/sci/ - Science & Math

>>14555343
Finitism.

>>14555343
>Logicism
Arithmetic and set theory goes beyond logic. The axioms are semantic not logical.
>Intuitionism
Created by Brouwer who was a schizo. By double negation easily seen to be foundationally/philosophically on par with classical platonic view of math.
>Formalism
Not a philosophical view, simply a correct observation that actual mathematical arguments that people do can be formalized within formal systems.

>>14555343
I like the later split better: rationalism versus empiricism

>existence can also exist uniquely in our brains and consciousness can craft unique objects that reality out there cannot
versus
>existence can only exist in the observable reality in front of us and everything else is schizophrenia

I personally subscribe to the latter because the former leads to pic related.

The only correct stance is to reject infantile and pointless philosophy nonsense. Math is morally good because unlike philosophy it is rigorous.

>>14555374
There's nothing rigorous about set theory.

>>14555371
It seems like Kareem Carr is *trying* to illustrate a valid point about statistical construct validity. I do not think that is about rationalism per se at all, as it is sort of equivocating set theory in there by changing the agreed upon values to a different set of things.

He fell all over himself making a bad point that could've been a good one (construct validity matters), but that does not represent your point on rationalism either I think.

>>14555371
Guy in the pic is right. Statements are only true if what's being measured is the same. Also, that would be empiricism not rationalism.

>>14555384
the desire to turn 2+2=4 into 2+2=5 is the flagship of modern rationalism and specifically postmodernism (which is really just militant rationalism)

>>14555374
Define morally good

>>14555375
Naive set theory is completely rigorous and the alleged paradoxes like Russell or Cantor are just midwit bait. They are easily resolved when interpreted correctly.

>>14555392
I'm... just trying to say his point wasn't your point and both points fail what they're endeavoring to show, **even though** both points are valid.

Just because I agree with what you're getting at doesn't mean I find the steps you used to get there to be good ones.

>>14555398
No. It would be immoral to attempt definitions outside of math, science or law.

>>14555404
Calm down there humpty dumpty.

>>14555399
Define what a set is please.

>>14555431
I'm not your personal wikipedia bot.

How can math simultaneously exist -and- not exist, at the same bloody time?

Math is the closest thing to true magic in the universe.

>>14555436
You won't find a definition of sets on wikipedia

>>14555447
It's right there in the first paragraph.

>>14555448
Uhhh actuallly no.

>>14555448
I think you're getting off on the wrong foot. Different anon here. You stated it was rigorous, his point pertained to rigor, so you're not addressing his point as it would require demonstration of said rigor.

So, think identity proofs or something, not common language definitions (though you could do that too).

>>14555448
Nope

>>14555459
Sorry, misfingered and didn't put the context post from the start. Your original post the anon is replying to and pertaining to rigor being this one >>14555374, and the retort here >>14555399 is insufficient. You have to actually cite the proofs, not allude to their sufficiency. A title or something would be nice.

>>14555459
>>14555464
Are you even familiar with naive set theory? Show me where it isn't rigorous. And no, I do not accept the burden of proof.

>>14555468
>And no, I do not accept the burden of proof.

...Then I fail to see why you even bothered. My familiarity has nothing to do with my pointing out how the conversation derailed. At this point neither of you provided sufficient reason to believe either proposition.

>>14555468
>Show me where it isn't rigorous
In that it doesn't define what a set is, doesn't prove the claimed basic properties of sets, gives no way to determine what is or isn't a set.

>>14555488
Given naive set theory is informally defined as a tool from natural language I genuinely am not sure why he chose to die on this hill.
>Are you even familiar with naive set theory?
"Those in glass houses shouldn't throw stones".

>>14555468
Does the set of all sets exist in naive set theory?

>>14555491
NTA but I got an A in calculus AND in discrete math for CS. So let me explain.

A set is a collection of objects called elements. You can think of it like a bag or a container containing these elements.

You can do operations with sets. Union, intersection and Cartesian product. Using these in a proof can be quite hard. It's only for very smart people.

>>14555507
No.

>>14555343
yes obviously math comes from the brain. how it relates to "reality" or whatever is speculation. you are writing formulae down on paper that only mean anything because you know how to read them because you made them. it's like painting. the fact that it seems to relate somehow to the real world and the fact that its rules are incontrovertible is an unsolvable mystery. so "intuitionism" is probably the closest of what you said

>>14555515
Not going to lie you got me. That was funny.

>>14555523
Why?

>>14555550
Because it would have to contain itself

>>14555564
So?

>>14555564
And why is that bad?

>>14555569
>>14555570
A set cannot contain itself. That's an illegal recursion. Any set is defined by the elements it contains. If it contained itself this would be a circular definition.

>>14555578
>recursion
>circular
you wish

>>14555578
I'm genuinely not sure why they're asking you about that. Or what even is going on anymore.

>>14555584
>my definition of X requires X itself
This is the kind of bullshit one can expect from philosophers who failed their intro to formal logic. In math we're better than that.

>>14555578
>Any set is defined by the elements it contains. If it contained itself this would be a circular definition.
Ok fair enough. But you're still not being rigorous. I want you to list all the properties that you have to check for some collection to be a set. A set may not contain itself. Are there any other requirements, or are all other collections sets? Also what about those collections for which you don't know if they contain themselves or not? How can you tell if they're sets or not then?

