Clark, List: Moore has edited two volumes that may be of interest--*Philosophy of Mathematics: Selected Writings* with Peirce's own stuff, and *New Essays on Peirce's Mathematical Philosophy* with contributions from various people including Hookway and Moore.
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, Jan 9, 2017 at 10:30 PM, CLARK GOBLE <cl...@lextek.com> wrote: > > On Jan 9, 2017, at 8:35 PM, Jon Alan Schmidt <jonalanschm...@gmail.com> > wrote: > > CG: I agree that this definitely tends to make nominalism self-refuting > which I see as a problem rather than a strength. > > > A problem for nominalism or for realism? Is it legitimate for a > nominalist to deny that holding everything real to be singular is > self-contradictory, on the grounds that singularity is not a property? (I > am having that very argument with a self-professed nominalist in another > context right now.) > > I think arguments with that level of circularity are pointless whether it > be for realism, nominalism, materialism or whatever. All it really means is > you’ve injected your assumptions in so alternatives are self-refuting. > Which isn’t much of an argument. > > A stronger argument for realism to me is always the argument that the > fundamental laws of physics are necessary for there to be anything. > Effectively that’s what Krauss does in his book *A Universe from Nothing* > although > he isn’t quite philosophically sophisticated enough to realize that’s what > he’s doing. Once you require immaterial laws of physics to make everything > work, then you’re unable to really take a strong nominalist stand. It’s not > a knock down argument of course. For instance several people have noted > that if you start with objects with certain properties you can derive the > laws of thermodynamics and a lot else just from their symmetries. So that’s > a more nominalist argument but doesn’t work with quantum mechanics. > > None of these arguments are fully persuasive to someone skeptical. But I > suspect that’s true of any metaphysical argument which almost by necessity > has to be weak. I think Peirce has an answer there with his process of > inquiry. What we can’t doubt as a practical matter we hold as true. We just > need to investigate all the arguments, look at the alternatives with as > open an eye as possible, and then see what we believe that persists through > inquiry. Again, far from perfect but probably the best we can do. > > CG: I assume he’s somewhat platonic about mathematical objects. That is > more akin to Godel than the logicists or the constructivists. Yet honestly > if someone told me he was a logicist or a constructivist I’d not be at all > shocked either. > > > I am not that familiar with the alternatives, but Christopher Hookway, > Matthew Moore, and others seem to think that his views--especially his > emphasis on diagrammatic reasoning--are closest to mathematical > structuralism. As with other sciences, he was more interested in the > *methods *of mathematicians than the *objects *of their investigations. > > I’ll confess I don’t quite have as good a grasp on mathematical > structuralism as I do logicism, intuitionalism, platonism or > constructivism. Reviewing the SEP and wikipedia it does sound a lot like > Peirce (real but not necessarily actual). It also sounds a bit like > Armstrong Universals. > > But thanks for pointing that out. I’ve honestly not read up on foundations > in mathematics since college and we didn’t study structuralism then. I have > my evening’s reading set out for me. >
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