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

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.

-- 
Mikko