/sci/ - Science & Math

>>15889238
ZFC is schizo shit. We must return to finitism.

>>15889239
I'll take the position that ZFC isn't schizo enough. I yearn for quine atoms.

>>15889238
How much estrogen do I need to inject before this shit starts making any sense?

>>15889247
>>15889239
>>15889238
if we limit our models to those brainlets (you faggots) can understand, we'd still be in the pre-nuclear age (at best)

>>15889238
not sure, ask some random mathematician

>>15889249
and that's bad because...?

>>15889251
Why are these "schizo" models "bad"?

>>15889260
the normie violently rejects any idea that does not fit comfortably in his skull

>>15889260
Why would shizo stuff ever be good? Do you realize that in a couple hundred years they will laugh at us?

>>15889263
my friend there is nothing you can do to stop people centuries from now from laughing at your way of thinking. Personally I'll start dismissing "schizo" math when I see a reason to besides "I don't get it so it's bad >:("

>>15889260
The axioms are there solely to narrow us down to the model we want to consider. Clearly they aren't doing their job.

>>15889238
>we
miss me with that gay shit
I don't believe in satanism

>>15889273
Salva Urinal

>>15889238
>believe
Also if your opinion is that the statement in your image should be true, your objection to ZFC is not that it's unreasonable but that it's not specific enough.

>>15889238
>believe
Also if your opinion is that the statement in your image should be true, your objection to ZFC is not that it's unreasonable but that it's not specific enough.

>>15889239
Finitism has no finite theory of metamathematics and any (not completely useless/trivial) axiomatization of finitism will entail infinitely many finite objects.
Deal with it.

>>15889882
schizo you're

>>15891160
>will entail infinitely many finite objects
If you think you can entail things into existence, you're hallucinating.

>>15891233
Doesn't stop the fact that the formalization of finitism is a self-refuting enterprise

>>15891240
Formalizations are inherently finitistic

>>15891160
>>15891240
Is it really impossible to say the domain is finite in first order logic?

I only believe in C. ZF is ugly.

>>15891160
You are retarded. Pick up literally any book on metamathematics. The metatheory will be based on finitism. Finitism was literally born out of studying metamathematics.
These transfinite schizos are getting more retarded by the day.

>Doesn't stop the fact that the formalization of finitism is a self-refuting enterprise

>Is it really impossible to say the domain is finite in first order logic?

>if we limit our models to those brainlets (you faggots) can understand, we'd still be in the pre-nuclear age (at best)

>t. has enver studied logic

>>15889421
You are literally braindead. Ever heard of Godel?

>>15889239
Only good post ITT.

>>15889238
The craziest part is that ZFC has axioms that are not in any way self-evident, or obviously true, or intuitive. They're pure gimmicks. Math took a wrong turn sometime in the early 20th century.

>>15892408
By the way, I am not a finitist. I just don't think set theory, especially the Bourbaki kind which props itself up on ZF + other shit, is a suitable foundational mathematics.

The fact that set theorists have concluded that both continuum hypothesis and its negation are true is conclusive proof that they have refuted themselves imo

>>15892414
>By the way, I am not a finitist
Why not?

>>15892408
Aside from choice and replacement I think all of them are intuitive and self-evident.

>>15892414
if you think of "foundations" as a kind of metaphysical framework where all of mathematics comes from, then not only set theory is a bad foundation but also there's no way a good one is even possible.

if you think of foundations as just a different area of mathematics then things will make a lot more sense.
models of set theories are just like models of groups, and different set theories are different kinds of groups.

>>15891530
You can put a finite bound on it's size, like, you can say "the domain has at most 100 objects", or 1000, or 1 million. But if you don't want a specific bound then yeah it's impossible.

>>15892484
How is the axiom of infinity intuitive and self-evident?

>>15892506
You are brain damaged.

>>15892515
My IQ is so high it will integer overflow any of your puny your finitist systems, thus rendering me the most powerful retard on Earth.

>>15892513
All the axiom of infinity claims is that there is a set which contains the successor of its every element. I challenge you to name a natural number n such that n+1 is not a natural number.
Maybe you would argue that the collection of all natural numbers cannot be called a set, but it's a bit of a meaningless dispute because I can just name it something else. An improper class maybe.