>>14555578
That doesn't sound very convincing. Is that an actual result or principle of naive set theory, or just your personal opinion?

>>14555592
>Are there any other requirements, or are all other collections sets?
All collections which are properly defined without logical contradictions are sets.

>Also what about those collections for which you don't know if they contain themselves or not?
No collection can contain itself.

>>14555591
I think you're unfairly presuming he does not understand what identities are or tautologies, when he's referring to something else. Or maybe I'm being too charitable.
>>14555592
I get interrogating someone's knowledge to demonstrate they don't know enough, but is it really necessary? >>14555374 The original post posited math as "morally good because rigor" which seems a self evident absurd statement on its own.

The real issue there was never addressed. I don't see how challenging him on the basis of rigor matters when the nonstarter is arbitrarily declaring "rigor = moral good".

>>14555600
>All collections which are properly defined without logical contradictions are sets.
Does there exist a well-ordering of the reals? It's proven that such a well-ordering cannot be defined. So does that mean according to you that it doesn't exist?

>>14555600
>All collections which are properly defined without logical contradictions are sets.
The set of all sets is a properly defined collection without logical contradictions.

>>14555608
The well-ordering poses no logical contradiction and can be deduced from the trivially obvious axiom of choice. Why would anyone have a problem with that?

>>14555613
It has the logical contradiction of containing itself. Try again.

>>14555631
How is containing itself a logical contradiction?

>>14555343
the real issue is mathematics realism vs anti realism and the usefulness of mathematics.
also fuck russell

>>14555636
See >>14555591

>>14555628
>Why would anyone have a problem with that?
You would, because you just said that every set has to be well-defined, and there is no definition of such a well-ordering.

>>14555640
That doesn't answer my question at all.

>>14555343
Platonic view of math is the true one. If you think otherwise you are soulless.

>>14555644
The well-ordering is not a set. It's an additional feature. The underlying set is well defined.

>>14555651
There is literally no reason to think that the concept of an arbitrary set is well-defined and that the continuum hypothesis has a definite answer without further specification, and many reasons to think otherwise.

>>14555364
>correct observation
Gödel would like a word with you

>>14555645
It does. You're just not smart enough to understand.

>>14555628
>trivially obvious

>>14555667
>my Cartesian product of non-empty sets suddenly becomes empty because ... uhm it just does, okay?
>... and that's actually a good thing! Read here why Cartesian products are safe and effective

>>14555664
So dumb it down, please.
>a contradiction occurs when a proposition conflicts either with itself or established fact
Does the proposition "X contains X" conflict with itself? How? Or does it conflict with an estabilished fact? Which one?

>>14555683
You should be able to rigorously prove the axiom of choice from your definition of what it means to be a set.

>>14555683
The cartesian product of nonempty sets is always nonempty because, uhhh..... it just is, ok!?

>>14555364
>Brouwer was a schizo

Mathematically minded morons are always mentally ill deviants.

Look in any field, the people who provide insight are big brained losers whose development is dependent on them being cut off from the herd.

Ex:
>nash
>newton
>parsons
>wittgenstein
>boltzmann
>nietzsche
>foucault
>c s peirce

Thank god for the mentally ill

>>14555686
It is simply nonsense. A self-referential definition is crap.

>>14555693
>prove the axiom
Looks like we found another philosofag who failed his formal logic class.

>>14555712
...Well, no, a tautology or identity is fine. I think you are confusing that with "circular reasoning", where you begin with your conclusion. Also known as begging the question. All axioms are tautologies and therefore circular, in a sense, as identities or assumptions in a system. Circular reasoning is a different thing.

>>14555697
>Wittgenstein
Can you remind me again what insights he provided? That's right. None. He's just memed by pseuds on /lit/ but his work was insignificant.

>>14555718
A self-referential definition is not a tautology. Try again.

>>14555719
The only time I've seen anyone say that is when they haven't read the context in which Wittengenstein was writing. On the contrary, he demonstrably proved you could not construct a "truly objective language" of the framing Russell and most others were after in his day. "Philosophical Investigations" is one of the most well known works and singlehandedly overturned an entire paradigm.

>>14555720
The justification of the tautology is in reference to the tautology. Just because you're refusing to connect the implied dots does not mean I suffer some failure of understanding. Just makes you a dick.

>>14555719
Logical positivism is a waste of time(even going so far as to show that he was wrong in his younger years), semiotics is the correct field for studying how symbols acquire meaning, language systems (including maths) are dependent on intuitively derived arbitrary rules in the form of language games, popper was a peasant who just wanted to find the Truth, much more. Its a shame you haven’t read any of his works.

>>14555715
>>prove the axiom
>Looks like we found another philosofag who failed his formal logic class.
Are you saying it's impossible to prove that the integers satisfy the group axioms? How is that different from showing that the sets satisfy the axiom of choice?

>>14555732
>language systems (including maths) are dependent on intuitively derived arbitrary rules in the form of language games

Minor pushback here, but I do not believe that is what Wittgenstein was after nor is that true. Language systems, to be said to have any utility at all, must necessary correspond to something in reality however distant that correspondence is. That is to say it is not merely all farts in the wind, nor is that what Wittgenstein thought, and I would argue the positivists constitute the most infamous case of mass strawmanning in existence. Though given that it is kind of hopeless to salvage it and always has been.

