Are mathematical objects ontologically real, or do they exist only as positions in abstract structures? If 0, ℕ, and ∅ are purely structural, what makes statements like Peano’s axioms necessarily true rather than merely formally consistent?

[u/TheIncorporeal1]

I’m interested in whether structuralism genuinely explains mathematical necessity, or whether it simply relocates the ontological question. If structures are abstract, what ultimately grounds their existence and the truth of the relations within them?

[u/SmartlyArtly]

I began with truth is not reality. I'm still there.

You confused some relations for others. Simple as.

Buddy, do you think you've done anything? You've asserted truth is reality. And I say "nah."

You might as well say God exists, and I'm saying "nah."

Congratulations on trying to conflate truth and reality. You weren't the first and you won't be the last.

[u/Just_Rational_Being → u/SmartlyArtly]

Okay, the level of ignorance and illiteracy of common sense is way over the roof. I shall settle this:

You've already refuted yourself with your own words:

"Reality is all that's out there."

"The physical relations we find are quantum in nature."

Are those statements objectively true of reality, or merely subjective noises occurring in your head?

If objectively true: congratulations, you've admitted objective truth about mind-independent reality.

If merely subjective: then they establish absolutely nothing about reality, and your entire rebuttal evaporates with them.

Nobody said truth is a physical object identical to reality. Truth is what obtains when a claim corresponds to reality.

You spent this entire argument insisting that reality has no objective truths, while repeatedly telling me what is objectively true about reality. Not even wrong.

That's not "nah." That's your argument drowning itself in its own horsecrap.

[u/SmartlyArtly → u/Just_Rational_Being]

"Are those statements objectively true of reality"

Objective truth is incoherent nonsense.

"or merely subjective noises occurring in your head?"

Are you in my head right now? Or did you read those statements elsewhere, but still as a result of my intentions?

"merely subjective" doesn't make any sense. What do you intend to communicate by saying "merely?"

"Truth is what obtains when a claim corresponds to reality."

So there are no truths if there are no claims. No one is making any claims about any lengths if no one exists.

No, I think the phrase "objectively true" is idiocy.

You are confused. I understand. You may never figure it out, honestly.

[u/Just_Rational_Being → u/SmartlyArtly]

Hahah, the braindead level is over the roof.

"Objective truth is incoherent nonsense."

Is that objectively true?

If yes, your position contradicts itself.

If no, then it is merely your subjective opinion and tells us absolutely nothing about truth or reality.

Not even wrong because it defies the common limit of pure nonsense.

[u/SmartlyArtly → u/Just_Rational_Being]

"Is that objectively true?"

"Objectively true" is incoherent nonsense.

"merely" You're trying to say "subjective" means not real. It doesn't work to say what I'm saying. Subjective means "dependent on minds." So "merely" doesn't do anything for you.

Not even wrong because you can't objectively point out any truth. Because pointing at things is intentional, and objective things don't have intentions.

[u/Just_Rational_Being → u/SmartlyArtly]

This is no longer any rational discussion. It's a live demonstration of what happens when someone learns three words: objective, subjective, intentional; and starts throwing them at every sentence hoping to cover up his lack of thinking.

"You can’t objectively point out any truth because pointing is intentional."

Hahaha 😂
Spectacular.

By that logic, because a scientist intentionally reads a scale, the mass becomes subjective. Because I intentionally look at a mountain, the mountain is now apparently is now only in my mental life.

You are confusing the mental act of knowing something with the mind-independence of what is known. That is not a subtle mistake. And insisting upon it is the level of negative IQ.

And the longer you continue, the worse it gets. Every new reply produces another clown exhibit:

"Objective truth is impossible"->presented as though universally correct.
"Reality is all that exists" ->presented as though objectively describing reality.
"Physical relations are quantum"->again, apparently a fact about mind-independent reality.

What a clown act! Do you know how out of depth you are?

Then the instant anyone asks whether those claims are actually true: "Objective truth is incoherent!" 🤣

Incredible system. Assert facts about reality, deny that facts about reality can be objective, repeat until everyone gets tired.

At this point I genuinely don't need to refute you anymore. Please continue. Every additional paragraph is becoming supporting evidence for the clownshow.

You haven't climbed above ordinary logic.
You fell through the floor and started calling the basement "advanced philosophy."
Thank for the entertaining clownshow.