/sci/ - Science & Math

[Anonymous No.15231015]

>this statement is false
Statements do not talk. They are not people. Every statement is only meaningful if it is understood to come from a living, breathing, thinking organism. “This statement is false” would never be uttered by a human in real life, because it is as meaningless as simply saying “Statement.”

There are some serious problems with mathematics and logic, and that is why you end up with “paradoxes.” They are referring to objects that they can’t even understand. For example, you cannot give a non-circular definition of an infinite set. But very few people realize this.

[Anonymous No.15231024]

people pretending to know things they dont to feel like they understand something. many such cases. i got a suspician that a large amount of the axioms used in mathematics are incomplete and ill defined. what are most important ones anon?

[Anonymous No.15231036]

>>15231015
>Statements do not talk. They are not people.
cool, so just give up multiplication and the whole problem goes away

[Anonymous No.15231070]

>>15231015
Low quality posts are against the rules.

[Anonymous No.15231084]

>that art style
What you want is on p. 146 of "The Cartoon Guide to Computer Science" by Larry Gonick
https://archive.org/details/TheCartoonGuideToComputerScience/page/n149/mode/2up?view=theater
So one problem with
>this sentence is false
is the demand that you essentially define some logical system that is capable of handling a concept of time and then rigidly fix that interpretation of time, for example by simulating the control voltages in an electronic circuit, propagating each logic gate output terminal voltage driver to its receiving input terminals via connecting wires
For example, see 3.3.4 of SICP
https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/6515/sicp.zip/full-text/book/book-Z-H-22.html#%_sec_3.3.4

[Anonymous No.15231188]

>>15231015
What's the smallest number you can name in fifteen words or less?

[Anonymous No.15231191]

>>15231188
you can always invent a new word to describe a number. This is so embarrassing. Holy shit humans are retarded

[Anonymous No.15231197]

https://www.youtube.com/watch?v=mhIkyqLDl9M

[Anonymous No.15231202]

>>15231197
>useless and vague concepts lead to paradoxes
many such cases

[Anonymous No.15231230]

>>15231015
Your inability to understand a freshmen level logic class is not a fault in everyone else.

[Anonymous No.15231247]

>>15231191
Wrong

[Anonymous No.15231337]

>>15231015
>“This statement is false” would never be uttered by a human in real life, because it is as meaningless as simply saying “Statement.”
And people literally have said "this statement is false" many times. People have also said "Statement." many times as well. What is the truth value to those statements? Did the individual lie?

[Anonymous No.15231546]

>>15231202
Useful but general (which is when most concepts are useful). Vague means the paradox helps us make it unvague. Dumbass.

[Anonymous No.15232113]

Anyone brave enough to explain to me why Xeno's Paradox is wrong?

[Anonymous No.15232122]

>>15232113
neither Achilles nor the tortoise are ever actually standing still, so it's wrong because Xeno is a fucking liar

[Anonymous No.15232129]

>>15231188
Infinity (one word)

[Anonymous No.15232134]

>>15231015
Based common sense retard. You never even approach to making a compelling logical argument, but the spirit of what you're saying is probably true.

[Anonymous No.15232143]

>>15231015
I'm pretty sure it's logically ok to say a statement is false. I don't get how your last paragraph is related to the first though

[Anonymous No.15232172]

>>15232143
When you say something is false, it really just means that you disagree with it. So
>this statement is false
really just means
>this statement disagrees with itself
and if you believe statements are magically sentient beings then this means
>I disagree with myself
or
>I both agree and disagree with what I currently am proposing (nothing)

This shit is so retarded I don’t know anyone takes it seriously. People do not talk like this. Math and logic should simulate REALITY, or that which we experience

[Anonymous No.15232188]

>>15232113
Infinite subsections doesn't mean infinite time passes

[Anonymous No.15232191]

>>15232129
>not a number
>not small
You're retarded

[Anonymous No.15232194]

>>15232172
I experience people are assholes who don't understand truth and logic. I don't want math to mimic that, but with affirimitive action and racist math, it progressively is. Enjoy your new math "simulating REALITY"

[Anonymous No.15232235]

>>15231015
Everything I say is a lie.

Happy now?
OP is a brainlet who thinks he solved paradoxes by eliminating an irrelevant ingredient in his example.
Philosophy majors btfo. I swear philosophy is just where contrarians go to pick up pedantic tactics.

