Want to wade into the snowy surf of the abyss? Have a sneer percolating in your system but not enough time/energy to make a whole post about it? Go forth and be mid: Welcome to the Stubsack, your first port of call for learning fresh Awful youāll near-instantly regret.
Any awful.systems sub may be subsneered in this subthread, techtakes or no.
If your sneer seems higher quality than you thought, feel free to cutānāpaste it into its own post ā thereās no quota for posting and the bar really isnāt that high.
The post Xitter web has spawned soo many āesotericā right wing freaks, but thereās no appropriate sneer-space for them. Iām talking redscare-ish, reality challenged āculture criticsā who write about everything but understand nothing. Iām talking about reply-guys who make the same 6 tweets about the same 3 subjects. Theyāre inescapable at this point, yet I donāt see them mocked (as much as they should be)
Like, there was one dude a while back who insisted that women couldnāt be surgeons because they didnāt believe in the moon or in stars? I think each and every one of these guys is uniquely fucked up and if I canāt escape them, I would love to sneer at them.
(Credit and/or blame to David Gerard for starting this. Merry Christmas, happy Hannukah, and happy holidays in general!)
We have a new odium symposium episode. This week we talk about Ayn Rand, who turned out to be much much more loathsome than i expected.
available everywhere (see www.odiumsymposium.com). patreon episode link: https://www.patreon.com/posts/haters-v-ayn-146272391
Iām pretty sure that Atlas Shrugged is actually just cursed and nobody has ever finished it. John Galtās speech gets two pages longer whenever you finish one.
And I think the challenge with engaging with Rand as a fiction author is that, put bluntly, she is bad at writing fiction. The characters and their world donāt make any sense outside of the allegorical role they play in her moral and political philosophy, which means youāre not so much reading a good story with thought behind it as much as itās a philosophical treatise that happens in the form of dialogue. Itās a story in the same way that Platoās Republic is a story, but the Republic can actually benefit from understanding the context of the different speakers at least as a historical text.
Catching up and I want to leave a Gƶdel comment. First, correct usage of Gƶdelās Incompleteness! Indeed, we canāt write down a finite set of rules that tells us what is true about the world; we canāt even do it for natural numbers, which is Tarskiās Undefinability. These are all instances of the same theorem, Lawvereās Fixed-Point. Cantorās theorem is another instance of Lawvereās theorem too. In my framing, previously, on Awful, postmodernism in mathematics was a movement from 1880 to 1970 characterized by finding individual instances of Lawvereās theorem. This all deeply undermines Randās Objectivism by showing that either it must be uselessly simple and unable to deal with real-world scenarios or it must be so complex that it must have incompleteness and paradoxes that cannot be mechanically resolved.
Ok, lot to respond to here. Iām familiar with the relevant mathematics.
First, I think itās clear from the litany of failed attempts that you canāt write down a finite set of rules that tells us what is true about the world. At least to me, itās also intuitively clear that you canāt write down such a set of rules. That is not, without considerable auxiliary claims at least, a consequence of gƶdelās incompleteness theorem, nor does gƶdelās incompleteness theorem follow from it.
The essential issue here is that the incompleteness theorem deals with formal statements and formal reasoning in formal languages. There is a significant gap between the perfectly acceptable reasoning we use every day to understand the world around us, which if it can be written down at all often requires us to use informal language, and the sort of thing the incompleteness theorem addresses. There are real philosophical claims to be made and argued, which in at least implicit form go far back and have yet to be pinned down. For example, the sorites paradox can be understood as an (informal) proof that induction can fail in informal arguments. The whole thing, rather than being clarified, becomes more and more hopelessly complex the more one thinks about it.
I agree that inasmuch as objectivism pretends to formality it makes itself vulnerable to mathematical theorems, and surely would evaporate on contact with them. But the failure of the pretense to formality itself renders the issue moot.
Second, the question of what is or is not a āconsequenceā of this or that theorem is, given the nature of implication, a little difficult to pin down in borderline cases (are not all theorems a consequence of āT -> Tā?). Iām perfectly fine with calling cantorās theorem, the halting theorem, the incompleteness theorem, etc instances of lawvereās fixed point theorem. But there is significant work required to take the hypotheses of some of these types of theorems and maneuver things into such a position as to apply the FPT. So I donāt think itās a consensus opinion.
Third, if we want to describe a postmodern movement in mathematics, while Iām not sure about the dates, I get what youāre going for and it makes sense to me. But I think the description youāre putting forth here gives way too much weight to theorems. The movement toward a post-modern sensibility is imo much more marked by a movement toward guiltlessly abstract definitions and axioms. Consider the centuries of the torment that mathematicians experienced trying to justify or explain what negative numbers or complex numbers really are. In contrast, in the 20th century one has the definition of a scheme in algebraic geometry, a kind of space characterized by functions on it which are not really functions and which can be 0 at every point and yet not the zero function. What is the meaning of such a thing? Well, it is up to the individual mathematician to accept their own metaphors explaining that matter. Totally unthinkable a century prior. Examples of this sort of thing abound (for example, test functions in functional analysis). The movement toward such things was doubtless urged on by the impossibility theorems you refer to but goes far beyond them and is far more impactful imo.