The h Bar

@heather Unless you can raise a human being in complete cultural isolation and still have them be able to communicate with us, I do not see how you could assess what we think "naturally" about that, nor why you would characterize these beliefs as "knowing"

Bernardo Meurer

@ACuriousMind Not a, but a few. You can't assume they'd all come up with the same ideas I guess

heather

i'm trying to think of how to phrase what i mean.

Bernardo Meurer

I have doubts whether phrasing is the problem

ACuriousMind

@BernardoMeurer Well, the notion that there would be a "natural" human predisposition implies they'd all say the same :P In any case that is impractical even as a thought experiment, so little point in nitpicking it

Bernardo Meurer

@ACuriousMind Ah, I was about to suggest we stole some babies

Okay :P

heather

12:06 AM

"a set of morals that does not change over time, is not dependent on a specific study or idea, [and something]"

0celouvskyopoulo7

No need to steal them.

Go to an orphanage

They will gladly give them

Bernardo Meurer

@heather How the hell do you have a set of morals not dependent on ideas?

0celouvskyopoulo7

what are we even on about?

ACuriousMind

@0celouvskyopoulo7 Are you suggesting we make them? ::dons mad scientist goggles, then remembers no mad science is needed for that::

Bernardo Meurer

My children will run Linux

heather

12:07 AM

that was bad as well, crud, let me try again.

"a set of morals that does not change over time [and something]"

Bernardo Meurer

@heather So you want divine law?

ACuriousMind

So, we're looking for eigenstates of the moral Hamiltonian?

Bernardo Meurer

lol

heather

@Bernardo the problem with that is there needs to be one more condition.

0celouvskyopoulo7

Honestly, if you don't believe in god what is your moral barometer?

How do you know not to kill people

Bernardo Meurer

12:08 AM

@0celouvskyopoulo7 Hulk Hogan

0celouvskyopoulo7

Truly baffling

ACuriousMind

@0celouvskyopoulo7 I don't have one, I use a moral thermometer. Much better.

Bernardo Meurer

I use Linux's morald system daemon :)

Anonymous

@BernardoMeurer Na, they will know the benefits of using proprietary malware.

0celouvskyopoulo7

@ACuriousMind Btw, why is "F*k JEE, etc." allowed on the starboard?

Bernardo Meurer

12:09 AM

@blue If my kids even install Windows I will give them away

heather

@0celouvskyopoulo7 thank you, that is the point I'm trying to get across.

ACuriousMind

@BernardoMeurer There's a delightful ambiguity there where you don't specifiy whether the OS runs on them or on their computers.

Bernardo Meurer

@heather Your WHOLE point is that Fuck shouldn't be allowed on the starboard?!

heather

@Bernardo lol, no, I edited

0celouvskyopoulo7

@BernardoMeurer if I can get banned for a month for insulting JEE, can we please be fucking consistent

heather

12:10 AM

I realized too late what that looked like.

0celouvskyopoulo7

@heather I was trolling

Oops

heather

::shrugs:: fair enough.

Bernardo Meurer

@heather I was about to tell you he was being obnoxious

0celouvskyopoulo7

Maybe you should look up Universally Preferable Behavior

heather

should I really @0celouvskyopoulo7, or are you still trolling?

0celouvskyopoulo7

12:12 AM

I am always trolling to some extent, but I actually recommend it.

@ACuriousMind Merci.

ACuriousMind

@heather It's not a point. How would a belief in god make anything better?

Mostafa

@BernardoMeurer eh, before I leave (4:40AM); I've had this "ethics and religion" discussion a thousand times with people with various point of views. To summarize: you'd have a very hard time defining ethical action without a God.

ACuriousMind

Why is believing in a god from which a set of morals derive any better than just directly believing in the moral system itself?

Mostafa

@ACuriousMind How are you going to derive a moral system yourself?

ACuriousMind

If your concern is "legitimacy", you've just shifted the question why that god is legitimate

heather

12:14 AM

@ACuriousMind because a God can create an absolutely legitimate moral system as I mean it.

0celouvskyopoulo7

@heather Basically, UPB boils down everything to violence. They also make a distinction between morals and ethics (maybe). I don't understand the details, but the basis makes sense.

And the author is 100% atheist.

heather

because God is by definition all-knowing and perfect @ACuriousMind

ACuriousMind

@Mostafa I never claimed moral systems can be derived.

