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

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.

-- 
Mikko