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 7/6/2026 2:10 AM, Mikko wrote: > On 04/07/2026 16:29, olcott wrote: >> On 7/4/2026 2:22 AM, Mikko wrote: >>> On 03/07/2026 19:43, olcott wrote: >>>> On 7/3/2026 4:39 AM, Mikko wrote: >>>>> On 02/07/2026 17:45, olcott wrote: >>>>>> >>>>>> https://en.wikipedia.org/wiki/Stipulative_definition >>>>>> Cats are animals, if you disagree then you are necessarily incorrect. >>>>> >>>>> You may use "cats are animals" as a part of the defintion of "cat" >>>>> or of the definition of "animal" but not both. However, above you >>>>> have done neither, so you haven't excluded the possibility that >>>>> "cats are animals" is a statement about the real world. >>>> >>>> cats ⊂ animals >>>> animals ⊃ cats >>>> They prove each other, thus only one of them is >>>> an atomic fact. Atomic facts are facts that cannot >>>> be derived from other facts. >>>> >>>> In my actual system cats would inherit from animals >>>> in the knowledge ontology / simple type hierarchy. >>> >>> In that case the sentence "cats are animals" does not tell anyting >>> about the real world. >> >> It tells us exactly one thing. > > Which thing? If the meanings of the words are already known it does > not tell anything that is not obvious from those meanings. > "cats" ⊂ "animals" "animals" ⊃ "cats" Is to be construed as the first time that anyone has every seen those finite strings. We are defining the English meaning of words to a computer program that starts as a completely blank slate. The end result of defining every "atomic fact" of empirical general knowledge is that the computer has complete general knowledge of the world. -- 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).