Anonymous

@heather Heh, that's funny. I don't believe in God but I do have a moral "barometer" so as to say. I don't see the use of "God" here.

ACuriousMind

@heather So I define my moral system to be perfect. Problem solved, I guess?

Bernardo Meurer

12:14 AM

@Mostafa God can't actually talk to people, so fundamentally it's all the same

Kant manages it nicely without a God AFAIK

Mostafa

@ACuriousMind define.

Bernardo Meurer

Categorical imperative and so on

heather

@ACuriousMind but how can you say that if you yourself are not perfect?

0celouvskyopoulo7

@blue A religious moralist would argue that your moral barometer is inherited from society, and society inherited its from religion.

ACuriousMind

@heather How can I say it of god, either?

0celouvskyopoulo7

12:15 AM

It's a good argument.

But let's not pretend that any of the religions are perfect.

In fact, what the hell is this conversation about?

Anonymous

@0celouvskyopoulo7 Not really. Many of the things that my society considers as a sin isn't a sin according to me.

Bernardo Meurer

We should just inherit our morals from Kanye

Because he is perfect

heather

@ACuriousMind I'm considering a God who is by definition perfect - I guess I'm considering the Christian God here, but most gods are considered perfect by their believers.

0celouvskyopoulo7

@blue But the things you consider sins are also considered sins by society, presumably.

Any person can have looser morals, sure.

ACuriousMind

@heather Well, but if you say that I cannot say that my moral system is perfect by definition because I am not, then why would I be able to say it of god?

heather

12:17 AM

ah, I see what you're saying. because I'm not perfect, how do I know if God is perfect?

Bernardo Meurer

THIS IS ALL SET THEORY

0celouvskyopoulo7

God is by definition perfect

God is a closed set and has no isolated points

ACuriousMind

@heather That's...not really what I'm saying, I'm just turning your argument back on you, but yes.

0celouvskyopoulo7

@BernardoMeurer No, it is topology

Anonymous

@0celouvskyopoulo7 Yeah, but you can't say I derived them from the society. My principle is rather simple. Anything that is directly or indirectly harmful to someone else is immoral according to me. I try to minimize the immoral acts that I commit.

0celouvskyopoulo7

12:19 AM

@blue That principle is at the core of society. Don't say you came up with it on your own.

Anonymous

According to me there's nothing like "perfectly moral"

Mostafa

@ACuriousMind The problem here is how and based on what assumptions you define ethics.

ACuriousMind

@blue The question of what the proper "minimization" looks like is the eternal utilitarian's quest for the correct utility function. You've just hidden your entire moral system in the "weighting of harm", so to speak.

0celouvskyopoulo7

And that's a terrible principle, how are you supposed to get ahead in life?

heather

@ACuriousMind hmm. Well, I could argue specifically to the Christian God and how He says that He is perfect and how I believe that that message has been accurately passed to us, but I don't think that really answers your question. I admit my definitions are bad, but I still believe an absolutely legitimate moral system can exist - I also disagree with Bernardo's system still. So I suppose I need to do more reading =)

0celouvskyopoulo7

12:20 AM

"Harmful" is too vague.

What is @BernardoMeurer 's system?

Bernardo Meurer

@0celouvskyopoulo7 Type theory

0celouvskyopoulo7

is that some CS thing?

Bernardo Meurer

:^)

heather

@0celouvskyopoulo7 Bernardo's is that of a societal contract we collectively agree too - so sort of a democratically created moral code. He agreed that his system cannot be absolutely legitimate, but he disagrees that there is such a thing as an absolutely legitimate system.

ACuriousMind

@heather Well, until you define "absolutely legitimate moral system" I can neither refute nor affirm that belief :P

Anonymous

12:21 AM

@0celouvskyopoulo7 Maybe. But again I don't see the role of God and Religion here. It may be "derived" but is definitely not the same system that religious people follow. Anyone who is isolated from the society can also come up with a similar moral code just by logical thinking.

heather

@ACuriousMind xD yeah, I'm trying too, like I said, my definitions are terrible. I don't know how to convey my meaning rigorously and non-vaguely.

0celouvskyopoulo7

@blue I am not arguing that God has anything to do with anything, because I don't believe in a God. But I do believe that religion plays a role in morality because the basic rules we are taught as children come from religion.

heather

anyway, I've got to go for a little bit, i'm going to eat dinner.

