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> The prime numbers would also be irreducible if there weren't mathematicians, though. This is a lot more philosophically fraught. If you believe that mathemat

> The prime numbers would also be irreducible if there weren't mathematicians, though. This is a lot more philosophically fraught. If you believe that mathematical entities exist in some acausal, nonphysical realm separate from the activity of beings doing math, you need to explain how those beings can access them. If you take Brouwer’s position that mathematics is the free languageless creation of the mind, then it’s no longer true that prime numbers would be irreducible if not for mathematicians.

claudiawerner 7y ago
That's true, and I accept that - though my claim was more intended to attack the notion that a certain analysis is useless just because the thing being analyzed would exist otherwise - whether that existence is due to initial theorists (i.e primes are a creation of the mind) or whether it's due to their non-physical existence as Platonic forms was a little beside the point of what I was trying to say. I meant it more in the way that we could say science would still exist even if Popper hadn't theorized falsificationism.
Nasrudith 7y ago
I don't see how that follows personally - mathematics are about configuration of information which may or may not be descriptions that exist within reality. Impetus based momentum could be described mathematically but that doesn't mean it exists. Which highlights Hegel's central flaw in derivation - possibilities are infinite without any grounding assumptions. At best you would get a smaller but still infinite subset compared to literally everything (all valis equations vs all equations even 2 = 1). There is no need to "access" what may simply be rederived. It isn't a physical place. The only constraints are on what configurations are possible within the system attempting to describe it. You can't describe 0 to 1024 with only a single bit. In a "world of silence" with no "life" capable of describing primes it would still hold that the smallest non-1 divisions of 6 particles would be 2 and 3 and for 7 it would be 7 - even though there is nobody around to understand this.
- claudiawerner 7y ago
  It's worth noting that the idea that mathematical forms are mind-independent and can be "accessed" is taken seriously by non-crackpot philosophers. It's not a settled matter. See the SEP[0] entry for some of the debates surrounding it. A nice passage is: >This counterfactual independence (as we may call it) is accepted by most analytic philosophers. To see why, consider the role that mathematics plays in our reasoning. We often reason about scenarios that aren’t actual. Were we to build a bridge across this canyon, say, how strong would it have to be to withstand the powerful gusts of wind? Sadly, the previous bridge collapsed. Would it have done so had the steel girders been twice as thick? This form of reasoning about counterfactual scenarios is indispensable both to our everyday deliberations and to science. The permissibility of such reasoning has an important consequence. Since the truths of pure mathematics can freely be appealed to throughout our counterfactual reasoning, it follows that these truths are counterfactually independent of us humans, and all other intelligent life for that matter. That is, had been there been no intelligent life, these truths would still have remained the same. [0] https://plato.stanford.edu/entries/platonism-mathematics/ https://plato.stanford.edu/entries/platonism-mathematics/
tim333 7y ago
You can suppose we can figure they exist using logic and reasoning rather needing access to some mystical realm.

claudiawerner 7y ago

That's true, and I accept that - though my claim was more intended to attack the notion that a certain analysis is useless just because the thing being analyzed would exist otherwise - whether that existence is due to initial theorists (i.e primes are a creation of the mind) or whether it's due to their non-physical existence as Platonic forms was a little beside the point of what I was trying to say. I meant it more in the way that we could say science would still exist even if Popper hadn't theorized falsificationism.

Nasrudith 7y ago

I don't see how that follows personally - mathematics are about configuration of information which may or may not be descriptions that exist within reality. Impetus based momentum could be described mathematically but that doesn't mean it exists. Which highlights Hegel's central flaw in derivation - possibilities are infinite without any grounding assumptions. At best you would get a smaller but still infinite subset compared to literally everything (all valis equations vs all equations even 2 = 1). There is no need to "access" what may simply be rederived. It isn't a physical place. The only constraints are on what configurations are possible within the system attempting to describe it. You can't describe 0 to 1024 with only a single bit. In a "world of silence" with no "life" capable of describing primes it would still hold that the smallest non-1 divisions of 6 particles would be 2 and 3 and for 7 it would be 7 - even though there is nobody around to understand this.

claudiawerner 7y ago
It's worth noting that the idea that mathematical forms are mind-independent and can be "accessed" is taken seriously by non-crackpot philosophers. It's not a settled matter. See the SEP[0] entry for some of the debates surrounding it. A nice passage is: >This counterfactual independence (as we may call it) is accepted by most analytic philosophers. To see why, consider the role that mathematics plays in our reasoning. We often reason about scenarios that aren’t actual. Were we to build a bridge across this canyon, say, how strong would it have to be to withstand the powerful gusts of wind? Sadly, the previous bridge collapsed. Would it have done so had the steel girders been twice as thick? This form of reasoning about counterfactual scenarios is indispensable both to our everyday deliberations and to science. The permissibility of such reasoning has an important consequence. Since the truths of pure mathematics can freely be appealed to throughout our counterfactual reasoning, it follows that these truths are counterfactually independent of us humans, and all other intelligent life for that matter. That is, had been there been no intelligent life, these truths would still have remained the same. [0] https://plato.stanford.edu/entries/platonism-mathematics/ https://plato.stanford.edu/entries/platonism-mathematics/

tim333 7y ago

You can suppose we can figure they exist using logic and reasoning rather needing access to some mystical realm.