11-14 18:28 (diff) Jdthood (/* First incompleteness theorem */)
• 2005-11-14 17:52 (diff) Jdthood (/* First incompleteness theorem */)
• 2005-11-14 17:49 (diff) Jdthood (/* First incompleteness theorem */)
• 2005-11-14 17:22 (diff) 130.161.177.118 (anon) (/* Second incompleteness theorem */)
• 2005-11-14 11:42 (diff) Rasmus Faber (rv. See talk (en:WP:NOR))
• 2005-11-14 11:19 (diff) Biedermann (/* Proof sketch for the first theorem */)
• 2005-11-14 11:15 (diff) Biedermann
• 2005-11-14 11:07 (diff) Rasmus Faber (rv inline comment)
• 2005-11-14 11:06 (diff) Biedermann
• 2005-11-14 11:00 (diff) Biedermann
• 2005-11-12 19:49 (diff) Trovatore (/* Misconceptions about Gödel's theorems */ Lucas' argument is treated elsewhere in article. It's POV to say it's "not at all correct".)
• 2005-11-12 00:45 (diff) Trovatore (rv)
• 2005-11-11 23:58 (diff) 198.208.159.17 (anon) (/* Second incompleteness theorem */)
• 2005-11-11 23:49 (diff) 198.208.159.17 (anon) (/* First incompleteness theorem */)
• 2005-11-11 20:48 (diff) 130.161.177.122 (anon) (/* First incompleteness theorem */)
• 2005-11-11 20:26 (diff) 130.161.177.122 (anon) (/* First incompleteness theorem */)
• 2005-11-11 19:25 (diff) 130.161.177.122 (anon) (/* First incompleteness theorem */)
• 2005-11-11 19:24 (diff) 130.161.177.122 (anon) (/* First incompleteness theorem */)
• 2005-11-11 19:24 (diff) 130.161.177.122 (anon) (/* First incompleteness theorem */)
• 2005-11-11 19:15 (diff) 130.161.177.122 (anon) (/* Meaning of Gödel's theorems */)
• 2005-11-11 06:47 (diff) Trovatore (rv)
• 2005-11-11 06:31 (diff) 69.180.16.124 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 22:35 (diff) Trovatore (/* Examples of undecidable statements */ Don't confuse with absolute undecidability)
• 2005-11-10 22:30 (diff) Trovatore (/* Examples of undecidable statements */ ibid)
• 2005-11-10 22:29 (diff) Trovatore (/* Examples of undecidable statements */ in some specified deductive system)
• 2005-11-10 22:21 (diff) Trovatore (/* Examples of undecidable statements */ copyedit, make hypotheses of independence results more explicit)
• 2005-11-10 22:14 (diff) (minor) Trovatore (/* Meaning of Gödel's theorems */ An -> a)
• 2005-11-10 20:04 (diff) 130.161.177.99 (anon) (/* Examples of undecidable statements */)
• 2005-11-10 19:58 (diff) 130.161.177.99 (anon) (/* Examples of undecidable statements */)
• 2005-11-10 19:56 (diff) 130.161.177.99 (anon) (/* Meaning of Gödel's theorems */)
• 2005-11-10 19:55 (diff) 130.161.177.99 (anon) (/* Meaning of Gödel's theorems */)
• 2005-11-10 19:41 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:39 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:32 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:29 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:26 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:25 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:24 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 19:23 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:22 (diff) 130.161.177.99 (anon) (/* Second incompleteness theorem */)
• 2005-11-10 19:20 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 19:15 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 19:09 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 19:08 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 19:07 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 19:01 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 18:59 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 18:57 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 18:52 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 18:49 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 18:47 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-10 18:43 (diff) 130.161.177.99 (anon) (/* First incompleteness theorem */)
• 2005-11-09 01:43 (diff) 70.57.196.186 (anon) (/* Minds and machines */)
• 2005-11-09 01:40 (diff) 70.57.196.186 (anon) (/* Discussion and implications */)
• 2005-11-08 02:28 (diff) SpuriousQ (rv, please see en:WP:NOR)
• 2005-11-07 12:50 (diff) Biedermann (/* Proof sketch for the first theorem */)
• 2005-11-07 12:48 (diff) Biedermann (/* Proof sketch for the first theorem */)
• 2005-11-07 12:35 (diff) Biedermann (/* Proof sketch for the first theorem */)
• 2005-11-07 12:29 (diff) Biedermann (/* Proof sketch for the first theorem */)
• 2005-11-06 19:45 (diff) (minor) BeteNoir (Refined categorization)
• 2005-10-31 21:08 (diff) (minor) Gdm (sp)
• 2005-10-29 11:31 (diff) 128.232.246.146 (anon) (/* External web pages */)
• 2005-10-29 11:30 (diff) 128.232.246.146 (anon) (/* Books */)
• 2005-10-29 11:25 (diff) 128.232.246.146 (anon) (/* External web pages */)
• 2005-10-29 11:24 (diff) 128.232.246.146 (anon) (/* External web pages */)
• 2005-10-13 12:20 (diff) 81.197.64.82 (anon) (/* First incompleteness theorem */ Fixed the statement of the theorem. We can construct the Gödel sentence regardless of the consistency of the theory.)