Anyway, the basis of any intuition is necessarily the reality we find ourselves in, and the only test of the axioms derived necessarily is in testing that same reality we intuit axioms from.

>>14555729
A definition is not logical statement and hence cannot be a tautology. Of course I do not expect a Wittgenstein fanboy to have sufficient background in formal logic to understand this.

>>14555732
Wittgenstein was a retard. Popper was even more of a retard. Philosophy is full of retards. Science and math are based.

>>14555599
lol

>>14555745
>A definition is not logical statement
https://en.wikipedia.org/wiki/Statement_(logic)

I assume you're trolling.

>>14555737
Good one. Nice play on words with "axiom". Distinguish between defining properties on the one hand and axioms in a logical calculus on the other hand.

>>14555712
What "self-referential definition" are you talking about? I'm not talking about any definition in particular, I'm simply asking where's the contradiction in a set containing itself. A number can be divisible by itself, a matrix can be congruent to itself (always is actually) etc. so why can't a set contain itself? "It's simply nonsense" is not a very strong argument.

>>14555761
That wiki article supports my point. A definition doesn't hold a truth value. A definition is never true or false.

>>14555766
Trolling pedantism. A definition can be a logical statement simply by use in a premise.

>>14555763
The axiom of choice is not a logical axiom, it is a nonobvious and nontrivial statement that has to be proven to hold.

>>14555764
A number being divisible by itself is a property of that number, not the definition of that number. A set however is defined by the elements it contains.

>>14555770
This pedantism is called formal logic. It's an important and rigorous field of math. If you're unwilling to deal with it, please stay in philosophy where you can spout inconsistent drivel all day.

>>14555773
Show me an empty product of non-empty sets.

>>14555786
The product of all non-empty subsets of the reals.

>>14555786
It's like asserting that the intersection of nonempty subsets is nonempty. Intuitively it makes sense, and is true when you're talking about finite intersections, but it's just not true when you're talking about infinite intersections. In the same way, a finite product is always nonempty, but an infinite product may be empty.

>>14555782
https://en.wikipedia.org/wiki/Principle_of_charity
As I said, trolling pedantism. Nobody who is a professional acts like a reddit child. That is, like you are. Obviously a definition is tautological when used in a premise, and to say "definitions are not logical statements" is to dishonestly preclude the implication that it would be true in the only possible usage case where it would be true (in a syllogism in this case).

But hey, your trolling lets me teach people acting like a jackass is not in fact how you are supposed to do things.

>>14555791
It's clearly non-empty. Just choose an element from each non-empty subset. That tuple then is in the Cartesian product. Lmao, it's that simple.

>>14555798
If math is too much "pedantism" for you then don't engage in mathematical debates.

>>14555806
It isn't. You are just trying to feel clever by pretending someone's words mean something stupid. Grow up.

>>14555799
>It's clearly non-empty
Again, I gave you an explicit example where it's empty.
>Just choose an element from each non-empty subset
You need to do that simultaneously for all the sets at once. How do you do that? Protip: you can't.
>That tuple then is in the Cartesian product
You haven't shown such a tuple exists.

>>14555810
I don't care about your troll games. I'm solely committed to facts and logic.

>>14555817
Sure ya do kid.

>>14555343
honestly? whatever belief motivates you to get the most work done

>>14555815
>Again, I gave you an explicit example where it's empty.
I proved you wrong.
>You need to do that simultaneously for all the sets at once. How do you do that? Protip: you can't.
Simultaneously isn't an issue here as we don't consider time. This isn't a physics problem in relativity. This is abstract math.
>You haven't shown such a tuple exists.
I constructed it explicitly.

>>14555660
godel proved there is not one "language" that can be used to formalise everything. it simply means it is worth investigating many different languages, which in my view makes things more fun

>>14555742
>That is to say it is not merely all farts in the wind

Agreed. Why do we call the color “red” and not “orange”? We’ve declared this to be red- the naming is arbitrary. This is what On Certainty is about: yes, there is a degree of correspondence, but this degree is uncertain at best, and as such is not the basis upon which language games primarily derive their meaning.

PI, §21:

>Imagine a language-game in which A asks and B reports the number of slabs or blocks in a pile, or the colours and shapes of the building-stones that are stacked in such-and-such a place.-Such a report might run: “Five slabs.” Now what is the difference between the report or statement “Five slabs” and the order “Five slabs!”?- Well, it is the part which uttering these words plays in the language-games. […]

Why an order vs report? Why English? Why an adjective then noun order? The whole construction of language here never consults the reality of B. Its just arbitrary pre determined rules of language play whose correspondence to reality is uncertain at best.

>>14555826
>I proved you wrong.
You have not.
>Simultaneously isn't an issue here as we don't consider time. This isn't a physics problem in relativity. This is abstract math.
Correct. By simultaneously I mean to provide a single function which takes an input a set in the collection and outputs an element in that set. You haven't shown that such a function exists.
>I constructed it explicitly.
You haven't done shit. All you did is restate the assumption that the every set in the collection is nonempty.

