[abrezas]

The concept of prime numbers and the prime numbers themselves is a different thing.

Unicorns don't exist but statements about them aren't meaningless. Fictionalism accepts the concept of mathematical entities but denies their existence in the real world.

[catnaroek]

> The concept of prime numbers and the prime numbers themselves is a different thing.

I'm okay with that, and haven't said anything suggesting otherwise. However, if you want to reject the existence of mathematical objects in the real world, you have to reject the existence of mathematical definitions too, because mathematical definitions are mathematical objects just like any other. So, if the definition of “prime number” doesn't exist in the real world, then any statement about prime numbers is meaningless in the real world.

> Unicorns don't exist but statements about them aren't meaningless.

Unicorns don't exist in the real world, but the definition of “unicorn” does - just grab any dictionary. It's on the basis the existing definition that you can say “unicorns don't exist”. On the other hand, you may reject the definition of “horse”, but, if you don't, you have to accept that horses exist in the real world. And, if you do reject it, then you also have to reject statements about horses as completely meaningless.

> Fictionalism accepts the concept of mathematical entities but denies their existence in the real world.

The question of whether mathematical objects exist in the real world is ill-posed in the first place. It's like asking if love can be stored in boxes.

[abrezas]

At some point mathematical objects are defined with meta-mathematical definitions (axioms etc), so we can accept definitions based on those terms.

But in any case. You obviously do not believe that mathematical objects exist in the first place and it the question is ill posed based on your concept of reality and existence.

That's understandable, but the debate is about which is the right definition of existence reality etc. If you are not interested in this discussion and know the answers then you have nothing to gain from this paper or this discussion.

[catnaroek]

> At some point mathematical objects are defined with meta-mathematical definitions (axioms etc), so we can accept definitions based on those terms.

“Metamathematics” doesn't exist in isolation from the rest of mathematics. If you reject the existence of mathematical objects (in the real world or elsewhere), you must also reject the existence of metamathematical definitions (in the same context), because the former include the latter.

> But in any case. You obviously do not believe that mathematical objects exist in the first place and it the question is ill posed based on your concept of reality and existence.

I only denied the meaningfulness of asking whether mathematical objects exist in the real world. The terms “real world”, “reality”, etc., I prefer to reserve for that which can be apprehended through physical experience. The distinguishing feature of reality is that you can't reject its existence (in the same way I hypothesized rejecting the definition of the word “horse” in my previous comment) - your senses force you to accept it. If someone cuts through your skin with the intention to bleed you to death, you will feel pain. You may resign yourself to your fate, but that won't make the pain go away. On the other hand, if you find it useless, annoying, etc. to do mathematics, all you need to do is stop doing it.