• 2005-10-09 03:10 (diff) 68.184.203.254 (anon) (trough -> through)
• 2005-10-04 07:51 (diff) 195.74.11.130 (anon) (/* Second incompleteness theorem */ Made a few technical corrections, e.g. the missing "or a logical axiom" in the definition of Con(T).)
• 2005-10-03 13:57 (diff) (minor) MathMartin (/* Gentzen's theorem */ link)
• 2005-10-01 22:04 (diff) SpuriousQ (rv , no original research en:WP:NOR)
• 2005-10-01 10:44 (diff) Biedermann (/* First incompleteness theorem */)
• 2005-09-30 06:57 (diff) (minor) Siroxo (less choppy wording, link)
• 2005-09-29 12:57 (diff) 195.74.11.130 (anon) (Fixed my fix of the statement of the first incompleteness theorem.)
• 2005-09-29 12:50 (diff) 195.74.11.130 (anon) (Corrected the statement of the theorem and restored "true". The usage of true is explained in the paragraph following the statement of the theorem.)
• 2005-09-25 14:21 (diff) (minor) YurikBot (robot Modifying: bg, he, hu, ja, ru, uk, zh)
• 2005-09-25 09:57 (diff) Docbug (Removed space at start of paragraphs that were causing spurious block-quotes (note that this didn't show up on the diff))
• 2005-09-24 16:17 (diff) Trovatore (Now change Gödel)
• 2005-09-24 16:13 (diff) Trovatore (rv curpsbot-unicodify)
• 2005-09-21 20:24 (diff) (minor) Curpsbot-unicodify (1 &#<num>; → Unicode • 47 &<name>; → Unicode • 1 link(s): [_ ]+ → [ ])
• 2005-09-21 09:00 (diff) (minor) YurikBot (robot Adding: gl)
• 2005-09-20 21:24 (diff) 67.70.47.253 (anon) (removed nonessential use of the word "true" in a context in which it was not defined)
• 2005-09-15 20:27 (diff) 164.113.102.76 (anon) (/* See also */)
• 2005-09-14 12:39 (diff) (minor) Timwi (/* First incompleteness theorem */ bit of added clarity I think)
• 2005-09-07 18:44 (diff) SpuriousQ (rv, statement is correct as is)
• 2005-09-07 13:26 (diff) 66.31.90.30 (anon) (/* First incompleteness theorem */)
• 2005-09-04 00:50 (diff) (minor) GrinBot (bot) (robot Adding: hu Modifying: io, it)
• 2005-08-30 23:32 (diff) 69.193.231.73 (anon)
• 2005-08-29 18:00 (diff) OwenX (/* Gentzen's theorem */ typo)
• 2005-08-29 17:59 (diff) OwenX (/* Gentzen's theorem */ fix power-of-power problem)
• 2005-08-27 22:08 (diff) (minor) SpuriousQ (wikify, say 2nd thm consequence of 1st)
• 2005-08-26 06:44 (diff) SpuriousQ (/* Minds and machines */ rewording some things)
• 2005-08-26 06:17 (diff) SpuriousQ (/* Second incompleteness theorem */ more wiki and friendly)
• 2005-08-26 05:55 (diff) SpuriousQ (/* First incompleteness theorem */ tried to make more user friendly)
• 2005-08-26 05:40 (diff) SpuriousQ (/* Second theorem */ explicit statement of the theorem)
• 2005-08-19 05:37 (diff) (minor) Sundar (Reverted edits by 69.115.124.23 to last version by Sam Hocevar)
• 2005-08-19 05:36 (diff) 69.115.124.23 (anon)
• 2005-08-14 12:21 (diff) (minor) Sam Hocevar (/* Second theorem */ spelling)
• 2005-08-13 21:27 (diff) Sigfpe (/* Books */)
• 2005-08-09 11:45 (diff) 131.174.32.252 (anon) (using named entities.)
