> On Jan 9, 2017, at 8:35 PM, Jon Alan Schmidt <jonalanschm...@gmail.com > <mailto: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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