>>15892563
> the axiom of infinity claims is that there is a set which contains the successor of its every element
> a set
a what now?
>I challenge you to name a natural number n such that n+1 is not a natural number.
I do not disagree with this.
>Maybe you would argue that the collection of all natural numbers cannot be called a set
A what now? What's a set?
Finite set theory is provably consistent and coherent. It has a well-defined model. Set theory with infinity is schizo nonsense and the word set becomes meaningless.
If you disagree, explain in simple words what is meant be a set in transfinitist schizo world.

>>15892520
It's impossible to overflow my finitist system given that in "my" finitist system, there are infinitely many natural numbers (as there are rational number, integers, gaussian integers etc).

>>15892572
>explain in simple words what is meant be a set in transfinitist schizo world
A collection of objects which can itself be considered as an object.

>>15892580
Can the collection of all collections be considered an object?

>>15892583
No, that would be a proper class.

>>15892584
Why can't a proper class be considered an object? What can be considered as an object?

>>15892576
My IQ is also a real number whose digits solve the halting problem
checkmate finitists

>>15892590
So your IQ is nonexistent.

>>15892586
>Why can't a proper class be considered an object?
Because a proper class is defined to be a class which is not a set.
In this case specifically, if the collection of all sets had a successor or power set, one immediately obtains a contradiction, as there are clearly sets that were previously unaccounted for.
>What can be considered as an object?
Any well-founded collection or image of a well-founded collection.

>>15892596
>mfw finitists think they can do calculus without all the reals

>>15892602
>Any well-founded collection or image of a well-founded collection.
*Or the empty set, of course

>>15892603
>yfw scientists believe you can do science without superstition

>>15892602
>Because a proper class is defined to be a class which is not a set.
> X is not a set because it's a proper class
> X is a proper class because it's not a set
Round and round we go hereafter.
>if the collection of all sets had a successor or power set, one immediately obtains a contradiction
Have you considered that this could mean that your whole notion of set is nonsensical?
> Any well-founded collection or image of a well-founded collection.
So the real reason that the collection of all sets is not a set is that it's not well-founded?

>>15892618
>Round and round we go hereafter.
Certain collections are made proper classes because treating them as sets lead to contradictions.
Technically speaking, in ZFC alone there is no notion of proper classes, and the existence of those collections which can only be described as such is independent.
>Have you considered that this could mean that your whole notion of set is nonsensical?
How so? Not all collections can be considered as objects, that's all there is to it. Finitary set theories also have collections that only be described as proper classes.
>So the real reason that the collection of all sets is not a set is that it's not well-founded?
It's not so principled, in alternative set theories there are often collections which are not well-founded but can be considered as objects (Quine atoms for example). If it's well-founded it can be considered as an object but the converse is a matter of preference.

>Why do we beleive in ZFC when grading math homework again?
ftfy
btw, you can't learn math properly unless you pay an institution of higher learning to hire a grader to grade your homework

>>15892640
So you don't know what a set is.

>>15892670
Sets cannot be defined except in terms of further yet to be defined notions. All theories require primitive notions which cannot be further explained within the theory without introducing circularity.

>>15892670
Give your definition of a set and explain how it precludes transfinite sets.

>>15892513
Doesn't answer your question, but I feel like it's worth mentioning that if you reject the axiom of infinity, or even if you take its negation, one can still construct infinite sets. Just not the inductive set.

>>15892674
everything is a set
therefore, if something exists, then it is a set

>>15892686
> one can still construct infinite sets
proof?

>>15892735
The set of all natural numbers except 2 satisfies the negation of infinity because there is an element (1) whose successor (2) is not an element of the set.

>>15892723
set of all sets which don't contain themselves cannot exist, etc.

>>15892741
prove that set exists from ZFC - Inf please
you just gave the conjectured statement
you didn't provide a proof, hence it isn't a theorem

>>15892847
I can't prove it exists because it's not a logical consequence - there are models of ZFC - Inf without it, just as there are models with it.

ZFfin is bi-interpretable with PA.

>>15889249
Please explain how infinite sets blew up atoms.

>>15892741
If I take that set and union it with {2} I get the naturals which contradicts ~Inf.

>>15892602
>A collection of objects which can itself be considered as an object.
well, the proper class of all sets is clearly a collection of objects and it itself is an object as it can be manipulated and reasoned about. and yet it's not a set. which means that your quoted explanation is inadequate.

>>15893298
This. A better example would be the primes.

Still waiting for the finitist definition of set.

>>15893570
unordered collection without duplicates

>>15893572
Unordered? It's trivial to show that there exists a well-ordering for any given finite set.