• 2005-08-07 02:31 (diff) 208.191.226.210 (anon)
• 2005-07-27 20:41 (diff) 82.153.208.107 (anon) (/* Gentzen's theorem */)
• 2005-07-27 16:16 (diff) (minor) Doradus (/* Meaning of Gödel's theorems */ Make parenthesized sentence into a bona fide sentence; simplify link; remove nested parentheses)
• 2005-07-26 14:15 (diff) (minor) GabrielF (rv vandalism)
• 2005-07-26 14:14 (diff) 65.167.251.42 (anon) (/* First incompleteness theorem */)
• 2005-07-26 14:09 (diff) 65.167.251.42 (anon) (/* Second theorem */)
• 2005-07-26 02:41 (diff) (minor) SpuriousQ (/* Examples of undecidable statements */ fixed another kurskal)
• 2005-07-25 22:56 (diff) The Anome (/* Examples of undecidable statements */ "Kurskal's" is a typo)
• 2005-07-25 22:54 (diff) The Anome (/* See also */ link fix)
• 2005-07-25 22:53 (diff) The Anome (fmt fix, again)
• 2005-07-25 22:51 (diff) The Anome (fmt)
• 2005-07-25 21:53 (diff) 201.235.86.104 (anon) (/* Gentzen's theorem */)
• 2005-07-20 06:58 (diff) (minor) YurikBot (robot Modifying: tr)
• 2005-07-15 14:54 (diff) (minor) Aatu (Added the qualifier "constructive" before ordinal to the explanation of ordinal analysis)
• 2005-07-15 14:45 (diff) (minor) Aatu (Removed the unnecessary "that" in the second provability condition)
• 2005-07-11 12:53 (diff) (minor) Aatu (/* Discussion and implications */)
• 2005-07-11 12:49 (diff) Aatu (The "alternative view" is just pure sillyness. A statement is undecidable in a theory regardless of whether one interpretes it to be about Gödel numbers of formulas or not.)
• 2005-07-11 12:46 (diff) Aatu (Removed silly gibberish about "finitistic induction" and such like. As a good look at any decent textbook will tell you no such thngs are relevant to Gödel's theorems.)
• 2005-07-10 13:21 (diff) 82.69.39.138 (anon)
• 2005-07-10 13:06 (diff) 82.69.39.138 (anon)
• 2005-07-08 23:08 (diff) 205.201.32.6 (anon) (/* Gentzen's theorem */ minor typo)
• 2005-07-07 13:26 (diff) (minor) Aatu (Added the requirement of consistency in the explanation abotu the connection between the two notions of undecidability)
• 2005-07-07 13:21 (diff) (minor) Aatu (Added the word "natural" prior the word "number" in the definition of omega-consistency)
• 2005-07-07 13:17 (diff) Aatu (Clarified the distinction between two senses of undecidability)
• 2005-07-07 13:01 (diff) Aatu (Removed confusing and partially inaccurate statements.and replaced them with better explanations)
• 2005-07-05 22:24 (diff) Paul August (/* Examples of undecidable statements */ copyedit)
• 2005-07-05 21:36 (diff) 209.68.147.85 (anon) (/* Examples of undecidable statements */ word problem)
• 2005-07-05 16:26 (diff) 72.1.133.129 (anon) (Disambiguated the [Consistency] link.)