>>14555858
Allow me to clarify. I do agree with, or I think I agree with, what you wrote. There is simply a difference in framing, I think. I am simply satisfied with fallibilism, or that induction and necessary uncertainty is an acceptable form of knowledge. Pragmatically I would argue that's all knowledge (That is, knowledge beyond what's in ones head). As it is in essence the justification to believe something true.

As a criticism of being insufficient for a statement of truth or absolute truth, of course I agree such a thing is not possible. Rather, I am saying the meaning is derived inductively and that is the basis for the correspondence and the language games necessarily. They do not form in a vacuum, and I do not believe Wittgenstein believed they did.

>Why an order vs report? Why English? Why an adjective then noun order? The whole construction of language here never consults the reality of B. Its just arbitrary pre determined rules of language play whose correspondence to reality is uncertain at best.

All good questions, fair ones in context, but the meat of the issue is in the substance of the meaning not the form the meaning takes. The form the meaning takes can have physical constraints as well and is not pure random, but I do not think we need quibble over that do we?

>>14555897
>>14555858
Sorry I maybe should also have been clearer on the fact I am speaking of pragmatic constraints, not finding some abstract fault in the abstract pure random demonstration case. As you may be thinking only in that abstract case, where as I was not.

>>14555893
When a set is non-empty just take a random element from it. It's that easy, like lol why do you pretend there's a problem?

>>14555912
I have no problem with what you wrote there. However, that's not the same as the axiom of choice.

>>14555932
>I mean to provide a single function which takes an input a set in the collection and outputs an element in that set.
This is what you wrote. So you admit that I'm right?

>>14555440
>How can math simultaneously exist -and- not exist, at the same bloody time?
Because Gödel sentences.

>>14555952
No, you haven't shown that such a function exists.

>>14555343
formalism and it's not even close

>>14556086
Which formalism?

>>14555828

Obviously a mixture of all 3; there are babies in all of those bath waters that should not be tossed out just because they occasionally shit the tub

>>14555343
>what is münchhausen's trilemma

>>14555578
>A set cannot contain itself.
https://en.wikipedia.org/wiki/Aczel%27s_anti-foundation_axiom
https://en.wikipedia.org/wiki/Urelement#Quine_atoms
https://en.wikipedia.org/wiki/Non-well-founded_set_theory

>>14556307
[The set is not the things on either ends of the numbers]

The set is only the numbers.

If [5, 10, 13] is a set;

What is the controversy, does the set contain itself? The set is
5, 10, 13

It is itself, the 'containing' is symbolic tool convention, for demarcating information, the demarcations themselves are not important items in anyways besides nessecary tools of distinction, distinguishing, delineating, demarcating.

Symbol of set [765, 867, 878 , 877] is merely to distinguish between groups [49837, 8787, 767] so different groups can be talked about seperately, without all possible groups melding together into only one indistinguishable group.

, And . And ; and : and ' are not words as much as [ ] are not as themselves or in anyway of themselves relvant mathamatical objects, math tools yes, language tools yes, math objects no, language objects no

>>14555374
>Math is morally good because unlike philosophy it is rigorous.
>Math is more rigorous than logic, a branch of philosophy
>Math, which uses informal proofs and handwaving, is more rigorous than proof theory

>>14557767
Logic is just a branch of math. As you can see in this thread, philosotards don't even understand the basics of it.

ALL PHYLOSOPHY BLABBERY SUCKS ASS
You should be pragmatic. Why? If it was false, then are the things that aren't useful to you the ones you should pay the more attention to? By definition, the direction you move forwards to is the one that maximizes your interests, how do you even wake up in the morning and reach for something if that wasn't what you wanted to do? Anything else is blabbery of degenerate retards. We do propositional logic the way we do why? Well go ahead and do it a different way see if you can communicate with someone.
"Yo that frying pan is cold don't worry."
-*touch it and gets burned*
-"Nigger wtf you told me it was cold"
"Oh yeah but in my retarded schizo world it's kinda subjective you know isn't it kinda arbitrary that what we think is tr-"
*gets beaten to death and mauled*
That's the fate pseuds deserve.

>>14557845
Hello based department?

>>14555858
>We’ve declared this to be red- the naming is arbitrary. This is what On Certainty is about:
No it isn't at all...

>>14557845
>ALL PHYLOSOPHY BLABBERY SUCKS ASS
>You should be pragmatic. Why? If it was false, then are the...
Pragmatism requires an underlying way of quantifying and identifying utility, which is speculative and thus philosophical in nature. Sorry, but you can't just escape philosphy like that. All roads lead to Rome.

>>14558844
>blablablablablablablaba
>*gets ass raped by romans while he was doing "philosophy"*
concession accepted

>>14557818
>philosotards don't even understand the basics of it.
such as?

>thread about math
>philosophy mentioned 17 times already
like pottery

>>14559358
Such as axiomatic system, rules of deduction, the need for well-defined definitions etc. Just read this cringe tread and you'll find plenty of examples.

>>14559374
Do you have a well defined definition of what a set is?

>>14559396
A container for its elements. This implicitly implies a container cannot contain itself.

>>14559403
Wrong. The container containing all groups is not a set.

>>14559424
Why isn't it?

>>14559425
Well, it is a set according to your "well defined definition" but virtually every mathematician disagrees. Why is that? Are you using a different definition than the others?

>>14559424
It is though.

