On 9/21/2012 12:56 PM, Jason Resch wrote:
On Fri, Sep 21, 2012 at 1:55 PM, meekerdb <[email protected] <mailto:[email protected]>> wrote:On 9/21/2012 8:59 AM, Jason Resch wrote:On Sep 21, 2012, at 8:13 AM, Rex Allen <[email protected] <mailto:[email protected]>> wrote:On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch <[email protected] <mailto:[email protected]>> wrote: On Sep 18, 2012, at 9:19 PM, Rex Allen <[email protected] <mailto:[email protected]>> wrote:On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam <[email protected] <mailto:[email protected]>> wrote: Rex, Do you have a non-platonist explanation for the "discovery" of theMandelbrot set and the infinite complexity therein?I find fictionalism to be the most plausible view of mathematics, with all that implies for the Mandelbrot set. But ;et me turn the question around on you, if I can: Do you have an explanation for how we "discover" mathematical objects and otherwise interact with the Platonic realm?We study and create theories about objects in the mathematical realm just as we study and create theories about objects in the physical realm. So in the physical realm, we start from our senses - what we see, hear, feel, etc. From this, we infer the existence of electrons and wavefunctions and strings and whatnot. Or some of us do. Others take a more instrumental view of scientific theories.Right, and we have similarly inferred the existence of primes, fractals, non-computable functions, etc.We invented counting, addition, etc and found it implied true propositions about primes, fractals, etc. To say they exist in the same way tables and chairs exist is going much further.All of our scientific theories are inventions too. We can only hope they bear some resemblance to reality.So you're saying that "thought" is another kind of sense?Thought is needed for inference and building theories, equally in the physical sciences and math.And that what occurs to us in thought can also be used as a basis to infer the existence of objects which help "explain" those thoughts?Right, like you might think up genesis and dualism, or big bang and materialism, or platonic truth and computationalism. These are ontological theories for what exists, and why we are here experiencing it. If you say math is fiction and only exists only as a story in our brains, then obviously you can't use platonic truth and computationalism as one if your theories of existence. I think the fact that mathematics can serve as a theory for our existence shows absolutely that mathematical theories and physical theories are on equal footing. We can gather evidence for them and build cases for them, find out we were wrong about them, and so on. Why do we believe in quarks, electrons, strings, etc.? Because they can explain our observations. Why do I believe in the platonic realm? For the same reasons.But we believe that electrons interact causally with us because we are made from similar stuff - and by doing so make themselves known to us...right? How do Platonic objects interact causally with us? Via a Platonic Field? PFT - Platonic Field Theory?How did the warping of space and time cause Einsteins brain to figure out relativity? I think you are looking at it in the wrong way. Our brains seek good explanations. They sometimes find one. That's all that is going on. Now you say our explainations when it comes to mathematics are fiction, but if that is so, why not say the same of the physical theories? Why not say the big bang is fiction, or matter is fiction?They are stories which we intend to have referents independent of the stories (theories). I don't see how this is any different from our mathematical theories though.
It is different. It's confusing because arithmetic (to take an example) is both a theory about discrete objects, 1apple + 1apple = 2apples, which requires a correct interpretation like any theory of physics, 1raindrop + 1raindrop = 1raindrop, but it's also a closed story without any external referents, s(0)+s(0)=s(s(0)). This is what makes mathematics (and logic and language) useful; you can abstract from the physical world to the Platonia story, manipulate it by some rules, and if you did it right interpret the result back in the physical world. But that doesn't mean language and logic and mathematics exist in the same sense.
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