• 2005-07-04 05:46 (diff) 24.46.225.163 (anon)
• 2005-07-04 05:02 (diff) 128.107.253.40 (anon) (/* Second theorem */)
• 2005-06-30 20:40 (diff) SpuriousQ (moved mind/machine content into own section)
• 2005-06-30 01:54 (diff) Ancheta Wis (/* Scientific articles */ (received 17 Nov 1930, published 1931))
• 2005-06-28 19:53 (diff) 209.222.242.194 (anon) (/* Gentzen's theorem */)
• 2005-06-24 06:23 (diff) SpuriousQ (/* First incompleteness theorem */ spelling, some clarification)
• 2005-06-23 21:01 (diff) 81.197.78.34 (anon) (/* Misconceptions about Gödel's theorems */)
• 2005-06-23 21:00 (diff) 81.197.78.34 (anon) (/* First incompleteness theorem */)
• 2005-06-23 20:07 (diff) 208.180.232.38 (anon) (/* First incompleteness theorem */ Added a couple periods. Changed some occurrences of "it's" to "it is". Deleted a redundant "or not".)
• 2005-06-23 17:35 (diff) (minor) Magidin (Corrected typo (basicly -> basically))
• 2005-06-23 16:54 (diff) 63.117.182.97 (anon) (Fixed typo)
• 2005-06-23 13:22 (diff) 195.74.11.130 (anon) (/* Gentzen's theorem */)
• 2005-06-23 13:13 (diff) 195.74.11.130 (anon) (/* Second theorem */)
• 2005-06-23 06:34 (diff) SpuriousQ (/* Discussion and implications */ Martin Davis's response to Penrose)
• 2005-06-22 13:05 (diff) 195.74.11.130 (anon) (/* Gentzen's theorem */)
• 2005-06-22 12:44 (diff) 195.74.11.130 (anon) (/* Second theorem */)
• 2005-06-22 12:15 (diff) 195.74.11.130 (anon) (/* First theorem */)
• 2005-06-20 18:38 (diff) (minor) SpuriousQ (/* Discussion and implications */ typo, more clarity)
• 2005-06-20 06:18 (diff) (minor) Tim Starling (/* Gentzen's theorem */ missing word)
• 2005-06-20 00:39 (diff) Mathbot (bot) (Robot assisted spelling.)
• 2005-06-19 12:01 (diff) (minor) Neilc
• 2005-06-18 08:52 (diff) (minor) SpuriousQ (another typo)
• 2005-06-18 08:49 (diff) (minor) SpuriousQ (typos)
• 2005-06-18 08:47 (diff) SpuriousQ (added more about minds and machines)
• 2005-06-17 08:11 (diff) SpuriousQ (Gibbs lecture)
• 2005-06-16 22:01 (diff) Chalst (/* See also */)
• 2005-06-16 14:29 (diff) Paul August (Removed content which makes no sense to me (see talk))
• 2005-06-16 08:18 (diff) Rcaetano (removing "real world applications")
• 2005-06-15 19:13 (diff) 18.187.0.48 (anon)
• 2005-06-09 06:15 (diff) 140.247.149.143 (anon) (/* Meaning of Gödel's theorems */)
• 2005-06-09 04:38 (diff) (minor) Doradus (Move misplaced paragraph down into Gentzen's theorem section)
• 2005-06-06 14:00 (diff) (minor) Graham87 (/* First theorem */ fixed typo)
• 2005-06-04 22:20 (diff) 62.205.124.211 (anon) (/* Real World Applications of Godel's Ideas */)
• 2005-06-03 22:13 (diff) 70.57.69.159 (anon)
• 2005-05-29 10:54 (diff) Celendin
• 2005-05-29 10:53 (diff) Celendin (/* External web pages */)
• 2005-05-29 10:52 (diff) Celendin
• 2005-05-29 10:51 (diff) Celendin (/* Proof sketch for the first theorem */)
• 2005-05-16 21:38 (diff) 85.206.195.42 (anon) (/* Meaning of Gödel's theorems */)
• 2005-05-08 22:21 (diff) 209.90.162.56 (anon) (io)
