Platonism without Plato


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”

On a Particularly Difficult Question

coming from here


Let’s start this with an obvious question: “Why are you so concerned with math?”

It has to be answered for any description to make sense. Looking back, it does appear that my interest is just because of Kant’s interest. No, and:

It’s not good that our root instinct is a lazy Cartesian skepticism, but it does make my job easier. That was something earlier writers had to inflict; it being the default lets us move quicker.

Ask a college kid what Truth capital T is and they’ve already absorbed the right lessons: truth is a construct determined by your culture’s valuations and epistemic suppositions, therefore we’ll never be able to actually arrive at the Truth. “It’s subjective.” Moreover, logic is dependent on language, which is dependent on culture; reason needs categories to manipulate, which are dependent on [relative thing]; trying to interpret the empirical world is a problem because you can never step outside yourself, data isn’t “there,” it must be uncovered, hence the flaws of naive science.

I say this like I’m mocking the arguments, but I do really mean this is the correct way to start. Not only are we in the cave, that cave is in a metacave. Don’t trust yourself to trust the outside world, reason splinters out of a bunch of psychological flaws and biases, inner fickledom influences outer fickledom, there is a great gnashing of teeth.

Nietzsche, who I will quote this once and then avoid until [distant post]:

Once upon a time, in some out of the way corner of that universe which is dispersed into numberless twinkling solar systems, there was a star upon which clever beasts invented knowing. That was the most arrogant and mendacious minute of “world history,” but nevertheless, it was only a minute. After nature had drawn a few breaths, the star cooled and congealed, and the clever beasts had to die.

One might invent such a fable, and yet he still would not have adequately illustrated how miserable, how shadowy and transient, how aimless and arbitrary the human intellect looks within nature.

We should be extremely skeptical that the human intellect can touch on anything True, much less even vaguely functional. I do mean that as a starting point: get as deep into skepticism as you can, or else what follows won’t be as baffling as it should be.

If human reason were worth a damn, there would be no question about the status of math. Only in light of its complete and total vapidity do we realize how baffling it is that Leibniz can think about geometry real hard, Maxwell can apply that hard thinking, and now we have computers. Continue reading “On a Particularly Difficult Question”

Aeon Piece

Old readers: I have a short essay in Aeon:

Whence comes nihilism, the uncanniest of all guests?

It’s something like a condensed version of the Uruk Series, and much shorter than most essays here. (I didn’t ditch this blog for other publications; I’m working on them, more posts here in a few days.)

People coming from Aeon: Hi. Thanks for reading. The Aeon essay is (kind of) a condensed form of a series I wrote here (the index of which is here), and a few odds and ends.

The most relevant pieces are this one on Seeing Like a State, this on Karl Polanyi, and this on gri-gri. All of those are much longer than the Aeon piece (and my tone is less neutral). Eventually it goes into Eric Hoffer, Christopher Lasch, and some other stuff.

I haven’t addressed Nietzsche very explicitly (although I mention him at the end of the series), nor differing conceptions of nihilism. I plan to in the future. Sorry.

At the moment, I’m writing a new series. It’s about Kant and mathematics, and how that leads into early phenomenology. The first post is here. It will likely make people with different philosophical commitments angry.

I feel like people are going to ask this, so: Qohelet’s Ossuary is intended to be a list of quotes pulled from history books. I’ve been bad about updating it.

My email is luukeep at if anyone has questions.

Euthyphro Dilemmas as Mathematical Objects

introduction to series ii


introduction to series ii


This blog has recently been grasping at the notion of values, either directly or by reference to nihilism. I’ve mostly failed, because I need vocabulary that I don’t really have, because the question isn’t really the question it looks like. This is an oldnew question, in precisely the way that most things are oldnew questions.

This is the old form of it: Socrates asks Meno what virtue is. Meno, reasonably, replies with a list of actions that are good things to do. Socrates, reasonably, answers that there must be some essence of “virtue” that connects all of these things, a value or judgment or faculty of judgment that determines the “good” from the “bad.”

No one can figure it out, which leads to the Meno problem. The Meno problem is this:

A man cannot search either for what he knows or for what he does not know. He cannot search for what he knows–since he knows it, there is no need to search–nor for what he does not know, for he does not know what to look for.

So, it seems that knowing virtue is impossible. Socrates then leading-questions a slave boy into doing geometry, which proves something about inborn knowledge, and Socrates suggests that knowing things maybe comes from reincarnation. Kind of. Either way, knowledge of “virtue” is, at least plausibly, as objectively valid as mathematics. To really drive the point home, Socrates relays a series of poetic invocations of the gods and tells a myth about the afterlife. Meno asks him how true any of that is, and Socrates responds by saying “Eh.” and also “We’ll be better men if we think it is, because it will make us brave enough to question things.”

This is really weird. It’s not obvious that math is anything like virtue. Moreover, it’s not clear that math is itself objective, which is underlined by the fact that it’s reliant on a mythical interpretation that presupposes its own existence. Finally, Socrates forces acquiescence by calling it “better” to believe in true knowledge, but the point about not knowing about knowing is that it means you can’t tell what’s “better” and what’s “worse.”