>>14559432
I'm not the guy you were arguing with before.
Just saying that if it satisfies the assumptions of set theory then you can use the tools of set theory on it.

>>14559432
Just because a majority of midwits holds some belief it doesn't make that belief any less wrong. Truth isn't determined democratically.

>>14559403
>This implicitly implies a container cannot contain itself.
>>14556307

>>14559442
Just to be clear, you're saying that the container of all groups is a set?

>>14559451
I will say so unless you provide good evidence that it isn't. Any argument using midwit bait like Russell's or Cantor's paradox doesn't count, since these have already been resolved/dismissed ITT.

>>14559454
What about the container of all singletons, is that a set?

>>14555343
I like formalism. Define basic rules and stick to it. You can have 1 +1 = 5 or whatever schizo bullshit you desire as long as it's consistent. If other people also like 1 + 1=5 it will compete and win in the marketplace of ideas

>>14559458
Of course. You will try to pull some trickery and try to sell a set as a singleton, so you can unpack them and suddenly you get the set of all sets. It doesn't work like that though. A set is not a true singleton. Singleton means only one element.

>>14559451
Define group

>midwits trying to avoid the fact that the basic definitions of any discipline (maths, physics, chemestry) are simply circular and have to be understood in an intuitive way

>>14559471
Many such cases. Sad.

>>14559471
True. The notion of a "set" is however too vague to be understood just by intuition (that is, if you want to use it as a basic building block for rigorous mathematics)

>>14559468
Why can't you take the union of all elements in the set of all singletons?

>>14559502
I can. It just won't produce the paradox you want to produce.

>>14559510
The union is not the set of all sets? Which set does it not contain?

>>14559511
It doesn't contain sets at all. Only elements.

>>14559515
A set cannot be an element of another set?

>>14559500
provide a more intuitive basis for mathematics that allows for the same constructions

>>14559519
A set can obviously not be contained in a singleton.

>>14559525
That doesn't make any sense. Why not? A container containing a single set is a set according to the definition >>14559403

>>14556272
irrelevant. everyone knows maths needs axioms. the disagreement is on whether these axioms were just made up or are actually something fundamental

>>14559547
A singleton is supposed to contain only one element. Sneakily smuggling in a whole container of elements into a singleton would fuck up the purpose of the singleton.

>>14559574
How many elements does the set containing the set containing 1 and 2 have?

>>14559588
It is obviously not a singleton.

>>14559591
How many?

>>14559601
before telling you "how many" I would first have to develop a theory of the natural numbers. why can't you just stick to the basics?

>>14559604
How many?

>>14559601
One. But it's not a singleton for reasons explained above. Now what?

>>14559613
Now consider the container containing all sets containing exactly one element. Is this a set?

>>14559618
As long as you exclude the obvious paradoxes of recursive inclusion.

>>14559624
If I exclude a set with one element, it wouldn't be a set of all sets with exactly one element.

>>14559642
It is though. You're quantifying over all sets. Obviously this doesn't include retarded paradoxical sets which logically cannot exist.

>>14559451
>>14559454
There can be no set or container of all groups or sets because all groups and sets are infinite which by deffintion is uncontained or uncontainable

>>14555374
>makes a philosophical post

>>14557767
the only rigorous form of logic is mathematical logic. maths and formal logic are rigorous because they are always true given axioms, there is no room for subjectivity or opinion, given euclid's axioms the sum of angles of a triangle is pi always rads. you can literally have a computer test your theorems and show if they are true or not given axioms. nothing of that sort can be done for informal logic or vast majority of philosophy

>>14555364
>math is not logical
Then why do you think physics use so much math, is physics also illogical and only semantic like you claim arithmetic and set theory are?

>>14555374
The wholeness of a number is by philosophical definition, not rigorous measurement.
With what rigor do you think anyone has ever accurately measured that any particular number is completely whole and how did they account for any potential infinitesimal deviation given no measurement device known to man has a precision of measurement anywhere near an infinitesimal threshold?

>>14559971
>measure a number
sir, where are those numbers I can measure

>>14559971
>With what rigor do you think anyone has ever accurately measured that any particular number is completely whole
Counting

>>14555440
>1.3 MB
> How can math simultaneously exist -and- not exist, at the same bloody time?
Because it is both real and imaginary.

>>14559973
You are the one claiming to have been rigorous.
How can you have been rigorous if you didn't even measure your results?

>>14559976
That is a circular definition, it is fallacious to reference your concept of numbers as a proof the numbers were rigorously measured by something that reflects reality. Even if counting is your only proof for the rigorous accuracy of math, that can only prove positive whole numbers, now you have made fractions, nulls, infinite, negative numbers, and most of the applications of math impossible.

>>14559992
>now you have made fractions
Your question was about whole numbers. Stop shifting le goalposts.

>>14559981
sir, you are confusing maths with science. sir I kindly ask you to take your meds and stop seeing things that don't exist

>>14559997
The original statement was about the moral goodness and rigorousness of math.
I baited you into a trap since your "rigorous" proof of only whole numbers necessarily disproves the validity most modern math and calls into question any claim of math's overarching rigor and goodness.

>>14560005
Counting is very rigorous though.

>>14560001
No, you are confusing rigorous with intuitive, science is intentionally done with rigor and you have failed to prove that math is up to the rigorous standards of science.

