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

On 7/8/2026 2:35 AM, Mikko wrote:
> On 06/07/2026 16:51, olcott wrote:
>> 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.
> The computer does not know that there is a real world.
> It just does wbat it is made to do.
> 

As I have said many many dozens of times we encode
all of the "basic facts" of general knowledge both
empirical (the facts of the actual world) and analytical
knowledge into a finite set of axioms.

-- 
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).