Re: Readings in (some of the) foundations of mathematics --- tree of knowledge

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.
A complete finite list of "atomic facts" of general
knowledge tells us everything that can be expressed
in language. This finite list also has all of the
kinds of relations between these facts.

-- 
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).