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Circularity in the argument that Gödel's incompleteness theorems undermine Hilbert's program

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#logic #formal-languages #incompleteness #formal-proofs #formal-systems
107
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How to prove the property of being a tautology is hereditary under the Rule of Substitution?

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#logic #propositional-calculus #formal-systems
47
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Meaning of Provable recursiveness

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#number-theory #first-order-logic #computability #peano-axioms #formal-systems
238
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Why Löwenheim–Skolem theorem asserts the non-existence of such predicates in 1st order logic

Published on
#model-theory #foundations #peano-axioms #formal-systems
91
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In the axiomatic treatment of natural numbers, can we define what a natural number is?

Published on
#axioms #peano-axioms #formal-systems
53
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Decoding Gödel's number inside Gödel's number

Published on
#logic #incompleteness #formal-systems
83
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prove this theorem $\vdash (\exists x_i (A\to B)\to (A\to \exists x_i B))$

Published on
#logic #predicate-logic #formal-systems
1k
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Difference between Hilbert's program and Russell & Whitehead's Principia Mathematica

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#logic #axioms #formal-systems
9.2k
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Regular Expression of alternative 0's and 1's?

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#formal-languages #regular-language #regular-expressions #formal-systems
108
Views

Strong logical system without principle of explosion

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#logic #peano-axioms #formal-systems
112
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Incompleteness of formal systems as opposed to completeness of a non-formal theory

Published on
#number-theory #incompleteness #formal-systems
308
Views

What do the ZFC axioms look like in terms of subset?

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#set-theory #axioms #formal-systems
44
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Logical systems and formal proof

Published on
#reference-request #formal-proofs #formal-systems
149
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Proving the rules of a complicated game are well defined

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#computer-science #recreational-mathematics #combinatorial-game-theory #formal-systems
198
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Is there a formal system which is generally accepted, and how is it called?

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#formal-systems

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