Re: Readings in (some of the) foundations of mathematics --- tree of knowledge
olcott <[email protected]>
| Newsgroups | sci.logic,comp.theory,sci.math,comp.ai.philosophy |
|---|---|
| Organization | A noiseless patient Spider |
| Message-ID | <[email protected]> |
On 6/27/2026 8:13 PM, dbush wrote: > On 6/27/2026 7:59 PM, olcott wrote: >> On 6/27/2026 6:33 PM, dbush wrote: >>> On 6/27/2026 7:27 PM, olcott wrote: >>>> On 6/27/2026 5:53 PM, dbush wrote: >>>>> On 6/27/2026 6:44 PM, olcott wrote: >>>>>> On 6/27/2026 5:33 PM, dbush wrote: >>>>>>> >>>>>>> So you're claiming the sentence "no number is equal to its >>>>>>> successor" in Q is "off topic". >>>>>>> >>>>>>> Rejected, as it is a semantically valid sentence in the language >>>>>>> of Q. >>>>>> >>>>>> If there is no finite sequence of inference steps >>>>>> between x and the axioms of Q then PTS stipulates >>>>>> that x is not semantically valid in Q. >>>>> >>>>> And since x = "no number is equal to its successor" is semantically >>>>> valid as per the definition of Q, PTS must be discarded as useless. >>>>> >>>> >>>> So you also have no idea what Stipulative definition is. >>>> >>>> A stipulative definition is a type of definition in which >>>> a new or currently existing term is given a new specific meaning >>>> >>>> https://en.wikipedia.org/wiki/Stipulative_definition >>> >>> Not allowed, as "semantically valid" is already defined, and "no >>> number is equal to its successor" meets that definition. >>> >> >> Proof Theoretic Semantics (PTS) supersedes and overrules this. > > Then PTS is discarded as useless because it rejects "no number is equal > to its successor". > PTS is just the same as when a word is undefined then it has no meaning. TCS says that if an English word has no defined meaning in English then we will just pull one from Chinese. -- 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).