Secret

Horizon: A 4D Video Game (ITP Thesis Show 2014)

►

what it would be like to walk in a direction that is of mixed time and space coordinates

ACuriousMind

I personally think that there is no "rigorous" ethics in the sense you're probably looking for, which is what I'm getting at with my requests to define your terms.

Anonymous

12:25 AM

@0celouvskyopoulo7 I disagree. Even irreligious societies have a moral code. For example- China. (en.wikipedia.org/wiki/Irreligion_in_China)

0celouvskyopoulo7

For thousands of years China was religious.

A person does not have to be religious to be influenced by religion.

ACuriousMind

@0celouvskyopoulo7 "the basic rules we are taught as children come from religion" - highly debatable, as you'll find many directions of moral philosophy also e.g. in ancient Greek moral philosophy where I'd have trouble showing definite religious origin. The record is probably distorted by both believers and non-believers to make it fit their narrative. You'd need very careful examination of historical evidence, of which I'm not even sure it exists, to establish that claim.

0celouvskyopoulo7

@ACuriousMind In modern western society?

Mostafa

Why do you need to define a moral code in the first place? If you don't believe in God (and nothing further than the physical world), then you can define whatever system of ethics you like.

ACuriousMind

And even then, you could still not exclude the existence of prior non-religious moral codes of which just no record survived beyond their traces in the religious moral codes. It's pretty hard to make that claim with any sort of confidence, I'd say.

0celouvskyopoulo7

12:31 AM

@ACuriousMind I never claimed that religion is the source of morals. It's a tool in delivering them.

ACuriousMind

@Mostafa Kant, Bentham, Rawls and basically every other moral philosopher would like a word with you (unless you mean "can" in the sense of "are able to", in which case you are trivially correct even in the case a god exists :P)

@0celouvskyopoulo7 Then I have misunderstood your claim entirely

0celouvskyopoulo7

@ACuriousMind That's ok.

@ACuriousMind I tried reading Lurie's "Higer Topos Theory"

Didn't get past page 2

ACuriousMind

If that's the thing I'm thinking of, I don't think I got much further :D

0celouvskyopoulo7

I was on nLab and they referenced it

I mistakenly thought it would be helpful

Anonymous

12:48 AM

@ACuriousMind I had a something to ask you: Is it necessary to learn German language on a visit to Germany or does the average population more or less understand English? ( I was thinking of applying to Germany for a research internship next summer).

ACuriousMind

@blue Most Germans will be able to communicate with you in (possibly broken or horribly pronounced) English, though the ability to do so is inversely correlated with age in my experience.

In fact, I know several foreign students who are a bit upset about the Germans switching to English once they realize the other person speaks that better, so they get little chance to practice their German :P

Anonymous

@ACuriousMind Oh I see. Hehe. Thanks :)

Anonymous

The German words sound really classy though. I'd love to learn the language someday.

Mostafa

1:16 AM

@blue The German words sound really classy though. are you sure you don't have French (or any other language) in mind?!

@ACuriousMind Can you pronounce backpfeifengesicht? Is that "p" after "back" really necessary?!

Avantgarde

^

You want classy? Try Urdu. I am yet to find a language classier than that

ACuriousMind

@Mostafa Yes and yes (although you might find that many speakers indeed pronounce the p only weakly or not at all, it's clearly there in Standard German)

Mostafa

@Avantgarde Urdu should have a lot of words in common with Persian, right?

0celouvskyopoulo7

@ACuriousMind can confirm

Avantgarde

@Mostafa I would think so. Urdu is very similar to Hindi. Maybe some Urdu words have Persian roots.

Probably even Arabic

Mostafa

1:21 AM

@Avantgarde you know what Chai means?

Avantgarde

Yeah. Tea

Mostafa

@Avantgarde :)

Avantgarde

@Mostafa How do you know about chai? Were you testing my Hindi/Urdu? :P

Mostafa

@Avantgarde In Persian it's chai too

Avantgarde

@Mostafa Ah, I see. Probably one of the many commonalities

Just win baby

1:26 AM

but is it made the same?

Avantgarde

Mostly no

ACuriousMind

@Avantgarde Wait, so people ordering "Chai tea" are drinking "tea tea"?

Great.

Avantgarde

^exactly

Mostafa

@Avantgarde Persian literature and poems are full of adventures about India (and even China. basically, countries on the silk road; but mostly India)

0celouvskyopoulo7

God, actually writing down diffeomorphisms and proving they are so is a pain in the butt

Mostafa

1:28 AM

Even the architecture is very similar

rob

@ACuriousMind Frequently people pay for their chai tea using cash money they got by typing their PIN number into an ATM machine.