Plato is a motherfucker, he does have a point, I’m ignoring it, moving on. Continue reading “Euthyphro Dilemmas as Mathematical Objects”

Links and Thanks


I don’t really do links pages. I did one, once, but decided against continuing it. The links that I’d post are directly taken from links pages of other blogs, which feels more than a little parasitic.

Instead, I’ll post an annual list of my favorite articles. Since it’s hard to remember all of the articles of the past year, there’s no possible way this is fully accurate, which really makes this a list of articles that left a lasting impression. It’s by no means fair or objective; most of these are personal reading habits that I’m pretty sure a lot of my readers share.

This is also not in any order. I’ll limit myself to twelve, because there are twelve months in the year and twelve is the superior number. Continue reading “Links and Thanks”

Banish Plump Mouse Deer and Banish All the World

on new atheism, kind of; this one might actually get me in trouble


epistemic status: pretty sure about some parts, very uncertain but leaning towards “likely” in others


People have been talking about the new atheists again.

A. Leo Oppenheim, Ancient Mesopotamia:

The cuneiform documents of the end of the second millenium and the first half of the first millenium B.C. contain a number of isolated indications which, taken together, reveal that a small number of old and important cities enjoyed certain privileges and exemptions with respect to the king and his power. They apparently had legal status which differed in essential points from that of any other community. In Bablyonia, these cities were Nippur, Babylon, and Sippar; in Assyria, the old capital Assur and, later, Harran in Upper Mesopotamia. In principle, the inhabitants of these “free cities” claimed with more or less success, depending on the political situation, freedom from corvee work, freedom from military service […], as well as a tax exemption which we are not able to define in specific terms.  […]

The privileges of the inhabitants of these cities were under divine protection. Their legal status was referred to as the kidinnūtu (“status of being under the aegis of the kidinnu,” probably some kind of standard) […]

Revealing the status of these privileged city-dwellers is a passage in the ritual texts describing the ceremonies performed during the New Year’s festival in Babylon. On that occasion, the king was permitted to enter the innermost sanctuary, but he could do this only after the high priest had taken from him all the insignia and indumentaria of kingship and humiliated him by slapping his face and pulling his ears.

If an atheist appeared in Sippar, how would they be perceived? Let’s say they’re materially all-in with the Sipparians: hates Nebuchadnezzar, wants Sippar to be truly free, sees the state religion as merely one obstacle to that end. Maybe that’s not even a big deal, it’s just some small part of the general ideology, “I mostly care about economic concerns, but sure, atheism is a part of that.”

Would you, a Sipparian, perceive them as: a) a true friend to the kidinnutu; b) an agent of the king looking for material gain? Continue reading “Banish Plump Mouse Deer and Banish All the World”

Notes on Values


coming from here, but much more abstract. epistemic: mostly endorsed, but kind of vague and occasionally overgeneralizes


Values get used as axioms in debates, shorthand in conversation, symbols of judgment. x is bad because y because that leads to idleness, x is bad because y which is basically docetism, x is the worst because y was Hitler.

The problem with Godwin’ing is that it’s too blunt, but the underlying concept is genuinely desirable. It’s inefficient to restate every axiom; one wants to reduce the conversation to shared values and move on. Often we sense that something is bad, and then later justify that by a more socially known value. Hence, my description of them as organizational tools. We categorize and argue based by moving backwards towards a common term.

What these are is trickier. “People just want safety, food, comfort, a good place to raise our family.” True, but also true of badgers. None of those are high enough to resolve most of our problems.

Smart phones are bad because they distract you from x, but that x isn’t an easy nod at Maslow’s lower levels. People aren’t forgetting to eat over Instagram, if not simply because they need to take their foodie pics. “Distraction is bad” for reasons that don’t apply to mustelids. According to [newspapers] that’s political, as in “distracted right to the voting booth with a MAGA hat.” That’s not an accident.

Older norms are gone (religious, etc.), and our nice, “ethical” platitudes collapse on themselves here: “Do what you love!” But what if I love gorging on snapchat? “You only live once, enjoy it!” If I genuinely like spending all my time on facebook, then shouldn’t I be doing exactly that? Hence, Trump. Politics are the last high value high enough to answer the question. It’s the highest organizational tool we have (we have a vague metaphysic of “truth”; connecting these is for a longer piece) that’ll respond to this kind of concern.

See also: aesthetics. “They’re subjective.” They definitely aren’t, at least not how you mean that, but whatever. I can’t think of a single “important” (read: good) work of culture that wasn’t “important” (read: ingroup politics) in direct proportion to its political content. If it gets slammed, then it failed to live up to those. One googles: “We need to talk about [artist]” and 9/10 the top hit is a problematic list of problematics. Someone is going to start screaming about the academy awards and diversity ignoring the quality of the art, and fair. But the right does this too, e.g. “I loved American Sniper!” It’s probably unfair to judge a nation by the ineptitude of its propaganda, but…

I’m not trying to be obtuse, art has political content, duh, clear, mind blown. That doesn’t change that fact that political content is often the least interesting aspect of art, and English departments reading more theory than English is almost certainly the third seal pretending to be a “deep, compelling” look at the seventh. It’s neither deep nor compelling, it’s lazy and obvious. A fucking eighth grader could tell you that “there are some themes of gender in Hemingway”, why do you need a bungled continental to do the same?

See also: science. Continue reading “Notes on Values”