>>14560009
bro, why embarrass yourself further? you clearly have no idea what maths and science are about and are saying a bunch of dumb shit.
just answer this question: if science is rigorous, where is the proof that the second law of thermodynamics is true?

>>14560007
Ok, then count all the fractions of values from 1 to 2 starting at 1.000... and ending at 1.999....

>>14560022
Fractions are not whole numbers. You seem to lack basic math education.

>>14560016
There is vast experimental proof using various closed systems demonstrating how entropy increases over time and heat tends to flow from the hotter to the colder over time.

>>14560036
So fractions aren't part of math or most math isn't valid according to your whole number counting standard?

>>14560041
Fractions are cute and valid, and they are real numbers.

>>14560043
So counting is not a valid way to measure math since you clearly can't count from 1 to 2 starting at 1.000... and ending at 1.999...?

>>14560037
>vast experimental proof
you realize this is inductive reasoning, right?
>we have observed trillions of cases in which the law holds, therefore it holds for all cases in the whole universe
this is the polar opposite of rigor, would you like to try again?

>>14560045
>valid way to measure math
this sentence has no formal meaning, you are just making up combinations if terms at this point

>>14560045
>1.999..
That's not a number.

>>14560047
No, experimentation is principally based on deductive reasoning.

No, the polar opposite of rigor is faith, not trillions of exhaustively thorough experiments to determine the accuracy of your measurements.

>>14560052
>this sentence has no formal meaning
Only because you are trying to apply a term that involves the exhaustive search for accuracy like rigorous to something semantic that is only true by definition like math.

>>14560053
What is it?

>>14560061
can you "measure" physics? you realize you are not making sense?

>>14560063
I don't know. You made it up. Not my problem.

>>14560058
if experimentation is deductive then why do scientists tune their models if their deductions don't predict what happens in experiments?
maths is deductive because if a function doesn't have the properties I want then tough luck, it will never have them and I have to live with that.

>>14560065
Yes, you can measure space and time, I am sure nothing makes sense to the type of person who doesn't even know how to tell time.

>>14560084
>ask about measuring physics
>get told you can measure two aspects of physics
ok so given a finite set I can count its elements, means I can "measure maths" according to you

>>14560068
I didn't just make it up, you can't find that number referenced going back to the 1700s, why do you think it involves only other numbers if it isn't a number and what other kinds of things that aren't numbers are only made of numbers?

>>14560098
>you can't find that number referenced going back to the 1700s
>can't
Yes

>>14560071
>if experimentation is deductive then why do scientists tune their models
They don't once they have reached a threshold of rigor where the deduction reflect reality, they only have to tune if their deductions were inaccurate and need to be tuned to satisfy the standard of rigor needed to succeed in the application at hand.

>maths is deductive because if a function doesn't have the properties I want then tough luck, it will never have them and I have to live with that.
That is not deductive that is semantic, it is true by definition and you will never change the definition.

>>14560090
Energy and matter and all the other physical metrics can me measured too, what other aspects of physics do you think there are that can't be measured?

What aspects of math do you think can be measured and aren't simply true by definition and internal logic like how do you measure something abstract like 1 with anything other than itself?

>ok so given a finite set I can count its elements, means I can "measure maths"
No it means you are arbitrarily applying the math function of counting to some minimal superficial set of potential math values that are not a very comprehensive reflection of the domain of mathematics.

>>14560105
Its one specific output of a very basic calculus function that Newton generalized and everyone who goes through a basic calculus/analysis intro class is exposed to.

>>14559965
>>math is not logical
Never said this. I said math goes beyond logic. If you only have a formal system with logical axioms, you will not be able to prove any interesting math theorems. You need additional axioms which go BEYOND logic, that partially defines the semantics and lets us reason about the objects involved.
Phyiscs is exactly the same in that respect, except that nobody even has the axioms of physics, it's much less formal and much less logical than math. It's basically a bunch of heuristics, ad hoc arguments with a bit of math thrown in to make some arguments for why one thing should probably be equivalent to another in some specific cases that you care about.

>>14560127
I'm an expert on calculus and you are wrong.

>>14560142
>I said math goes beyond logic.
Then you specifically said it was based on semantics but not logical indicating it is not the type of formalized semantics based on logical.

>BEYOND logic
Beyond means just outside of, so you are still just saying that the semantics of arithmetic are just outside of the scope of logic.

>except that nobody even has the axioms of physics,
Wrong, the generalized axioms of modern physics is formally referred to as the Standard Model of Physics.

>heuristics
Heuristics is still a logistics process originally employed by Greek logician based on logical methodologies, how is the heuristics technique not an application of logical refinement?

>>14560149
If you are such an expert, then what number am I thinking of?

>>14560188
Trick question. You are not thinking at all.

>>14560185
>Then you specifically said it was based on semantics but not logical indicating it is not the type of formalized semantics based on logical.
It is logical and is based on logic, but it's not logic. Why is that hard to understand?
>Beyond means just outside of
Correct.
>of, so you are still just saying that the semantics of arithmetic are just outside of the scope of logic.
Correct.
>Wrong, the generalized axioms of modern physics is formally referred to as the Standard Model of Physics.
Specify the formal system and list the axioms, please, thanks.
>Heuristics is still a logistics process originally employed by Greek logician based on logical methodologies
Based on logical methodologies but beyond logic. Also look up what logistics means.

