Re: The simple essence of Proof Theoretic Semantics
olcott <[email protected]>
| Newsgroups | sci.logic,comp.theory,sci.math,comp.ai.philosophy |
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| Organization | A noiseless patient Spider |
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On 7/1/2026 9:03 PM, olcott wrote: > Q cannot do the ∀x without an infinite sequence of steps. So your phrasing is good: Q would need something like an infinite sequence of steps (or a single principle that summarizes them) to get the ∀x. Since formal proofs must be finite, and Q lacks the tool (induction) that would allow a finite proof of the infinite claim, the universal statement remains unprovable. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).