@MaliceVidrine: So have you asked your question yet?

No, I sort of thought I might have a way through on my own. As of now I'm not sure if I do, though :p

I'm perhaps overly adverse to asking "unnecessary" questions.

@MaliceVidrine That's not unlike me haha. But usually I spend 100 times as much time trying to figure out the answer myself as the amount of time it takes for Noah or Asaf to give an answer on Math SE or MO.

@user21820 - But maybe if I do it by myself enough I'll develop their powers some day? :P

@MaliceVidrine There seems to be an optimal stopping point.

=P

But it's so hard to tell what it is for each question.

It really is. It's yet another source of my second guessing. Do I just have a stream of ideas that aren't very fruitful, or do I keep giving up on decent ideas too soon? I'm pretty sure one of these is true, but I don't know which.

@MaliceVidrine It's helpful to have a friend to bounce ideas off. Unfortunately, those with aligned interests and background are hard to find too haha..

And my interests keep drawing me to the intersection of New Foundations and topos theory, so basically the tiniest sliver in all of mathematics. I don't usually mind my eccentricity but I may have made a terrible mistake.

I was going to say, and especially so if we're interested in foundations very different from ZFC.

Of course, if I actually asked questions, maybe someone would actually turn out to be interested...

Yours is NF-related. Mine is just something else lol.

I thought you could ask on MO anyway, since I saw Thomas Forster answer some NF-related questions before.

My eccentricity is hardly limited to NF, but that's the one that's on-topic here :P

Heh. What other quirks do you have? If you don't mind telling, of course.

I actually spent a week with Thomas and Randall Holmes not long ago. They're both allergic to the category theory, though.

Hahaha.

Did they say why?

I'm an obsessive rat-fancier, 80% of what I watch is horror movies, I write storylines for roleplaying games that draw equal inspiration from Robert W. Chambers and Douglas Adams, and my bookshelves feature Aleister Crowley about as prominently as they do Peter van Inwagen and Neil Gaiman.

Which is to say nothing of the incompetence with which I handle virtually every social interaction.

They're both very comfortable with and very practiced in traditional model theoretic techniques, so the category theory seems alien to them, I think.

And I think they're skeptical (and perhaps rightly so) that there's anything to say with category theoretic tools that isn't just a rephrasing of the usual model theory.

I see.

Why did you single out Aleister Crowley, Peter van Inwagen and Neil Gaiman?

Just curious.

Aleister Crowley as the more recognizable name of the occult literature I have around; Peter van Inwagen as one of the more recent philosophers I've read most of the works of, while also one with eccentric ontological views; and Gaiman as a more recognizable name among the comic books I have around.

I count them as a reasonably representative cross section of the erratic nature of my library and interests.

That's a rational response. He was a con man and a cult leader at the very least.

Still, wrote some interesting stuff.

Yup. I'm very much a ratio of two integers.

=P

heh

Anyone who thinks Crowley just seems like a real cool dude has some screws loose. For one, he himself said part of the reasons he moved to America later in his life was to avoid the allegations a young woman made against him... And knowing him, I don't particularly doubt the allegations.

So now you know why I asked; people don't normally say that a person X features on their bookshelves unless they like X.

Insofar as I can separate the writings from the person, I like his writings. I don't typically have an opinion about the character of authors I read, unless I think they might have enough of a platform to cause people harm.

@user21820 - Btw, here's the question I was thinking about asking (with the topos-theory, reference-request, soft-question, and intuition tags) math.meta.stackexchange.com/a/4726/102781

@MaliceVidrine I suppose it's a fine question, though as I said it's way outside my area.

I will, then, take "not obviously terrible" as enough of an excuse to post it :P

Though probably someone will still ask you to mention the particular coherent theory you have in mind.

Yeah, I just want to delay all the typing as long as possible. It's not a particularly complicated theory, but all of my expository efforts came out really long-winded.

Essentially it's the theory of (a coherent formulation of) extensionality, with a group of set-like permutations $f_{g,n}$ where $g$ is an element of some fixed metatheoretic group, and $n$ is a natural number.

In a language where $\notin$ is a primitive predicate symbol along with $\in$.

@MaliceVidrine What's the n for?

For any $n$, $f_{g,n+1}(x)$ is axiomatized so as to be the image of $x$ under $f_{g,n}$. So $f_{g,n}$ is "apply $f_{g,0}$ to everything $n$ steps down into the membership structure"

It's a device needed to make sure the permutations respect the membership structure in the appropriate way, in the context of a language that can't actually express the comprehension instances needed for taking images of functions.

(or at least I think it's needed. I wasn't able to think of a way around it.)

I think the actual axioms would be clearer, but if you do write them you might as well include it in your post haha..

Yep. It's very specifically motivated by an NF thing, which is almost logically equivalent with being difficult to understand.

Ugh. Wannabe smart-arses who don't want to say "any object" or "anything" because we don't know what "thing" or "object" mean.

It's a good thing I am not the autocratic ruler of m.se, because I would ban for that sort of thing :P