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Godel's Incompleteness Theorems & the Laws of Thought

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#incompleteness
478
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Circular logic in the concept of Godel numbers

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#logic #incompleteness
146
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For any statement independent of $\mathsf{ZFC}$, can we prove it is independent of $\mathsf{ZFC}$?

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#logic #set-theory #axioms #incompleteness
116
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Relative completeness of first order arithmetic

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#logic #set-theory #computability #incompleteness
44
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Is PA complete when multiplication is bounded?

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#arithmetic #first-order-logic #incompleteness
368
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Why doesn't the incompleteness theorem answer the decision problem?

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#incompleteness #decision-problems
92
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To what extent does Goedel's 2nd incompleteness theorem extend?

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#first-order-logic #incompleteness
538
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While using the method of proof by contradiction, are we "assuming" consistency?

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#logic #proof-theory #peano-axioms #incompleteness
33
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Completeness for pure arithmetical sentences?

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#first-order-logic #incompleteness
373
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Is the axiom of induction required for proving the first Gödel's incompleteness theorem?

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#logic #first-order-logic #peano-axioms #incompleteness #second-order-logic
69
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Math's inconsistency: can we prove that some statements are False and only False?

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#incompleteness
58
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Closure of a theory under consistency

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#logic #soft-question #incompleteness
623
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Does infinity cause incompleteness in formal systems? Is a finite formal system complete?

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#set-theory #infinity #formal-languages #incompleteness #finitism
463
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What is the effective axiomatization in Godel's incompleteness theorem?

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#logic #incompleteness
116
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The use of soundness in the Kritchman-Raz proof and Berry's paradox

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#logic #computability #incompleteness #kolmogorov-complexity

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