Just win baby

After last and final call :-)

Avantgarde

@Mostafa I see. Very interesting. There are certainly quite a few Persian influences in Indian culture. Apart from language, food is another aspect

ACuriousMind

@rob In the age of digital payment, I'm not sure "cash money" really is a duplication, but nicely done ;P

Just win baby

Bit coin?

rob

1:31 AM

Some people might use digital e-currency

Avantgarde

@Mostafa And I recently discovered that a musical instrument (Santoor) is known in Iran too. Not sure how popular it is there, though.

Mostafa

@Avantgarde Yeah very popular actually

Avantgarde

@Mostafa I see. I watched a video of Persian santoor (or santur?) being played. The instrument looks the same, but has a sound different than the one in India

Yes, that one

Mostafa

The Persian variant is apparently written as Santur in English

en.wikipedia.org/wiki/…

Its sound^

Avantgarde

Yep. It's got a different sound than the Indian one, but good, nonetheless

Mostafa

1:38 AM

This one is more clear (same music):

fa.wikipedia.org/wiki/…

Avantgarde

I agree about the architecture too

Mostafa

This is almost entirely Santur^

@Avantgarde Yeah for example Taj Mahal

Avantgarde

Yeah

This is the Indian version:
https://youtu.be/_udbwA6uIA0

2

Mostafa

@Avantgarde ♥‿♥

Avantgarde

I really don't like tea though

Just win baby

1:46 AM

Coffee?

Avantgarde

I like coffee yeah

Mostafa

@Avantgarde Taj Mahal is really crazy!!

Just win baby

They were going to build a duplicate out of black marble.

Mostafa

There are many similar mosques in Iran (although mostly are not as good as Taj Mahal IMO)

0celouvskyopoulo7

@ACuriousMind Ah, genius!

Avantgarde

1:50 AM

@Mostafa I visited it long ago, I vaguely remember the details. It has the architecture similar to that of a mosque, but it's not a mosque. It's a mausoleum.

Mostafa

@Avantgarde Yeah I meant the architecture

I like the pictures taken from the interior (especially the dome)

Just win baby

en.wikipedia.org/wiki/Black_Taj_Mahal?wprov=sfsi1

Mostafa

@Justwinbaby Didn't know that!!

This is a mosque in Isfahan, for example:

Interior of the dome

Avantgarde

very elaborate

Mostafa

@Avantgarde Exactly!!

0celouvskyopoulo7

1:58 AM

@ACuriousMind I had forgotten about the backwards triangle inequality

Just win baby

@Mostafa in today's world that would amount to Obama building a Black House.

Mostafa

@Justwinbaby :-)

Just win baby

;-)

Mostafa

@Justwinbaby Trump' s already built his Taj Mahal:

Trump Taj Mahal

Trump Taj Mahal is a closed casino and hotel on the Boardwalk in Atlantic City, New Jersey, United States, owned by Trump Entertainment Resorts, a subsidiary of Icahn Enterprises. Hard Rock International and other investors announced plans in March 2017 to purchase the property and convert it into the Hard Rock Hotel & Casino Atlantic City. The casino was inaugurated by its then-owner Donald Trump in 1990, and was built at a total cost of nearly one billion dollars. Restaurants at the Taj included Dynasty, Il Mulino New York, Moon at Dynasty, Robert's Steakhouse, and Hard Rock Cafe. It was also...

Avantgarde

:P

0celouvskyopoulo7

2:03 AM

@ACuriousMind is using $\mathfrak T$ for a set a sin?

Just win baby

Next he'll turn the White House into a hotel & casino

Avantgarde

lol

Mostafa

Why is the room in slow motion

Just win baby

In what sense is nonstandard notation a sin? @0celouvskyopoulo7

Unless its ambiguous :P

0celouvskyopoulo7

2:37 AM

it's not nonstandard

I just need another $T$

I don't really like $\mathcal T$

Secret

3:23 AM

> However, from the way things are looking like right now, that bigger theory is likely to be even weirder than QM, and it is likely to force you to give up principles that we hold even more tightly than locality and realism, such as the possibility to set up independent experiments in different places

But the moment this is allowed, we cannot have replicable experiments anymore, not unless it is carried out in the same region and same conditions

Just win baby

5:42 AM

Hi @dmckee how goes the job hunt?

