On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch <[email protected]> wrote:
> On Sep 18, 2012, at 9:19 PM, Rex Allen <[email protected]> wrote: > > On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam < <[email protected]> > [email protected]> wrote: > >> Rex, >> >> Do you have a non-platonist explanation for the "discovery" of the >> Mandelbrot 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. So you're saying that "thought" is another kind of sense? 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? 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? It's not much different from how we develop theories about other things we > cannot interact with: the early universe, the cores of stars, the insides > of black holes, etc. > > We test these theories by following their implications and seeing if they > lead to contridictions with other, more established, facts. > > Just as with physical theories, we ocasionally find that we need to throw > out the old set of theories (or axioms) for a new set which has greater > explanatory power. > So you think our current mathematical theories are not "true" in any metaphysical sense - but rather are approximations of what exists in Platonia? Is there an equivalent of the idea of "domains of validity" that holds in some circles in physics? I'm not sure any of this counts as being evidence in favor of Platonism... How is it that we are able to reliably know things about Platonia? > > > The very idea of knowing implies a differentiation between true and false. > > Nearly any intelligent civilization that notices a partition between true > and false will eventyally get here. > > True in what sense? A coherentist conception of truth? A correspondence conception of truth? How do we know truth? Do we have an innate "truth sense"? Does the ability to know truth require free will? For instance: If we say a statement is true because it is true, that is different than saying it is true because our neurons fired in a way that determined our response. If all our decisions were predetermined from the moment of the big bang then rational discussion is meaningless. Whether or not anyone agrees with you has nothing to do with the truth of your claim. Their beliefs were "hardwired" from the beginning of time. It follows then that your own beliefs are not based on their truth value. You believe what you believe because your neurons have determined that you will believe in this rather than that. SO - what is this "truth" stuff, really? > > > I would have thought that quarks and electrons from which we appear to be > constituted would be indifferent to truth. > > > The unreasonable effectiveness of math in the physical sciences is yet > further support if Platonism. If this, and seemingly infinite physical > universes exist, and they are mathematical structures, why can't others > exist? > > > Which would fit with the fact that I seem to make a lot of mistakes. > > But you think otherwise? > > > We are imperfect beings. > What is the source of imperfection? Where does it come from? What explains it? Objectively, intrinsically, absolutely imperfect? Have you heard the term "Works as coded", with respect to software development? So I can write a program that has a bug in it - and the computer will run it perfectly. The computer will do exactly what I told it to do. The program works as coded. When running my program, the computer is perfectly imperfect. I am the source of its imperfection. However, in a functionalist theory of mind - I am actually just executing my own "program" right? Given the initial conditions of the universe and the causal laws that govern it - I could not do other than I did when I wrote that buggy code. I also "work as coded". I also am "perfectly imperfect". And since in this view I am not the source of my own imperfection - the universe's initial conditions and causal laws must be that source. But what explains that imperfection? But - maybe there really is no such thing as imperfection? It's all just made up...like mathematical truth. Maybe? Rex -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. 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