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

On 09/07/2026 06:12, olcott wrote:
> 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.

A computer can process those axioms as programmed but it cannot
relate them to the real world because it is not aware of the
real world.

-- 
Mikko