I'll have much more to say on this later. For now, I'll just note that it was never very clear to me how literally Plato meant Forms to be taken. Also the author here doesn't seem to recognise that a mental concept, even if requiring a mind to conceive it, nevertheless does have a (non-physical) existence; this doesn't avoid the prospect of an additional, non-physical component of reality - far from it ! And as for the nature of numbers, see Plato's Parmenides, then take some aspirin because you'll have an almighty headache.
Originally shared by Event Horizon
As a non-mathematician, I am not kidding myself in regards to my comprehension of the complexities of mathematics. Similarly - as a non-physicist, chemist, complexity-theorist (etc.) I am not pretending to know the intricate applications and efflorescent theoretical emergence of mathematical regularity and symmetry in nature.
The central idea of Platonism is this: mathematical objects exist independent of our conception of them. Without minds, numbers would still be “out there”.
Contrary to what you might think, Platonism is the standard, accepted metaphysical theory by the majority of mathematicians – with big philosophic implications. If Platonism is true, it means that you can have a meaningful non-spatial, non-temporal existence; that the mind has access to this realm; that “real infinities” exist; and that the realm of abstract objects has a close connection with the regular universe – numbers are, in a sense, omnipresent throughout our world.
The author is aspiring to an explanatory completeness and concision of definition that does not actually exist, even by the logic he seeks to use to cultivate such a secure ontological bunker from which to pontificate. The issues are more subtle than those indicated here.
The author seems to displace the Platonic Forms of Mathematics with Platonic Forms of Logical Necessity; decrying the existence of mathematical Forms by supplanting them with logical Forms. This is misdirection, not resolution. If logic is pre-existing, then this logic is an a priori Universal in precisely the same way that mathematics is when considered as a Platonic Universal.
http://steve-patterson.com/the-metaphysics-of-mathematics-against-platonism/
Oh my, that's quite an about page. So Rhys Taylor, what foundational errors are you making in astronomy?
ReplyDeleteChris Greene All of them, probably.
ReplyDeleteMy goodness, that about page - and the link to "everyone is wrong except me" - is so full of himself I'm tempted to delete this post in order to deprive the poor bastard of the few additional hits he'd get. It's for his own good. Hopelessly mad by the sounds of things.
ReplyDeleteMy impression is that Plato took his theory of the Forms quite literally, he built quite a lot of theory on top of that foundation. Also, Aristotle was partly responding to that theory in his Metaphysics. (Indeed, read in context, a lot of Aristotle is a conversation with Plato.) So even if Plato didn't take himself seriously everyone since has.
ReplyDeleteI think the article is more or less correct. Concepts are in the mind. Map is not the territory, etc etc. Linguistic systems (including logic and math) reflect and represent observed regularities in the universe. Concepts exist only in information processors (brain, etc). Perhaps the most well known example where this can be examined is the concept of time which exists as a construct but doesn't seem to exist as a material processes. Or something like that.
ReplyDeleteAnd my own take on the matter : http://astrorhysy.blogspot.com/2018/09/this-equation-shows-you-cant-quantify.html
ReplyDelete