Oct 26, 2014 05:14 PM
Rebecca Newberger Goldstein’s “Plato at the Googleplex: Why Philosophy Won’t Go Away” is published by Atlantic Books
http://www.prospectmagazine.co.uk/blogs/...n-teach-us
EXCERPT: The philosopher and mathematician AN Whitehead described the history of philosophy as a “series of footnotes to Plato”. Do you agree with him?
If that were the case, what a silly field philosophy would be! A 2,400-year-old man had all the answers? I would like to think that what he meant was that this methodology, this view of maximising coherence, was begun by Plato and that he also formulated questions from a wide range of different areas of inquiry—mathematics, epistemology, metaphysics and political theory—and saw their commonality. In that sense, you can say that all philosophy follows in Plato’s footsteps.
Was Plato a “Platonist” in the modern sense of being committed to a claim about the existence of abstract entities, numbers for example?
The one area of philosophy in which Platonism is constantly referred to is philosophy of mathematics. There was apparently a survey done by the American Mathematical Association and something like 98 per cent of mathematicians described themselves as “Platonists”. There is [in mathematics] very much a sense that you’re discovering rather than inventing. So this is a kind of commitment to the existence of the abstract, but necessarily in insolation from the physical—the structure of physical reality is given by the abstract, but the abstract can’t be reduced to sensory particulars. So it doesn’t have to involve a commitment to a kind of Platonic “heaven” that Russell, for example, makes fun of; it can be the claim that reality can’t be intelligible without referring to abstractions which cannot themselves be reduced to anything other than themselves.
Was Plato a Platonist? Well, there’s the Platonism of the forms which I think he gave up. In the Parmenides, he really criticises the theory of forms. It’s interesting that Socrates is a young man there and he can’t answer Parmenides’ questions. In the Timaeus, which is one of my favourite dialogues, it’s not the forms, it’s mathematics that is the key to intelligibility.
Every theoretical physicist I’ve ever known has believed that not only is reality given to us in the language of mathematics, but that when we have two empirically adequate theories, you go with the one that has the most beautiful mathematics—that’s in the Timaeus too. That’s a Platonism that’s still working. When my scientist friends say that the structure of reality is given in the most beautiful mathematics, I say to them, “That’s a metaphysical argument you’re using right there.” Steven Weinberg said of string theory, “Maybe it’s not true, but we’re going to find some application for it, because never in the history of science has it been the case that such beautiful mathematics didn’t somehow reveal reality.” Whoah! That’s Plato!
http://www.prospectmagazine.co.uk/blogs/...n-teach-us
EXCERPT: The philosopher and mathematician AN Whitehead described the history of philosophy as a “series of footnotes to Plato”. Do you agree with him?
If that were the case, what a silly field philosophy would be! A 2,400-year-old man had all the answers? I would like to think that what he meant was that this methodology, this view of maximising coherence, was begun by Plato and that he also formulated questions from a wide range of different areas of inquiry—mathematics, epistemology, metaphysics and political theory—and saw their commonality. In that sense, you can say that all philosophy follows in Plato’s footsteps.
Was Plato a “Platonist” in the modern sense of being committed to a claim about the existence of abstract entities, numbers for example?
The one area of philosophy in which Platonism is constantly referred to is philosophy of mathematics. There was apparently a survey done by the American Mathematical Association and something like 98 per cent of mathematicians described themselves as “Platonists”. There is [in mathematics] very much a sense that you’re discovering rather than inventing. So this is a kind of commitment to the existence of the abstract, but necessarily in insolation from the physical—the structure of physical reality is given by the abstract, but the abstract can’t be reduced to sensory particulars. So it doesn’t have to involve a commitment to a kind of Platonic “heaven” that Russell, for example, makes fun of; it can be the claim that reality can’t be intelligible without referring to abstractions which cannot themselves be reduced to anything other than themselves.
Was Plato a Platonist? Well, there’s the Platonism of the forms which I think he gave up. In the Parmenides, he really criticises the theory of forms. It’s interesting that Socrates is a young man there and he can’t answer Parmenides’ questions. In the Timaeus, which is one of my favourite dialogues, it’s not the forms, it’s mathematics that is the key to intelligibility.
Every theoretical physicist I’ve ever known has believed that not only is reality given to us in the language of mathematics, but that when we have two empirically adequate theories, you go with the one that has the most beautiful mathematics—that’s in the Timaeus too. That’s a Platonism that’s still working. When my scientist friends say that the structure of reality is given in the most beautiful mathematics, I say to them, “That’s a metaphysical argument you’re using right there.” Steven Weinberg said of string theory, “Maybe it’s not true, but we’re going to find some application for it, because never in the history of science has it been the case that such beautiful mathematics didn’t somehow reveal reality.” Whoah! That’s Plato!
