@Benyam_Alem is harder to contradict than many might assume.
There's only one thing I know for absolute certain: I think, and therefore I am.
Some might quibble -- but who is "I" in that sentence.
Answer: it is whoever or whatever believes itself to be thinking.
BUT -- none of that can reliably contradict @Benyam_Ahem, regardless.
Why not? Well, I seem to be certain that I exist and think -- but how can I "prove" those things to anybody else? I'm confident that I can persuade (most) people of those things. But can I make them impossible to disbelieve, or prevent them from being subject to some conceivable alternative explanation? Nope.
I could be a machine, planted on Earth to resemble a human being. It's highly unlikely. But it's not impossible.
But what about the reflexive property A = A ?
It's actually an axiom, and provides one of the necessary traits for an equivalence relation.
But, except in the entirely conceptual Platonic World of Forms (which is not actually present anywhere in our physical universe), where can you find two, actual items that are genuinely identical to the smallest part?
The number 1 is merely conceptual -- you can't find "it" except in the mind.
The numeral 1, which merely represents the concept -- stands for the cardinality of all sets that possess the quality of "oneness" -- and is printed or otherwise created -- yet no pair of printed or otherwise readable numeral 1s will actually be identical down to each single subatomic particle.
What about "Earth is orbiting the sun?" Well, I certainly believe it is. But are we sure that "Earth" and "sun" are actually giant, tangible oblate spheroids moving in space? Well, can anybody prove (beyond all conceivable doubt) that they aren't an illusion and that this isn't the cosmic equivalent of a video game?
Sure, this almost certainly ISN'T some video game. We can certainly be persuaded that it isn't. But can we prove it beyond all possible doubt?
No, @Benyam_Alem is on to something. We rely on faith and the acceptance of approximation far more than we realize.
And that's fine. Much faith and much approximation is beneficial, even "good" in a conceptual sense. At least in the opinion of whoever or whatever is typing these words.
So, I'll just end with: well played, @Benyam_Alem !
@Benyam_Alem is harder to contradict than many might assume.
There's only one thing I know for absolute certain: I think, and therefore I am.
Some might quibble -- but who is "I" in that sentence.
Answer: it is whoever or whatever believes itself to be thinking.
BUT -- none of that can reliably contradict @Benyam_Ahem, regardless.
Why not? Well, I seem to be certain that I exist and think -- but how can I "prove" those things to anybody else? I'm confident that I can persuade (most) people of those things. But can I make them impossible to disbelieve, or prevent them from being subject to some conceivable alternative explanation? Nope.
I could be a machine, planted on Earth to resemble a human being. It's highly unlikely. But it's not impossible.
But what about the reflexive property A = A ?
It's actually an axiom, and provides one of the necessary traits for an equivalence relation.
But, except in the entirely conceptual Platonic World of Forms (which is not actually present anywhere in our physical universe), where can you find two, actual items that are genuinely identical to the smallest part?
The number 1 is merely conceptual -- you can't find "it" except in the mind.
The numeral 1, which merely represents the concept -- stands for the cardinality of all sets that possess the quality of "oneness" -- and is printed or otherwise created -- yet no pair of printed or otherwise readable numeral 1s will actually be identical down to each single subatomic particle.
What about "Earth is orbiting the sun?" Well, I certainly believe it is. But are we sure that "Earth" and "sun" are actually giant, tangible oblate spheroids moving in space? Well, can anybody prove (beyond all conceivable doubt) that they aren't an illusion and that this isn't the cosmic equivalent of a video game?
Sure, this almost certainly ISN'T some video game. We can certainly be persuaded that it isn't. But can we prove it beyond all possible doubt?
No, @Benyam_Alem is on to something. We rely on faith and the acceptance of approximation far more than we realize.
And that's fine. Much faith and much approximation is beneficial, even "good" in a conceptual sense. At least in the opinion of whoever or whatever is typing these words.
So, I'll just end with: well played, @Benyam_Alem !