Do numbers exist in nature or are they human contructs?

[rainbow]

If Godel's theorem has any relevance to Svarty's question, then it would mean that the answer to "does a number exist if it's not counted?" is "unknown", rather than either yes or no...

...or alternatively both "yes" and "no" are simultaneously correct, and/or incorrect.

[Xamonas Chegwé]

If Godel's theorem has any relevance to Svarty's question, then it would mean that the answer to "does a number exist if it's not counted?" is "unknown", rather than either yes or no...

...or alternatively both "yes" and "no" are simultaneously correct, and/or incorrect.

Actually, Gödel's Incompleteness Theorems (there are actually 2 of them) state only that (i) ALL truths about the relations of natural numbers cannot be proven by any algorithmic system and (ii) that such a system cannot prove its own consistency. What it does not do is answer any metaphysical questions about the relationships between human intellect and arithmetic.

It also knows fuck all about cheese, or wanking, and is thus pretty much useless for any practical use.

[rainbow]

Actually, Gödel's Incompleteness Theorems (there are actually 2 of them) state only that (i) ALL truths about the relations of natural numbers cannot be proven by any algorithmic system and (ii) that such a system cannot prove its own consistency. What it does not do is answer any metaphysical questions about the relationships between human intellect and arithmetic.

It also knows fuck all about cheese, or wanking, and is thus pretty much useless for any practical use.

Quite so.

Godel.png (42.4 KiB) Viewed 460 times

[FBM]

Is an undefined number an existent number?

[Xamonas Chegwé]

Is an undefined number an existent number?

Undefined under which number system? And existent under which number system?

[FBM]

Is an undefined number an existent number?

Undefined under which number system? And existent under which number system?

Take your pick. Not sure it matters, ontologically speaking.

[mistermack]

If you believe that number only exist as human constructs, then by simple deduction, you don't believe in alien civilisations. How could civilisiation develop, without numbers? How could they develop any kind of technology?

Not just that, you would be claiming that alien technologies can never develop. Because without numbers they would be fucked.

The opposite is much more likely, that there are millions of alien technological societies, and they all use numbers. Even if there aren't, the numbers are still there, waiting to be found.

In which case, we humans didn't CONSTRUCT numbers, we discovered them.
And so did countless other intelligent creatures.

And so did evoulution, here on Earth. Two eyes, four legs, one dick, one arse. Evolution discovered those numbers, and settled on them, as the solution to a problem.

[Audley Strange]

If you believe that number only exist as human constructs, then by simple deduction, you don't believe in alien civilisations. How could civilisiation develop, without numbers? How could they develop any kind of technology?

Not just that, you would be claiming that alien technologies can never develop. Because without numbers they would be fucked.

The opposite is much more likely, that there are millions of alien technological societies, and they all use numbers. Even if there aren't, the numbers are still there, waiting to be found.

In which case, we humans didn't CONSTRUCT numbers, we discovered them.
And so did countless other intelligent creatures.

And so did evoulution, here on Earth. Two eyes, four legs, one dick, one arse. Evolution discovered those numbers, and settled on them, as the solution to a problem.

That seems like a very anthropic view. We are constructs of environmental adaptation, life that evolved in a completely different environment from ours, that might have completely different sense organs could have invented technologies that are based on something other than mathematics. Perhaps they are a gaseous colony of bacteria with emergent intelligence and float around in the upper atmosphere of their world, glide out of it on solar winds and use some kind dead reckoning based on reading the radioactivity signals of stars with something akin to a nose that smells them.

Don't get me wrong, I'm still not sure as to whether or not there are actual "Platonic Entities" underpinning the mechanics of (at least this local part of) the universe, but then it could be Plato's cave.

Fucking Plato.

[mistermack]

That seems like a very anthropic view. We are constructs of environmental adaptation, life that evolved in a completely different environment from ours, that might have completely different sense organs could have invented technologies that are based on something other than mathematics. Perhaps they are a gaseous colony of bacteria with emergent intelligence and float around in the upper atmosphere of their world, glide out of it on solar winds and use some kind dead reckoning based on reading the radioactivity signals of stars with something akin to a nose that smells them.

Don't get me wrong, I'm still not sure as to whether or not there are actual "Platonic Entities" underpinning the mechanics of (at least this local part of) the universe, but then it could be Plato's cave.

Fucking Plato.

Even if that could happen, it wouldn't be prevent my scenario from happening. At least we know that technologies CAN thrive using numbers. We only know of one technological world, so the score is numbers, 100 percent, others, nil.

But it seems pretty obvious to me that the numbers are there, available to be used by anyone or anything, so they're not a human construct, they're a property of time and space, available to anyone.

[JimC]

That seems like a very anthropic view. We are constructs of environmental adaptation, life that evolved in a completely different environment from ours, that might have completely different sense organs could have invented technologies that are based on something other than mathematics. Perhaps they are a gaseous colony of bacteria with emergent intelligence and float around in the upper atmosphere of their world, glide out of it on solar winds and use some kind dead reckoning based on reading the radioactivity signals of stars with something akin to a nose that smells them.

Don't get me wrong, I'm still not sure as to whether or not there are actual "Platonic Entities" underpinning the mechanics of (at least this local part of) the universe, but then it could be Plato's cave.

Fucking Plato.

Even if that could happen, it wouldn't be prevent my scenario from happening. At least we know that technologies CAN thrive using numbers. We only know of one technological world, so the score is numbers, 100 percent, others, nil.

But it seems pretty obvious to me that the numbers are there, available to be used by anyone or anything, so they're not a human construct, they're a property of time and space, available to anyone.

They can also be thought of as a property of how matter is organised in our particular Universe, into a series of discrete, separate entities, at many levels, that allow for a set theory containing discrete elements.

One could imagine a very different universe, perhaps only containing classical energy fields, with no quantum effects, where all aspects of physical reality change absolutely smoothly in magnitude and direction; no steps, no jumps, no discrete entities. If an intelligent alien form of life evolved in such conditions, it would have no concept of integers at all - it would be interesting to speculate on what aspects of mathematical theory we would have in common (calculus?), and what would be unique to each of us...

[mistermack]

They can also be thought of as a property of how matter is organised in our particular Universe, into a series of discrete, separate entities, at many levels, that allow for a set theory containing discrete elements.

One could imagine a very different universe, perhaps only containing classical energy fields, with no quantum effects, where all aspects of physical reality change absolutely smoothly in magnitude and direction; no steps, no jumps, no discrete entities. If an intelligent alien form of life evolved in such conditions, it would have no concept of integers at all - it would be interesting to speculate on what aspects of mathematical theory we would have in common (calculus?), and what would be unique to each of us...

In that context, you say absolutely, but you mean ''infinitely''. Yes?
That's not actually as easy as it sounds, to imagine. An actual infinity is supposed to be impossible in the physical world. Which is why quantum jumps make sense.

[FBM]

I'm pretty sure things have been observed, but not so sure numbers themselves ever have.

[Azathoth]

The whole discussion can be distilled to does 0 exist.

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[Azathoth]

I would say it does if you define it as a logical not

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[mistermack]

I'm pretty sure things have been observed, but not so sure numbers themselves ever have.

Depends what you mean by ''exist'' then. Physical things exist. And they have properties.
Do properties ''exist'' ? I think they do. If they don't exist, they can't cause change.
We don't observe gravity. We observe it's effect. It's the same with numbers. We don't observe the numbers, we observe their effects.