• 2005-05-07 04:41 (diff) CesarB (breaking up way overlong lead section; changing self-referential section (amusingly containing a link to en:self-reference) into the see also section)
• 2005-05-07 03:11 (diff) Mathbot (bot) ("Made section headings conform to the en:Wikipedia:Manual of Style#Headings. This is a semi-automatic update")
• 2005-05-06 02:52 (diff) 24.30.83.247 (anon)
• 2005-05-03 00:53 (diff) (minor) Cal 1234 (weird typo)
• 2005-05-02 19:23 (diff) 82.69.39.138 (anon)
• 2005-05-02 12:23 (diff) (minor) Cal 1234 (typo)
• 2005-05-02 12:14 (diff) Eric.dane
• 2005-05-02 12:10 (diff) Eric.dane (/* =Articles */)
• 2005-05-02 12:09 (diff) Eric.dane (/* External links and references */)
• 2005-05-02 12:04 (diff) Eric.dane
• 2005-05-01 06:30 (diff) 68.174.84.177 (anon)
• 2005-04-30 10:09 (diff) (minor) FlaBot (bot) (warnfile Modifying:fr)
• 2005-04-28 20:32 (diff) (minor) Xelloss (italian link added)
• 2005-04-28 08:20 (diff) 67.170.104.188 (anon) (grammer)
• 2005-04-28 08:13 (diff) 67.170.104.188 (anon) (Fixed typo. (none->one))
• 2005-04-27 15:42 (diff) 82.69.39.138 (anon)
• 2005-04-27 14:51 (diff) 82.69.39.138 (anon)
• 2005-04-27 14:34 (diff) 82.69.39.138 (anon)
• 2005-04-21 13:13 (diff) (minor) Smyth
• 2005-04-20 21:31 (diff) 134.164.204.67 (anon) (/* Discussion and implications */)
• 2005-03-29 17:37 (diff) Oleg Alexandrov (rv vandalism)
• 2005-03-29 16:05 (diff) 210.212.228.8 (anon) (/* Proof sketch for the first theorem */)
• 2005-03-26 13:23 (diff) (minor) Rodrigo Rocha
• 2005-03-26 13:22 (diff) (minor) Rodrigo Rocha (adding portuguese version)
• 2005-03-25 13:24 (diff) 147.26.164.142 (anon) (/* Meaning of Gödel's theorems */)
• 2005-03-25 02:20 (diff) 129.82.63.123 (anon) (/* Misconceptions about Gödel's theorems */)
• 2005-03-12 20:38 (diff) WoodenTaco
• 2005-03-01 17:28 (diff) 163.1.159.21 (anon) (/* Meaning of Gödel's theorems */)
• 2005-03-01 17:25 (diff) 163.1.159.21 (anon) (/* Meaning of Gödel's theorems */)
• 2005-02-12 17:47 (diff) (minor) Oleg Alexandrov (downcasing)
• 2005-02-08 17:08 (diff) (minor) MIT Trekkie (/* Discussion and implications: */ copy-edit: rm colon)
• 2005-02-08 10:22 (diff) Александър (+bg:)
• 2005-02-04 06:47 (diff) (minor) Tosha (/* External links and references */ ru)
• 2005-02-03 06:35 (diff) 12.222.109.61 (anon) (add tr)
• 2005-01-30 15:00 (diff) (minor) Sysy (removing a colon to link an ISBN =))
• 2005-01-21 11:08 (diff) (minor) Asbestos (/* Discussion and implications: */ link)
• 2005-01-08 17:01 (diff) 145.97.222.38 (anon) (/* Proof sketch for the first theorem */)
• 2005-01-08 16:57 (diff) 145.97.222.38 (anon) (/* Discussion and implications: */)
• 2005-01-08 10:47 (diff) 81.174.153.158 (anon) (/* Discussion and implications */)
• 2005-01-06 16:58 (diff) 24.44.134.224 (anon) (/* Misconceptions about Gödel's theorems */)
• 2004-12-28 18:57 (diff) 212.152.233.165 (anon) (Added the real "point" to the simplification of Gödels 1st Theorem, namely, that the unprovable (and undisprovable) statement really is true.)