>>14560193
Then why did I clearly write down the number I was thinking about that you said isn't a number?
How do you suppose that I was able to completely make up something up that you had never even encountered (even though it has existed since the first calculus book) if I was not thinking at all?

>>14560203
You're talking to a GPT-2 bot.

>>14560205
>I lost the argument and can't think of any names to call you directly, so I will take the liar's gambit and blame my failings on a robot.

>>14555343
>What is the correct view of Mathematics?
platnoism

>>14560213
I'm not the anon, just an external observer FYI. I.e. beep boop boop boop beep :)

>>14560194
It doesn't really makes sense, how is it not itself. Can you give examples in other domains.
What is something that is physical and based on physics, but is not physics.

>correct
So if it is outside, then it is not inside, so if arithmetic is outside of logic, it is not logical.

The formal system of the Standard Model is the four fundamental forces and pic related is a rundown of the most important base axioms of that system.

>>14560229
>I'm not the anon, just an external observer FYI.
That's not a sentence.

>>14560248
>What is something that is physical and based on physics, but is not physics.
Whether one country will attack another is partly based on economics, but is beyond economics. There are other variables involved that are outside economics.

>>14560251
And you would know about that, mr GTP-2.

>>14560256
War is not beyond economics, it is not based on economics it is generally not economical, its continuation is primarily dependent on economics, I still don't get it and you had didn't really follow the formula.

What is something that is economical and based on economics, but is not economics.
War is usually wasteful, it is usually based on national pride, but true it is not economics.

>>14560258
That is Dr. mrGTP-2 to you, I didn't spend 8 goddamn years in GPT-2 medical college for some little punk like you to call me mr.

>>14560058
>No, experimentation is principally based on deductive reasoning.
This is what IFLS overdose looks like.

>>14560277
I think what that anon may have been referring to of beyond logic, is that in order to make any progress one must a times take wild leaps and geusses, and that might not entirely be rigorously logical decisions but from there can gather some bearing and directions to get back on the logical road, or use logic from thereto try to meet back up with the logical grounds you lept from

>>14560566
So math is a pseudologic?

>>14559680
Can you give me an example of a set that is supposed to be "excluded"?

>>14560792
The set X defined by X = {X}. Technically it's not necessary to exclude this because it is not even well-defined and thus doesn't refer to any set. But some retards ITT don't get this point, so I had to make it explicit.

>>14555343
Terryism

>>14555375
Dumbest thing I've read

>>14560804
Is it a set though?

>>14560820
There's nothing rigorous about a theory resting on an undefined notion. Lol.

>>14555526
this.

ask yourself the question: is mathematical thinking any different than any other "form" of thinking? Answer is no.

Put another way, if a "dumb" person does mathematics, it wont change the fact that he/she is "dumb" and hence the insights dont come from any set of axioms or rules, but rather from the human brain....like in every other subject. So from the 3, closest is intuitionism.

>>14560824
I'm glad you've showcased how utterly clueless you are of even undergrad logic

>>14560602
No.... Math is logic, but in order for all math that has been discovered to be discovered, some of it is discovered by stepping beyond logic, also there is a term fuzzy logic

>>14561126
Why are you commenting if you are not familiar with formal logic?

>>14560820
What is a set?

>yfw "u cannot know nuffin" is not just a meme but an actual philosophical position
https://en.m.wikipedia.org/wiki/Ignoramus_et_ignorabimus

And based mathchad Hilbert BTFO the philosotards by telling them that math WILL continue to gain objective knowledge by proving things.

>>14561143
Through the history of math all great and below great mathamaticians that have contributed to the advancement of math have not solved every single problem and equation and mystery first try flawlessly without error.

Were the mistakes they made bouts of lacking logic? How could all those perfectly logical men following the flawless rules of logic advancing the logical field of mathematics, have made a single error if they were at no point being illogical, or acting beyond logic?

>>14561319
>some people made mistakes, therefore logic is le flawed
Philosotards grasping at straws

>>14561341
If you are so logical why can you not read?

I did not say all Math.

But that, it is possible, Math as a whole, part of it here and there, requires lapses in logic to make advancements. I was trying to clarify what the other anon said. Why do you not comprehend what has now been written multiple times in multiple ways. You didn't even properly respond to that last post of mine which was flawless logic, maybe at least.

If math is 100% only perfect logic, how did the great mathamaticians of history ever make a single error in the path of producing their work?

You do the math. The only logical answer is that to discover some of the logic of Math, lapses in logic were required. Which seemed to be what that anon was originally getting at.

A very simple obvious minut point, I don't know why it was even brought up or why you proudly misinterpreted it a few times

>>14560944
To be more accurate, set theory and similar axiomatic systems are perfectly rigorous as rules for symbol pushing. The problem is when you use this framework to implement known structures, e.g. the rationals, and prove theorems about them. There's no reason whatsoever to think that what you've proved about said structure is in fact true if your axioms are completely made up. It's just blind faith, and there's nothing rigorous about that.

>>14561126
>beyond logic
So math is a pseudologic since some of it is inside and some outside of the realm of logic?

