Is mathematics invented or discovered...

What is the basis for reason? And mathematics?

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VVilliam
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Is mathematics invented or discovered...

Post by VVilliam »

...or is some mathematics natural [part of nature - discovered] and other mathematics invented by humans?
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bahman
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Re: Is mathematics invented or discovered...

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Mathematics is a language about abstract relations between abstract objects. A part of mathematics refers to an aspect of reality, the part that we invented, and another part we discovered.
Skepdick
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Re: Is mathematics invented or discovered...

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Like all human instruments it's made of and inspired by what we've discovered, but the end result is invented.

My favourite perspective on the matter Confessions of an Apostate Mathematician
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VVilliam
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Re: Is mathematics invented or discovered...

Post by VVilliam »

Skepdick wrote: Wed Feb 24, 2021 12:12 am Like all human instruments it's made of and inspired by what we've discovered, but the end result is invented.

My favourite perspective on the matter Confessions of an Apostate Mathematician
So are you saying that there is no math which is inherently integral to nature [discoverable and not invented by humans]?
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Re: Is mathematics invented or discovered...

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VVilliam wrote: Wed Feb 24, 2021 5:16 pm So are you saying that there is no math which is inherently integral to nature [discoverable and not invented by humans]?
Yep. The universe doesn't appear in Mathematics. We only describe it with Mathematics.
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Terrapin Station
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Re: Is mathematics invented or discovered...

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I basically agree with the other answers. Like logic, it's based on observations of relations, but that doesn't mean it's the same as (observations of) relations, and so it amounts to a way that we think about relations, a language we've created to talk about relations. And then the bulk of it is actually built upon the languages we've constructed--we extrapolate from them to create additional structures, more advanced logic/mathematics.
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VVilliam
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Re: Is mathematics invented or discovered...

Post by VVilliam »

Terrapin Station wrote: Wed Feb 24, 2021 6:25 pm I basically agree with the other answers. Like logic, it's based on observations of relations, but that doesn't mean it's the same as (observations of) relations, and so it amounts to a way that we think about relations, a language we've created to talk about relations. And then the bulk of it is actually built upon the languages we've constructed--we extrapolate from them to create additional structures, more advanced logic/mathematics.
So therefore language was invented in order to try and describe what it is that we experience as real. We use the ability to makes sound, by inventing a way in which that sound can be understood...but we did not invent the ability to make sounds
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Terrapin Station
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Re: Is mathematics invented or discovered...

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VVilliam wrote: Wed Feb 24, 2021 7:08 pm
Terrapin Station wrote: Wed Feb 24, 2021 6:25 pm I basically agree with the other answers. Like logic, it's based on observations of relations, but that doesn't mean it's the same as (observations of) relations, and so it amounts to a way that we think about relations, a language we've created to talk about relations. And then the bulk of it is actually built upon the languages we've constructed--we extrapolate from them to create additional structures, more advanced logic/mathematics.
So therefore language was invented in order to try and describe what it is that we experience as real.
Again, "the bulk of it is actually built upon the languages we've constructed--we extrapolate from them to create additional structures, more advanced logic/mathematics."
We use the ability to makes sound, by inventing a way in which that sound can be understood...but we did not invent the ability to make sounds
Sure, we didn't intentionally create "the ability to make sounds," but obviously the ability for humans to make sounds only arose within humans.
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VVilliam
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Re: Is mathematics invented or discovered...

Post by VVilliam »

Terrapin Station wrote: Wed Feb 24, 2021 7:17 pm
VVilliam wrote: Wed Feb 24, 2021 7:08 pm
Terrapin Station wrote: Wed Feb 24, 2021 6:25 pm I basically agree with the other answers. Like logic, it's based on observations of relations, but that doesn't mean it's the same as (observations of) relations, and so it amounts to a way that we think about relations, a language we've created to talk about relations. And then the bulk of it is actually built upon the languages we've constructed--we extrapolate from them to create additional structures, more advanced logic/mathematics.
So therefore language was invented in order to try and describe what it is that we experience as real.
Again, "the bulk of it is actually built upon the languages we've constructed--we extrapolate from them to create additional structures, more advanced logic/mathematics."
We use the ability to makes sound, by inventing a way in which that sound can be understood...but we did not invent the ability to make sounds
Sure, we didn't intentionally create "the ability to make sounds," but obviously the ability for humans to make sounds only arose within humans.
Why would you think that is 'obvious'?

Are you aware that sound is closely related to math?
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Terrapin Station
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Re: Is mathematics invented or discovered...