• 2004-12-19 04:48 (diff) (minor) HarmonicSphere (/* Discussion and implications */ spelling: "all encompassing" -> "all-encompassing")
• 2004-12-08 18:50 (diff) 68.114.234.52 (anon) (/* External links and references */)
• 2004-12-08 15:08 (diff) 65.78.24.96 (anon)
• 2004-12-06 20:16 (diff) (minor) TXlogic
• 2004-12-03 01:35 (diff) (minor) Chinju (/* Examples of undecidable statements */)
• 2004-12-01 11:39 (diff) 194.100.190.241 (anon)
• 2004-11-25 02:17 (diff) (minor) Jumbuck (bot) (robot Modifying:es)
• 2004-11-23 10:22 (diff) DG (copyedit :))
• 2004-11-22 20:33 (diff) (minor) Hu (spelling, copy edit.)
• 2004-11-22 06:14 (diff) Simplebrain
• 2004-11-21 20:43 (diff) Simplebrain
• 2004-11-21 19:47 (diff) (minor) Lightst (Removing duplicated link to Spanish article.)
• 2004-11-21 13:10 (diff) Joseaperez
• 2004-11-20 11:24 (diff) (minor) Lightst (Adding link to the article in Spanish)
• 2004-11-12 14:53 (diff) (minor) Mellum (/* Misconceptions about Gödel's theorems */ formatting)
• 2004-11-07 07:43 (diff) 84.57.79.215 (anon) (/* Meaning of Gödel's theorems */)
• 2004-10-26 15:33 (diff) (minor) Toytoy (/* Proof sketch for the first theorem */ en:bona fide)
• 2004-10-26 05:36 (diff) 24.148.162.189 (anon) (/* Meaning of Gödel's theorems */)
• 2004-10-26 05:35 (diff) 24.148.162.189 (anon) (/* Meaning of Gödel's theorems */)
• 2004-10-22 18:12 (diff) 145.254.156.61 (anon) (/* Meaning of Gödel's theorems */ minor edit)
• 2004-10-22 18:11 (diff) 145.254.156.61 (anon) (/* Examples of undecidable statements */ minor edit)
• 2004-10-21 13:03 (diff) 129.125.145.218 (anon) (/* Meaning of Gödel's theorems */ don't use "we")
• 2004-10-08 22:32 (diff) 163.1.159.104 (anon) ((please!))
• 2004-10-07 10:51 (diff) 81.58.29.90 (anon) (/* Discussion and implications */)
• 2004-10-06 04:19 (diff) (minor) Sundar (/* Misconceptions about Gödel's theorems */ rv 'can' or 'may'?)
• 2004-10-06 03:59 (diff) 210.100.217.180 (anon) (/* Misconceptions about Gödel's theorems */)
• 2004-09-24 22:12 (diff) 66.148.172.122 (anon) (Removed bad/uninformative/useless link.)
• 2004-09-22 10:24 (diff) (minor) Chalst (+cat)
• 2004-09-22 07:35 (diff) Chalst (/* Discussion and implications */ disambig Rosser)
• 2004-09-13 23:41 (diff) Michael Hardy (/* Examples of undecidable statements */)
• 2004-09-07 00:47 (diff) (minor) Siroxo (/* External links and references */ fixes)
• 2004-09-06 21:02 (diff) (minor) Guanabot (Guanaco - robot: changing Windows-1252 characters to HTML entities)
• 2004-08-29 07:24 (diff) (minor) Owen (fmt.)
