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Can we be sure proofs have no errors?

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#logic #philosophy #proof-theory
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Proving the distributive law with natural deduction

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#logic #proof-writing #proof-theory #natural-deduction #formal-proofs
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Does Gödel's incompleteness theorem invoke a Law of Excluded Middle contradiction?

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#logic #proof-theory #incompleteness #peano-axioms
95
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Assumptions necessary to justify the method of proof by contradiction.

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#logic #philosophy #proof-theory
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Why and how is logic related to set theory?

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#logic #soft-question #philosophy #proof-theory
89
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Prove $\Sigma \vdash \lnot(\phi \rightarrow \psi)$ iff $\Sigma \vdash \phi$ and $\Sigma \vdash \lnot \psi.$

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#logic #propositional-calculus #proof-theory #formal-proofs #hilbert-calculus
453
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Proving soundness property of a Hilbert system

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#proof-verification #logic #propositional-calculus #proof-theory #hilbert-calculus
658
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Does natural deduction require a non-empty set of premises?

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#logic #definition #propositional-calculus #proof-theory #natural-deduction
1k
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Is many sorted logic really a unifying logic?

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#logic #model-theory #proof-theory #type-theory #higher-order-logic
183
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How can any proof of Gödel's incompleteness theorem be accepted considering systems of mathematics themselves are incomplete?

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#logic #proof-theory #incompleteness
116
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Can meta-languages disagree over what an object language proves?

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#logic #proof-theory
130
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Do there exist true statements with only one proof?

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#logic #proof-theory
59
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Can a sequent be valid if the conclusion contains atoms that are not in the premise?

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#logic #proof-theory #formal-proofs
134
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Need help for a proof ( sequent calculus )

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#logic #propositional-calculus #proof-theory #formal-proofs #sequent-calculus
106
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Symbolic Logic Proof?

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#discrete-mathematics #logic #proof-explanation #proof-theory

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