>>15893572
define collection

>>15892382
>has enver studied logic
zamn brainlet-kun, you made a typo and now you have lost :smirking_wojak:

>>15893082
>brainlet outing her low reading comprehension

>>15893854
why? do you not understand the word?

>>15893572
And why is the collection of the natural numbers verboten?

>>15893572
So the set [math]\bf N[/math] exists. Got it.

>>15893565
I'm pretty sure you can still construct it using replacement. I don't think you can have any infinite set in ZFC - Inf

>>15893905
Yes

>>15893866
>ree finitism bad
>if you don't use the axioms given in my logic 101 class you can't do Science!
>no i won't explain why those axioms are relevant to the real world
pseud

>>15892670
>>15892618
In your finite set theory, is {x|x not in x} a set?

>>15894235
how do you do derivatives in finitistic math?

>>15894235
>reee infinitism is bad
>you must use axioms my brainlet mind can comprehend
>noooo I won't try to understand
subhuman

Also, I don't think finitism is bad.
I think finautists on /sci/ being autistic about infinite sets should kill themselves. Infinite sets vs finite sets is so boring. It's superficial. It's entry level. That's why there are so many faggots on /sci/ talking about it. They don't have the ability to get beyond entry level. It's pathetically pop-sci tier.

If you want to have a real discussion about finitism that would be interesting.
Discussing philosophy of math.
But instead you're just being a subhuman-level debater.
You've found a contrarian position to defend, and for some retarded reason you want to fight about it.

>>15894220
>I don't think you can have any infinite set in ZFC - Inf
There are models with no infinite sets but I'm pretty sure it's independent.

>>15894256
Why would you want to do some schizo shit that makes infinitely many claims about things you are literally incapable of even referring to? Take some limits of things you're capable of talking about.

>>15894267
The retard here is the one who made a claim they can't support. Specifically that systems other people advocate in place of yours (in this case finitism) would prevent the development of nuclear technology. I don't see a reason for that to be true and you clearly don't either.

>>15889238
>believe in
imagine still not understanding how axioms work

>>15894284
>Why would you want to do some schizo shit that makes infinitely many claims about things you are literally incapable of even referring to? Take some limits of things you're capable of talking about.
Not an answer. How do you prove that the derivative of x^2 is 2x in finitistic math?

>>15894301
Reminder that Wildberger argues the power rule is an open problem.

>>15894301
>x^2 is 2x
not a finitardlet, but im curious, is x^n's derivative nx?

>>15894312
Yes except for n=5 for some reason

>>15894312
It's nx^(n-1)

>>15894301
What's this "derivative" shit you keep talking about and why should I care about it? I demand you define it using sets you can explicitly describe. None of this "..." nonsense that doesn't mean anything.

Even if derivatives are necessary for modern technology, which isn't obvious to me, the function 2x times the difference between adjacent points in the interval (0, 1) seems to approximate the change in x^2 between those two points. That gets more true as you choose a larger (0, 1) so it seems like a reasonable approximation to use while building things.

>>15894317
ah, good to know, thank you

>>15894322
>gets more true as you choose a larger (0, 1)
not a finitistic argument

>>15894338
Why?

>>15894342
because you're making a blanket statement about infinitely many things

>>15894301
>How do you prove that the derivative of x^2 is 2x in finitistic math
what makes you think that it is?

seriously, learn what axioms are before you try to shitpost about them you fucking idiot.

>>15894342
not that guy but you're implicitly using limits and those are defined using infinite sequences.

>>15894284
>The retard here is the one who made a claim they can't support. Specifically that systems other people advocate in place of yours (in this case finitism) would prevent the development of nuclear technology. I don't see a reason for that to be true and you clearly don't either.
I didn't say finitism would prevent the development of nuclear technology. You must be an ESL, or a retard, or baiting.

What I said was, if we limit ourselves to theories brainlets (like you) can understand, then we'd never have developed nuclear technology.
If you weren't cognitively deficient, you'd have immediately understood what I was saying. But I'll have to spell it out.
Nuclear technology requires models which brainlets can't understand. If we stuck to models which brainlets can understand, we wouldn't have nuclear technology. Brainlets can understand finite models, but not infinite models.
If we stuck to models that brainlets could understand, such as finite models, then we would be forbidden from using OTHER models which brainlets can understand, such as the models which lead to nuclear theory.

Let me REALLY spell it out for you. I really can't trust you are even midwit level, so I have to make it really clear.
Z is a model that let us develop nuclear theory.
Y is a model of mathematics with infinities.
These models are HARD. Dumbdumbs cannot understand Z or Y.
Dumbdumbs like simple models.
They like model A, a finite model of math, and model B, a newtonian model of physics.
A and B are EASY models, which brainlets CAN understand.

