coming from here
Pythagoras assigned cyclical motions to the planets. Circles are eternal, and thus the motion most suited for the motions of the heavens. This essay is about circles, as well, albeit the more homely human kind. It’s about racing so far in one direction that you wind up back at the get-go.
All theories have assumptions, all assumptions lead to their own conclusions. Inconsistency is not bad for the sin of pride, it’s bad because it makes you wreck yourself in conversations. Worse is inconsistency with power for reasons that are too obvious to lay out, [Goya etching here], etc.
This blog has recently been focused on the epistemology of mathematics. It has interesting and far-reaching consequences, but it’s often ignored as meaningless specialist nonsense and/or ivory tower shit.
Those consequences are the real interest, and I’ve explicitly stated that the end is modern phenomenology. But to get to [anything modern] you need Kant, to get to Kant you need Hume, to get to Hume you need Idealism, to get Idealism you need Plato.
Platonism (in math) is, essentially, the position that mathematical objects are real. They are as “out there” as a planet is “out there” (just not in space-time, spoiler alert). Because it’s hard to really precise this, here’s (hilariously) an entire appendix of people defining it.
Naive versions of Platonism are astoundingly common when it comes to the epistemology of mathematics. These aren’t “wrong” per se, they just lead to consequences counter to what we tend to want. I’m pretty sure this is because mathematics is secure enough that it’s the very last metaphysical “thing” we want to deny. The denial also leads to tricky questions about the physical sciences, i.e. the point of this series. Thus, we’re a lot more willing to grant ontological primacy to mathematics than we are to, say, “beauty” or “virtue.”
But also: Plato himself is a necessary nightmare to talk about. He’s a great example of why one should read primary sources, because “platonism” is historically sideways. This is bad enough that I have to write two separate articles. This one is on “Platonism.” The next will be on Plato.
When we talk about Platonism now, we’re not actually talking about a 4th century BC philosophical school. We’re talking about a 20th century one. Godel absolutely stomped the early analytic schools, and everyone wandered in a daze looking for a new position. Kind of, this is bad history, don’t @ me. I’m not going to get into that because [long] and [besides the point], but it’s consistent that Godel himself was a devoted Platonist.
It’s quite popular, so note that any criticisms I make will 100% have objections and counter-arguments. Platonism is the plurality position by this survey (PDF) of philosophers. (Q: Abstract objects: Platonism or nominalism? Results: Abstract objects: Platonism 39.3%; nominalism 37.7%; other 23.0%.) Since it says “abstract objects” rather than “mathematical objects”, that probably confounds full-blooded Platonism (“all abstract concepts exist”) with mathematical Platonism (“at least mathematical objects exist”), but I’ve yet to meet someone who thought that the abstract concept “beauty” is real but numbers are not. In other words, that 39.3% almost certainly covers all mathematical Platonists.
If I get around to talking about the analytics (way later), I’m going to have to return to Platonism, i.e. this is incomplete. I’m much more interested in arguments mustered for naturalism on Platonic grounds, both as a personal preference and for subsequent articles. Less in arguing for or against Platonism than in showing some of the consequences, and for those we basically assume it’s true. After all, this series begins with the question: “Why does math work in reality?” and Platonism is an answer to that question. It works because math is real, it doesn’t matter how frail the human mind is, somehow we frailed our way into the Truth of the World, take it and run.
Still, there’s a reason that a shocking number of otherwise-impartial descriptions of modern platonists use phrases like “bite the bullet” to describe their admissions. The consequences of the argument are wild, and for that one actually can turn back to Plato. It matters less whether he himself believed it than it does that he develops some of the results and, even if ironically, these went on to have some super weird consequences.
You might ask why start with Platonism, then. Long story short: [history] happened, modern Platonism is enough like what pre-modern philosophers were responding to that it’s basically fine. There was a long historical bit here, but it’s been banished to an appendix for taking up space without moving the argument forward.
I’ve praised the virtues of careful philosophical argumentation. In an act of stunning hypocrisy, I will now write a very reckless article about Plato and Platonism.
This is because I want to. Continue reading “Platonism without Plato”