• 2004-08-21 00:11 (diff) 82.42.16.116 (anon) (/* Discussion and implications */)
• 2004-08-21 00:10 (diff) 82.42.16.116 (anon) (/* Discussion and implications */)
• 2004-08-20 23:59 (diff) 82.42.16.116 (anon) (/* Discussion and implications */)
• 2004-08-20 23:56 (diff) 82.42.16.116 (anon) (/* Discussion and implications */)
• 2004-08-20 23:56 (diff) 82.42.16.116 (anon) (/* Discussion and implications */)
• 2004-08-20 23:47 (diff) 82.42.16.116 (anon) (/* Misconceptions about Gödel's theorems */)
• 2004-08-16 12:09 (diff) (minor) Suisui (fix ja)
• 2004-08-09 00:12 (diff) 218.24.206.79 (anon)
• 2004-08-02 17:58 (diff) (minor) Maksym Ye. (+uk)
• 2004-07-23 17:22 (diff) (minor) Mike Storm (/* Misconceptions about Gödel's theorems */ rewrote sentence to maintain NPOV)
• 2004-07-23 17:21 (diff) (minor) Mike Storm (/* Misconceptions about Gödel's theorems */ rewrote sentence to maintain NPOV)
• 2004-07-20 08:09 (diff) (minor) Bethenco
• 2004-07-17 22:08 (diff) 212.84.143.42 (anon)
• 2004-07-17 22:08 (diff) 212.84.143.42 (anon)
• 2004-07-14 09:38 (diff) Siroxo (+word problem, italicized statements of thms, improved wiki markup usage)
• 2004-07-12 22:47 (diff) (minor) 4pq1injbok (end in -> give rise to)
• 2004-07-05 15:06 (diff) (minor) Geoffroy (interwiki fr)
• 2004-06-17 15:53 (diff) (minor) C17GMaster (belive -> believe)
• 2004-06-15 17:04 (diff) 81.214.8.195 (anon)
• 2004-06-15 17:03 (diff) 81.214.8.195 (anon)
• 2004-06-15 17:03 (diff) 81.214.8.195 (anon)
• 2004-06-14 12:29 (diff) 144.134.98.66 (anon) (/* Discussion and implications */ layout fixes)
• 2004-06-14 12:24 (diff) 144.134.98.66 (anon) (/* Discussion and implications */ Addition of JR Lucas link)
• 2004-06-04 08:06 (diff) (minor) Siroxo (/* See also */ Added link to related thm (Lob's))
• 2004-06-01 22:49 (diff) (minor) Dysprosia (en:Category:Model theory)
• 2004-05-31 15:29 (diff) Lupin
• 2004-05-31 15:14 (diff) Lupin
• 2004-05-31 05:41 (diff) 206.116.225.223 (anon) (/* Examples of undecidable statements */)
• 2004-05-31 03:34 (diff) (minor) Siroxo (/* Meaning of Gödel's theorems */ Blow to Hilbert?)
• 2004-05-31 00:08 (diff) (minor) Dmytro (/* Misconceptions about Gödel's theorems */)
• 2004-05-29 02:11 (diff) 81.251.12.114 (anon) (entry added for refutation of Gödel's incompleteness theorem)
• 2004-05-27 22:50 (diff) 163.1.209.241 (anon)
• 2004-05-25 07:18 (diff) (minor) Charles Matthews (lk)
• 2004-05-06 02:16 (diff) Wikiwikifast (=See also=)
• 2004-04-12 14:52 (diff) Amoss (The halting problem is the archetypal example)
• 2004-04-11 03:34 (diff) (minor) Dcoetzee (Removed my own misleading edit)
• 2004-04-11 03:32 (diff) (minor) Dcoetzee (=Discussion and implications= Minor editing)
• 2004-04-11 03:22 (diff) (minor) Andris (=External links and references= corrected spelling)
• 2004-04-11 03:17 (diff) (minor) Dcoetzee (=Meaning of Gödel's theorems= ( -> ;)
• 2004-04-08 11:20 (diff) (minor) Gdr (Spelling of Gödel)
• 2004-03-28 10:34 (diff) 217.235.119.60 (anon)
• 2004-03-25 06:07 (diff) 61.242.218.122 (anon)
• 2004-03-25 03:34 (diff) 61.242.218.122 (anon)
• 2004-03-21 19:21 (diff) 219.88.177.50 (anon)
• 2004-03-21 19:14 (diff) 219.88.177.50 (anon)
• 2004-03-17 05:59 (diff) (minor) Bovlb (Reinsert word probably deleted in error)
• 2004-03-17 05:47 (diff) 66.93.38.80 (anon)
• 2004-03-14 17:21 (diff) (minor) Fropuff (delete repeated paragraph)
• 2004-03-14 06:30 (diff) Waltpohl (Being bold)
• 2004-03-11 16:48 (diff) 62.202.148.13 (anon)
• 2004-02-21 01:55 (diff) (minor) Camembert (no need for that capital R, i think)
• 2004-01-27 15:00 (diff) (minor) Reddi