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WVOQ #94 Willard Van Orman Quine - cleancut

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Author: h4ck3rm1k3

Tags: Orman Philosophy Quine Van Willard

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Quine.html - and �the clearer these terms are, the likelier it is that the truths couched in them will be obviously true, or derivable from obvious truths�.� BUT: This particular outcome is in fact denied us, however, since...

WVOQ #47 Willard Van Orman Quine - cleancut

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Author: h4ck3rm1k3

Tags: Orman Philosophy Quine Van Willard

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Quine.html - we could avoid asserting this axiom, and our development would be conservative. Page 10 10 consts ntou :: nat ⇒ Uaxioms ntou: inj ntou constdefs uton :: U ⇒ nat uton ≡ inv ntou 3.9 Falsifying Model from Failing Path We...

WVOQ #45 Willard Van Orman Quine - cleancut

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Author: h4ck3rm1k3

Tags: Orman Philosophy Quine Van Willard

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Quine.html - n) = (let fn = failing-path ns n in SOME fsucn. fsucn ∈ ns ∧ fst fsucn = Suc n ∧ (snd fsucn) ∈ set (subs (snd fn)) ∧ infinite (deriv (snd fsucn)) ∧ ¬ is-axiom (s-of-ns (snd fsucn))) If f is the failing path for...

WVOQ #44 Willard Van Orman Quine - cleancut

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Author: h4ck3rm1k3

Tags: Orman Philosophy Quine Van Willard

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Quine.html - provable. Alternatively, if s is not provable, we must exhibit a model where s is false. If s is not provable, then when we attempt to prove it using the rules of our system, we will not end up with a finite derivation. If...

WVOQ #38 Willard Van Orman Quine - cleancut

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Author: h4ck3rm1k3

Tags: Orman Philosophy Quine Van Willard

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Quine.html - depth of a node in the derivation tree, and aids inductive arguments. We also make an abstracting definition of a predicate to recognise a terminal sequent, that is, one that can be closed by an application of the rules Ax,...

WVOQ #26 Willard Van Orman Quine - cleancut

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Author: h4ck3rm1k3

Tags: Orman Philosophy Quine Van Willard

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Quine.html - in a model and extending this to formulas and sequents such that the extension respects standard Tarski semantics. For example, A ∧ B is true in a model iff A is true, and B is true. Looking at the rules, it is quite easy...