Mithrandir24601

7:40 AM

@BernardoMeurer "this sort of blatant immorality is marked as such" because it was the Bible (in the West anyway) that declared it 'blatant immorality' in at least a large number of cases. In other, general, words - it was considered a sin (regardless of whether it still is or not) and so it was considered 'immoral' and is still considered 'immoral'. Also, I've got to make the argument that gluttony's the very problem we're having with wealth distribution. Also: CONTEXT

Just win baby

chill out

Mithrandir24601

@ACuriousMind And if you define your moral system to be perfect, you're pretty much implying that you're perfect... I believe this is an extreme version of 'arrogance' :P

@Justwinbaby If that's directed at me, I am chilled out - just yelling 'context' because it's important and I watch Matt Easton's videos a lot (if you've never watched that, he says 'context' a lot and it gets ingrained pretty easily)

Slereah

8:10 AM

Is there a notation for the component of $O(n)$ that isn't connected to the identity?

Kenshin

8:54 AM

With regards to morality, there is no such thing as "right" and "wrong"

There is only individuals who experience emotions. If an individual feels bad when someone hits them, they define being hit as being "wrong". But really it isn't "wrong" to hit someone, but rather merely people don't like it when they get hit.

So they come up with this standard of "right" and "wrong" to ensure they and their loved ones don't get hit

Believing in "right" and "wrong" is an illusion

Slereah

The signature $(+---)$ is objectively wrong

Sorry particle physicists

Kenshin

9:40 AM

why is it tho

Shing

9:54 AM

Any people fluent at cosmology here?

Kenshin

yeah

basically cosmology = hubble's law

John Rennie

@Shing we are a bit short of cosmologists at the moment, but ask your question anyway and someone who knows the answer might see it.

Shing

@JohnRennie I remember a talk from MIT saying that entropy seems to decrease when it comes to gravity in universe (say, star forming). Not sure if it is a research topic nowadays, or just I got something wrong.

Kenshin

Entropy doesn't really apply on the cosmological scale in my opinion

Shing

@Kenshin Why?

John Rennie

10:07 AM

@Shing when a star forms you start with a high entropy dilute gas, and you end up with a much lower entropy compressed in the star. So yes the entropy of the gas forming the star does decrease.

But ...

Kenshin

@Shing why would it apply? If I have a planet orbiting a sun, why would entropy increase in this system?

Entropy assumes particles are random, and this is a nice approximation when looking at many small particles, but the truth is the universe isn't random

John Rennie

That's because as the gas falls inwards it gets hotter, and it has to shed that heat or it won't be able to form the star. It sheds the heat by radiating photons, and those photons also have an entropy.

If you want to calculate the total energy change you need to add the entropy of the star and the entropy of all the photons it has emitted while it was forming, and if you do that you find that the total entropy has increased not decreased.

Shing

here is the talk: techtv.mit.edu/videos/16282-the-second-law-and-cosmology

Thanks for explaining

Kenshin

10:29 AM

np

Slereah

11:02 AM

@BalarkaSen Is the set of diffeomorphisms equal to the set of all smooth automorphisms on a manifold

Balarka Sen

@Slereah What is an automorphism of a manifold?

To me automorphism by definition is a self-diffeomorphism

Slereah

Is that because a homeomorphism wouldn't preserve the smooth structure?

Hence not an automorphism

Balarka Sen

You said "smooth automorphism", so, yes.

Homeo(M) and Diffeo(M) has vastly different topology in general, I suspect.

Slereah

I guess the problem is that "automorphism" is only defined up to a structure

So automorphism would be Homeo for topological manifolds but diffeo for smooth ones

Balarka Sen

Yes, it depends on what category you are in. In the TOP category, an isomorphism of manifolds is homeomorphism (hence, automorphism is self homeomorphism), in DIFF category an isomorphism of manifolds is a diffeomorphism, etc etc

in PL category an isomorphism of manifolds is a PLeomorphism

Slereah

11:09 AM

Is that where the plesiosaurs live

Balarka Sen

Probably.

Slereah

11:20 AM

Is $\Bbb R^0 = \{ x \}$ a definition or is there a way to prove it?

ACuriousMind

@Slereah In what category are you taking that product? The empty product is always the terminal object (which can be proved from the universal property of the product).