- If we only used models brainlets could understand, such as A and B, then we wouldn't be able to use Z or Y.
- We need Z for nuclear technology.
- if we can't use Z, we can't get nuclear technology
- If we limit ourselves to brainlet models, we can't use Z
- if we limited ourselves to brainlet models, we wouldn't have gotten nuclear technology.

If this isn't simple enough for you, then you need to seek help.

>>15894347
I'm making a statement that for any interval you give me I can construct another interval where the previous equation I was talking about is closer to true. That isn't a contradiction any more than there allegedly being infinitely many natural numbers. Even if there were I'm not talking about them all at once like a lunatic.

>>15894368
>we used Z to get nuclear technology therefore if we don't use Z we can't get nuclear technology
ok retard

>>15894383
>>we used Z to get nuclear technology therefore if we don't use Z we can't get nuclear technology
>ok retard
Ah, you still don't understand.
Not going to waste my time on a subhuman.
Not going to read any more of your posts.
kill yourself

>>15894383
>I'm making a statement that for any interval you give me I can construct another interval where the previous equation I was talking about is closer to true.
>Even if there were I'm not talking about them all at once like a lunatic.
Yes you are, you just made a statement about "any interval"

>>15894425
I made a statement saying what is true of any structure satisfying certain axioms. You can construct something else from it. That is not the same thing as declaring all those structures to a be in a set.

How does model theory not prove platonism?

>>15889263
John Nash was a literal schizo and won the Nobel Prize in economics.

>>15894027
how many elements does it have?

>>15894301
>How do you prove that the derivative of x^2 is 2x in finitistic math?
(x+h)^2 = x^2 + 2x*h + o(h)
you absolute brainlet

>>15889238
Do you believe "2 + 2 = 4"? Why

>>15895788
No, since beliefs don't exist

>>15895788
because you can prove it

>>15895845
How can you prove it?

>>15895889
by explicit computation

>>15892484
The Axiom of Replacement and the Axiom pf Subsets have no business being called axioms. There's nothing intuitive about them, the only reason they're in the list is because Zermelo back-argued to them out of convenience.

>if I had these, I could do the math I want
It's bullshit.

>>15892486
Sorry I'm not in the "shut up and calculate" brain dead camp. If I were to treat math as just another game I'd rather get in a pod and plug myself into the matrix. If even math is nothing but a game, then all knowledge is just fictional theorycrafting.

Frankly, I'd rather blow my fucking brains off then wank like that. I also think it's a retarded and solipsistic view. Not sure where you disgusting bugmen came out from. You're yet another exemplar of the kind of low IQ robot paper pusher that I can't stand. All downstream from the fucked up early 20th century in mathematics.

Some people have a deeply rooted, spiritual need to actually think.

>>15892774
>muh liar's paradox repackaged for the nth time
Congrats. You've discovered language games. Those language games however say absolutely nothing about sets.

>a barber who shaves all people who do not shave themselves
Oh gee, PARADOX! Barbers must not exist then. I hate you autistic imbeciles from the bottom of my heart.

>>15895933
>>15892774
See what you morons don't get is that the whole "crisis" of the early 20th century in mathematics is only a crisis if you take the idiotic Hilbertine position that mathematics is nothing but a formal language/formal game. I know midwits/brainlets like to regurgitate all sorts of "results" from the period and wax eloquent about them, but that shit means dog shit if you do not make the moronic assumptions that Hilbert made.

Language paradoxes were a problem for those bugmen precisely because they did not want to conceive of mathematics as something other than a kind of language. It was the typical intellectual disease of the time. Just a passing (and utterly moronic) trend. Remnants of those bugmen still remain, tragically, but one death at a time your kind will slowly die and non-zombies will be able to talk to each other without all the noise you non-thinkers bring to the table.

>>15895931
>>15895933
>>15895938
Unhinged platonist schizophrenia. You talk a lot but I can bet you've never produced any of this good math yourself

>>15895485
what does o(h) mean in finitistic math?

>>15895938
Acknowledging that it's a language paradox doesn't make it go away. You still have to obey the rules of inference.

>>15895931
>There's nothing intuitive about them
thank god that you are not and will never be the standard for what intuitive is
>If even math is nothing but a game,
it is
>Frankly, I'd rather blow my fucking brains off then wank like that.
id love nothing more