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Architeuthus

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But birds have a number concept like ours. So numbers must be part of reality in some sense, and not purely a human construct. The labels are unimportant (1, 2, 3, 4, 5,... or I, II, III, IV, V,... both work, as do purely mental representations).

It isn't as if we generally teach all of the math which doesn't work for any useful purpose

Of course we do. It's called "pure math."
 
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Architeuthus

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Numbers are the territory when we're doing mathematics. But that territory is not real, it is invented.

Really? So it just happened that birds invented the same numbers?

And question for you: was 6 + 7 = 13 true before human beings existed? When did it become true?

Hydrogen has 1 and exactly 1 proton in its nucleus. This was true long before there were any humans. But there were no 1's present at that time. Just hydrogen atoms.

That's not entirely coherent. How could it be true at the time if there was no such thing as 1?
 
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essentialsaltes

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Really? So it just happened that birds invented the same numbers?

Western and Eastern cultures invented dragons, but that doesn't make dragons real.

Birds live in the same reality we do, so it's not surprising they developed similar descriptions. But those descriptions are not the reality.

And question for you: was 6 + 7 = 13 true before human beings existed? When did it become true?

If we stipulate there were no minds back then, then no minds could have thought it at that time. The statement could not have been instantiated or supported in any minds, since there weren't any. But that doesn't, I think, prevent it from being true at that time, if we're talking about the standard axioms of arithmetic. In a particular axiomatic system, the meanings and relations are fixed, and there is no reference to time or space in them. Peano didn't say "0 is assumed to be the first natural number, but only after 1500 AD." Unlike a rock or a sock, the concept of 0 doesn't have any time or place attached to it. It's not so much that I can imagine a 0 on the moon or in the Jurassic. But that 0 is nowhere and nowhen, because it is an abstract invented idea. In ordinary arithmetic, 6 + 7 = 13. It can't be otherwise.

In the system defined by ordinary arithmetic, what does 6 +7 equal...

when you're in a moving bus? It doesn't matter, in that system, it can't help but be 13.
if you're in Belgium? It doesn't matter, in that system, it can't help but be 13.
What if the 6 is on a moving bus, and the 7 is in Belgium? 6's and 7's can't be anywhere, but in that system, that sum must be 13.
What if the 6 is in the Jurassic and the 7 is in next week? 6's and 7's can't be in some particular time, but in that system, that sum must be 13.
 
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Resha Caner

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essentialsaltes

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Physical interactions. You've suggested hydrogen as an example, so the forces between the proton and the electron would be an interaction.

Physical forces/interactions are real.
 
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quatona

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No. "I", "part", "interaction" are labels (which describe the way we structure reality).
 
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quatona

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Even more puzzling: What is "the" and what is "and"?
 
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essentialsaltes

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Why? Why isn't "force" just a label - a construct of the human mind?

Sigh. "force" is a label, quite explicitly with the quotes. The interaction between the proton and electron is real. I can, in a way, point to it.

"Resha Caner" is a label. But I could point to you. You are a real thing.

"3" is label. But I cannot point to 3. 3 is not real. I can point to a pattern of ink shaped like '3' on a piece of paper, but that's just a numeral. I cannot point to 3.
I can point to a bowl of ice cream with three scoops in it, but there is no 3 in the bowl. It is only in my mind that I lasso together those things and label them 3. Some other mind might see me pointing at 1 bowl of ice cream, or 4 items on the table, or 1200 calories, or 5E25 atoms.
 
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essentialsaltes

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Some labels name real things, like "bowling ball"
Some labels name non-real things, like "unicorn"
The problem with numbers is not that they are labels, but that they have no real referent.

If we accept the axioms of Sherlockiana, it is a true statement that Sherlock Holmes lived at 221B Baker Street. This does not make Sherlock Holmes real. Mathematics is a similar kind of fictional enterprise about invented characters called numbers.
 
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TillICollapse

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And math is arguably a cognitive *tool* to help us understand how the world around us functions. Yes/no ?

ETA: Actually scratch that. I may rephrase that and use the word "language" instead of cognitive tool.
 
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Resha Caner

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Sigh. "force" is a label, quite explicitly with the quotes. The interaction between the proton and electron is real. I can, in a way, point to it.

Actually, you can't. What you can point to are particles moving. It is only in your mind that you lasso together those things and label them forces.
 
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Architeuthus

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I couldn't agree more. Numbers are part of reality, not merely a human construct.

I think this reduces us to the cases (a), (b), and (d).


... but then this seems to completely contradict the other post. Are there two different people logging into your account?
 
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essentialsaltes

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Actually, you can't. What you can point to are particles moving. It is only in your mind that you lasso together those things and label them forces.

No, the electron is really lassoed to the proton, and the earth is really lassoed to the sun. But grouping is not real.
 
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essentialsaltes

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And math is arguably a cognitive *tool* to help us understand how the world around us functions. Yes/no ?

It is a cognitive tool to help us describe the world around us.
 
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