On Saturday, March 8, 2014 2:37:50 AM UTC-6, Bruno Marchal wrote: > > A couple other accounts of how things might be that I take seriously are > (1) physicalism in the sense that arithmetical propositions might only be > true when physically realized, > > No problem, and indeed this would make comp false. of course, if you > really defend that thesis, you have to explain and prove the existence of > infinitely many prime numbers by using physics, and this without > presupposing addition and multiplication of integers. I am not even sure > how you will just defined what is prime number. >
Given a correspondence theory of truth and this kind of physicalism, mathematical theorems would be true if and only if there's a corresponding physical reality. So, for example, if the universe is finite, then there wouldn't be infinitely many prime numbers. Nor would there be infinitely many integers. But there would still be integers and primes. Numbers, addition, and multiplication would be patterns that our brains recognize in material things, at first due to experience counting objects, grouping them, and counting groups. We abstract those patterns to symbolic form in our heads or our writing for convenience, and we generalize the notation to cover a wide variety of patterns. But our process of abstracting and generalizing may omit important limitations (such as finitude) of the physical reality on which it was originally based. or even (2) relativism in the sense that arithmetical propositions might > only be true for humanlike brains, > > OK, but same remark. Defined human-like brain, and give me a proof that > 1+1=2 from that definition. > Due to our shared evolutionary history, humans share nearly all their brain architecture in common. Due to our shared cultural history, many of the humans we regularly encounter share much of their set of background assumptions and beliefs in common. It appears that there's no such thing as such a perfectly lucid and detailed description or set of instructions that one person could give another that eliminates the need for the other person to grok the meaning, i.e. to connect the ideas appropriately and fill in the missing information based on their own "wiring" and their own experience. (Take Edgar as an demonstration of this apparent fact. ;) Consequently, some suppose that communication with an extraterrestrial intelligence may fail due to there being an almost total mismatch in "wiring" and experience. (When language fails, we humans resort to pointing at objects and pantomiming, but without shared sensory systems and emotional responses, even that may well fail to be grokked by the alien.) It's also possible that the symbolic structure of our mathematics is dependent on our "wiring" and experience; indeed there is some evidence that the way humans use language is due to an evolutionarily recent genetic mutation. For these two reasons, our mathematical definitions, theorems, proofs, etc may only be suitable for use by other humans, and so by a pragmaticist alethiology, only true for humans. The usual proofs then apply, because we're humans. with an alethiology of the sort preferred by the American pragmatist school > of philosophy. > > keep in mind that you mention people who are Aristotelian, and the point I > do is only that IF comp is true, THEN such approach get inconsistent or > epistemologically non sensical. > Hm. Can you elucidate what you mean by saying they are Aristotelian? What is the key contrast? > Four options plus an ignorance prior and little evidence gives me about > 25% confidence for each. :) > > ONLY IF you develop your alternate assumptions. The idea that "1+1 is > prime" independently of human is far more simple (and used) than the idea > that "1+1 is prime" is relative to the human brain. > The axiomatic of natural numbers is far more simple than anything else. > You can always propose a much more complex theory to falsify a simple set > of axioms. > I don't know that the other cases I've mentioned are more complex. Physicalism just puts some mysterious "matter" first and makes math derivative of it. That may be wrong, but it's hard to see why it's more complex than comp's reversal of it. The relativism described above isn't an additional supposition added to math; it takes ideas from biology and linguistics to see what consequences there might be when they intersect with math. -Gabe -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