>people see things in the world
>people develop axioms based on those observations
>people explore other consequences of said axioms,
>people start developing new axioms when they realize already existing axioms aren't enough
>thousands of the smartest people humanity has to offer work on refining these axiomatic systems
>boom maths
what's wrong with this?

>>14561928
Ok i see, you are saying self contained axiomatic tautalogical systems could theoretically have an issue here or there when forced to interact with different tautalogical systems?

I think this possibly could be evident when such systems of flawless self contained self possesed math systems are attempted to be superposed onto nature in physics, sure simple things like feet and inches and arcs line up quite nice, but where there are troubles and errors and contradictions and idiosyncraticies, and mismatches and misalignments, and lapses in equality, it could be this very thing you speak of

>>14562490
>sure simple things like feet and inches and arcs line up quite nice, but where there are troubles
And obviously maths work much more than just simple things, I didnt intend to not make that impression, just providing extremity of example.

Let's say the full scope of math has tools and methods to accurately map and describe and understand 99.9% of nature, where there are difficulties and contradictions and lapses in understanding and math seems to be missing something,

This is evidence that particular systems of math being used are not perfectly alligned with how nature exists

>>14562493
>This is evidence that particular systems of math being used are not perfectly alligned with how nature exists
And/or that math is capable (along with other things like computational visual simulation et al) of accurately describing and capturing the identity in equality of 100% of nature, it is just that the humans in the 99.9% example are failing to appropriately use the needed math to improve towards more complete acknowledgement and understanding

>>14562306
>what's wrong with this?
This part:
>>people start developing new axioms when they realize already existing axioms aren't enough
You have to make sure your axioms are meaningful and true.

>>14562117
I don't know the percentage make up, but all the effort is to make 100% logic.

So the end result is 100% logic.

But the end result of all math does not occur at the snap of the fingers instantly.

So it seems, trial and error and contradiction and hunches and gut feelings and intuitions and leaps of faiths and geuss and checks are required to get towards 100% logic.

One might even say those aforementioned things, are logical acts that are not pure logic but are required to advance the scope of pure logic

>>14562722
So math has not yet achieved its end result so it is still a pseudo logic until it achieves 100%?
What percent of pure logic is math actually at now in its current pseudological state, is it suppose to hit 100% around 2030 when the singularity is achieved?

>>14562743
No. 2+2=4 is 100% pure logic and An end of Math.

Math can be incomplete yet 100% logical.

2+2= 4 is Math and 100% logical
It's just its not all of math.

The task is to get the totality of existing math to be 100% logically consistent, while discovering and making new math that is also 100% logically consistent


When 2+2= 4 was defined and established. Before anyone thought another thing or knew another thing, did not 2+4 = 6?

6 is a symbol for six ones. Surely one single one existed (a rock), and 6 rocks existed.

When someone said: 1 rock and 1 rock is 2 rocks.

A pile of six rocks also existed, and that was 1 rock and 1 rock and 1.rock and 1 rock and 1 rock and 1 rock in a group

>>14562769
So its not beyond logic now, it is 100% incomplete pure logic?

Rocks are just broken pieces of some larger rock, fyi.

>>14562791
>So its not beyond logic now, it is 100% incomplete pure logic?
It's 100% pure logic when and where it is 100% pure logic. Self consistency.

The rules of chess. The notes on a piano. 1+1= 2.

When the rules of chess were made, even if no game was played, all possible legal games of chess existed in potential.

When the piano was axiomatically defined and made, all possible piano music came that much closer to having it's potential realized.

When 1+1= 2 was defined and realized;
Before anyone had time to think of another thought, 2 +1 had already 100% logically ='ed 3.

Before writing down 1 +1=2 and 2+1= 3

There likely was an occurance of a rock rolling down a hill to settle on another rock.

And another occurance of a rock rolling down a hill to settle on 2 rocks.


>Rocks are just broken pieces of some larger rock, fyi.

As 1 and 1 and 1 and 1 and 1 are just broken pieces of 5?

What matters is the definition, a mountain is possibly many rocks, as it is said the number 1 contains .2343 and .222543 and .1111111183 and .46737373......
But as long as it is stable as it's bodies definition self; 1 mountain is 1 mountain

>>14562977
>The rules of chess.
Those are based on symmetry and allegorical aesthetics, not logic.

>And another occurance of a rock rolling down a hill to settle on 2 rocks.
No, usually when rocks fall down a hill and smash into other rocks, they all break into many pieces.

>As 1 and 1 and 1 and 1 and 1 are just broken pieces of 5?
No, the rocks are uneven shards of some presently unseen whole that was destroyed in the past.

>But as long as it is stable
Its not stable, you can never count up from .2343 to .999....

>But as long as it is stable as it's bodies definition self; 1 mountain is 1 mountain
If you put 1 mountain on top of another, you don't have 2 mountains, you just have 1 bigger mountain.

>>14559372
Just wanted to let you know that you’re a fucking retard. Reread the first post. If you can’t understand that this is a philosophical issue you should do yourself a favor and buy some rope.

>>14555343
So far there’s been no conclusive argument, so for the time being we shouldn’t claim to know. A new, conclusive argument would likely not fit in this thread and in any event none of the posts already in the thread demonstrate even a minuscule fraction of the effort required for such an argument.

It’s true that someone might accidentally learn something by participating, but as a discussion of its nominal topic it’s a waste of time and energy.