Slereah

@ACuriousMind You know me and categories

I'm more of a set theory guy

John Doe

Hi all

Slereah

11:38 AM

I can make 3D plots in latex now

Shing

Hi there

Slereah

I'm gonna make a cover for the book

With a fancy spacetime grid

Shing

Make 3D plots in Latex? So we can even plot with Latex?

Slereah

yeah

It helps to make shapes

Mostafa

12:02 PM

@Slereah PGFPlots?

Slereah

yeah

AccidentalFourierTransform

12:47 PM

is there anything better than a cold beer in the crotch?

I dont think so

yuggib

@Slereah It is not a definition

it is a trivial consequence of the definition of a product $\prod_{i\in I} A_i$

You can find the discussion in Bourbaki, E II.32

The only element of the product is the empty function

Just win baby

\o @yuggib

yuggib

@Justwinbaby o/

Bernardo Meurer

@Slereah Did you look at the paper? :P

Just win baby

Nice to see you back @yuggib how are you?

Slereah

12:54 PM

@BernardoMeurer Not yet

Let's look at it

Bernardo Meurer

Woohoo :D

yuggib

@Justwinbaby Not bad

a bit busy, but I'm ok

Just win baby

cool

Avantgarde

2 kewl

Slereah

Look at that fancy plot

@BernardoMeurer Just looking at the translation of the title it seems fairly bad

It should be "On very large classes of quantities with values that are not algebraic nor reducible to irrational algebraic numbers"

or something similar

Bernardo Meurer

1:08 PM

@Slereah Fixing

Slereah

Maybe even just "On very large sets of numbers that are neither algebraic nor reducible to irrational algebraic"

Bernardo Meurer

That sounds better

Slereah

1851 I don't think "sets" were really named

Hence the use of class

Bernardo Meurer

Damn, I hadn't thought of that

Slereah

yeah the first set paper proper was 1871

Bernardo Meurer

1:15 PM

this bitch didn't know about sets

Slereah

Well he did, just in the idea that people had of them back in the days

Just a collection of things

Of course what he means by "class" probably isn't what is meant by set today, either

Bernardo Meurer

Fair enough

Slereah

Since the notion of real numbers being a set was very controversial

Bernardo Meurer

Hm? Why?

Real numbers being a set seems very reasonable

Slereah

This doesn't encapsulate the notion of a continuum

You can't split a continuum into individual elements and put them in a bin

of course using reals as a set brings a lot of problems

what with the axiom of choice

Bernardo Meurer

1:17 PM

You can't? Isn't that what AoC is all about?

Slereah

Oh you can, it just gives you very weird results

with or without the axiom of choice

Bernardo Meurer

Choice is just wrong tho

Slereah

The absence of choice is worse in some ways, though

AccidentalFourierTransform

I support the axiom of life

3

Slereah

The problem is the choice of using set theory to express the real numbers

Bernardo Meurer

1:22 PM

ZFC is bullshit, long live Homotopy type theory :P

Slereah

wot

Homotopy theory is usually based on ZFC

Almost all math is, really

You have to go into weird theories

Bernardo Meurer

Aren't people trying to use type theory as a replacement for set theory?

Or something like that

Kenshin

Maybe but only so they can keep publishing stuff

ACuriousMind

@BernardoMeurer I think type theory belongs to the more categorial approach to foundations of math in contrast to set theory, yes. I'm not sure one should call either a replacement of the other, though

Bernardo Meurer

@ACuriousMind Well, it will have to replace it since ZFC is broken

:^)

Slereah

1:34 PM

Category theory is fairly oftened based on ZFC

I think most category theory constructions have the real numbers as a set

ncatlab.org/nlab/show/real+numbers+object

yuggib

Usually category theory is set in a Grothendieck universe

Slereah

real numbers are still a set, though

I'm not quite sure what alternatives exist, though

I'm sure some people proposed them, but it's probably early 1900's papers

yuggib

the existence of a Grothendieck universe that includes a given set $x$ is equivalent to a large cardinal existence property, and therefore it is not provable in ZF(C)

you need some large cardinal axiom

real numbers are a set in ZF

Slereah

Isn't Grothendieck universe just ZFC + classes?

yuggib

I would say both via dedekind cuts or cauchy completion of the rationals

@Slereah no

Slereah

1:42 PM

I've see category theory defined on ZFC + classes

yuggib

You may need countable choice, i.e. ZF+CC