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VVilliam wrote: Wed Feb 24, 2021 7:24 pm Why would you think that is 'obvious'?
Because we'd need some really wonky ontology to think that the ability to make human sounds somehow arose independently of humans.
Are you aware that sound is closely related to math?
It's not related to math in any special way. It's similar to any thinking about phenomena in a mathematical manner.
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Re: Is mathematics invented or discovered...

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VVilliam wrote: Wed Feb 24, 2021 7:24 pm Are you aware that sound is closely related to math?
Relations are closely related to math: https://en.wikipedia.org/wiki/Relational_algebra

Since you have deep interest in simulation theory. Relational algebra is basically the mathematical theory behind SQL databases.
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VVilliam
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Re: Is mathematics invented or discovered...

Post by VVilliam »

Terrapin Station wrote: Wed Feb 24, 2021 7:27 pm
VVilliam wrote: Wed Feb 24, 2021 7:24 pm Why would you think that is 'obvious'?
Because we'd need some really wonky ontology to think that the ability to make human sounds somehow arose independently of humans.
I see. But humans didn't invent sounds. They simply utilized their ability to make them, and invented language from that.
Are you aware that sound is closely related to math?
It's not related to math in any special way.
Related nonetheless. "Special" is besides the point as no one appears to be arguing anything is 'special'.
It's similar to any thinking about phenomena in a mathematical manner.
The math is in the sound and the sound was not invented by humans. The human instrument came with the ability to make sound rather than humans inventing sound.
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Terrapin Station
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Re: Is mathematics invented or discovered...

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VVilliam wrote: Wed Feb 24, 2021 7:52 pm I see. But humans didn't invent sounds. They simply utilized their ability to make them, and invented language from that.
Right. That's basically what I said:
"Sure, we didn't intentionally create 'the ability to make sounds'"--This means that we didn't invent it per se; invention is an intentional act.
"but obviously the ability for humans to make sounds only arose within humans."--in other words, we have to exist for human sounds to be a possibility.
The math is in the sound
I don't agree with this, as I don't agree that mathematics is identical to any objective processes or relations. Again, mathematics, at root, that is at least in its simplest forms, is a way that we think about objective relations (and then the bulk of mathematics is an extrapolation from that sort of thinking).
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VVilliam
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Re: Is mathematics invented or discovered...

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Terrapin Station wrote: Wed Feb 24, 2021 7:58 pm
VVilliam wrote: Wed Feb 24, 2021 7:52 pm I see. But humans didn't invent sounds. They simply utilized their ability to make them, and invented language from that.
Right. That's basically what I said:
"Sure, we didn't intentionally create 'the ability to make sounds'"--This means that we didn't invent it per se; invention is an intentional act.
"but obviously the ability for humans to make sounds only arose within humans."--in other words, we have to exist for human sounds to be a possibility.
The math is in the sound
I don't agree with this, as I don't agree that mathematics is identical to any objective processes or relations. Again, mathematics, at root, that is at least in its simplest forms, is a way that we think about objective relations (and then the bulk of mathematics is an extrapolation from that sort of thinking).
Yet 'the way we think' is determined through 'the brain we have' and we know that the brain we have is that which is revealing to us mathematics because mathematics is within the fundamental structure of the universe the brain exists within and the brain we have recognizes this and shows us.

Then [for some reason], we reject that mathematics existed before we did.
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Terrapin Station
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Re: Is mathematics invented or discovered...

Post by Terrapin Station »

VVilliam wrote: Wed Feb 24, 2021 8:09 pm
Terrapin Station wrote: Wed Feb 24, 2021 7:58 pm
VVilliam wrote: Wed Feb 24, 2021 7:52 pm I see. But humans didn't invent sounds. They simply utilized their ability to make them, and invented language from that.
Right. That's basically what I said:
"Sure, we didn't intentionally create 'the ability to make sounds'"--This means that we didn't invent it per se; invention is an intentional act.
"but obviously the ability for humans to make sounds only arose within humans."--in other words, we have to exist for human sounds to be a possibility.
The math is in the sound
I don't agree with this, as I don't agree that mathematics is identical to any objective processes or relations. Again, mathematics, at root, that is at least in its simplest forms, is a way that we think about objective relations (and then the bulk of mathematics is an extrapolation from that sort of thinking).
Yet 'the way we think' is determined through 'the brain we have' and we know that the brain we have is that which is revealing to us mathematics because mathematics is within the fundamental structure of the universe the brain exists within and the brain we have recognizes this and shows us.

Then [for some reason], we reject that mathematics existed before we did.
Do you think that brains could do anything unique? That is, anything that didn't exist prior to brains developing?
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