[romaniv]

If you don't know how to count, you learn arithmetic from people who do. Nobody owes you a proof that it "objectively exists". Neither does denying it constitute a valid disproof of every theorem in existence. Such is the nature of abstract concepts.

[haberman]

> Nobody owes you a proof that it "objectively exists".

And I don't owe anybody belief in weak arguments.

> Neither does denying it constitute a valid disproof of every theorem in existence.

Thomas Aquinas also offered "proofs" of God's existence that few people outside the Catholic faith take very seriously. For example you can read what Bertrand Russell wrote about him. Other arguments that purport to have "proved" things about religion (and this argument only barely escapes being religious in nature) rarely stand up to rational scrutiny, IMO.

[lmm]

Nonsense. You teach someone arithmetic by showing them concrete instances where it applies, counting apples or sticks or so on. You demonstrate that the abstract thing exists because there's something the same about putting two apples and two more apples together or putting two stones and two more stones together, and by observing one you can learn something about the other.

[gambler]

"You teach someone arithmetic by showing them concrete instances where it applies [...]"

What do you suppose the article above is doing?

[lmm]

I don't think the article makes any claim to objectivity.