[Anonymous No.15232238]

>>15232235
Meds now.

[Anonymous No.15232244]

>>15232238
Which part is crazy?
I just presented the same paradox in the form a human would utter.

[Anonymous No.15232253]

>>15232244
The part where you present a formulation of the paradox that originates with philosophers and then immediately start to sperg out about how philosophy bad for no discernible reason.

[Anonymous No.15232259]

>>15232235
>Everything I say is a lie.
This is vague. Does this mean that everything you have ever said was a lie? I highly suspect that you are just lying right now, so there is no paradox. Even if you said something like
>I can only tell lies. It is impossible for me to tell the truth
then again, everyone would just perceive this as a lie and go on about their day. So you would have to design some sort of organism or robot that actually cannot tell a lie. It would have to know which statements are true or false (or at least what it believes is true and false), and then purposely select from the false statements. Therefore it would never actually utter the statement “I can only lie” since it is true.

[Anonymous No.15232272]

>>15232244
>I just presented the same paradox
You didn't. No wonder a retard like you hates philosophy.

[Anonymous No.15232280]

>>15231015
There are problems in mathematics that are undecidable, so unprovability is not just for a couple of weird self referential statements.

https://en.wikipedia.org/wiki/Collatz_conjecture#Undecidable_generalizations

https://en.wikipedia.org/wiki/Diophantine_set#Application_to_Hilbert's_tenth_problem

Ultimately the results Godels incompleteness theorems, Tarskis undefinability of truth theorem, Russels paradox and and turings halting problem are all just basically the same "paradox" in different forms. This "paradox" actually is fairly simple, it stems from the combination of Lawveres fixed point theorem and the fact that negation has no fixed point.

https://www.emis.de/journals/TAC/reprints/articles/15/tr15.pdf

Here are some youtube videos explaining it.

https://www.youtube.com/watch?v=7N3iKB0OnOs&t=819s
https://www.youtube.com/watch?v=dwNxVpbEVcc

[Anonymous No.15232288]

>>15232272
It's just a simple self reference.
You could expand the 1-cycle to a 2-cycle with:
The next statement is true.
The previous statement is false.

You could go to an n-cycle with:
The next statement is true.
The next statement is true.
...
The first statement is false.

In a sense they are all capturing the same paradox.

[Anonymous No.15232308]

>>15232288
>The next statement is true.
>The previous statement is false.
meaningless. No one talks like this. And it’s ultimately just a contradiction: “I agree and disagree with what I am saying (nothing)”

So not only does it lack meaning, but it is a contradictory. Congratulations, you could not devise a more retarded statement if you tried.

[Anonymous No.15232314]

>>15232288
You sound severely retarded. There's nothing paradoxical about the statement "everything I say is a lie". If taken to be false, it follows that some things you say are true and some are not, which allows for "everything I say is a lie" to be a lie without inconsistency.

[Anonymous No.15232315]

>>15231015
>you cannot give a non-circular definition of an infinite set
You cannot give a non-circular definition of any word in the dictionary.
Your words are meaningless.

[Anonymous No.15232332]

OP wants you to think that rejecting Gödel's bullshit fallacy "let me redefine proof halfway through a proof" means that everything after Cantor has to be rejected.
This is historically inaccurate: Gödel's work is a perversion of Cantor's, Dedekind's, and Kronecker's work.

[Anonymous No.15232334]

>>15232315
infinite sets cannot be referred to by experience. Whereas the sun, trees, dogs, numbers, etc. can all be defined in relation to experience. Language is the map, so of course you cannot simulate the territory using the map alone. It is a reference

[Anonymous No.15232339]

(*)
>this statement is false
(**)
>you cannot give a non-circular definition of an infinite set
From a historical perspective, (*) has nothing to do with (**). In other words, OP is taking a historical revisionist perspective, but he isn't being honest about it.
Why not, OP?
Why won't you tell us the truth about the edit's you've made to history along the way to arrive at your slanderous conclusions about infinite sets?
By the way, there is certainly some scholarship on infinite sets that is as rotten as Gödel's theorems. No doubt infinite sets have proven themselves quite vulnerable to Gödel's tricks.
No doubt about it.
However, we can't throw away infinite sets quite yet. It is still *quite likely* that we can erect barriers to bad math that keep Gödel's magic tricks in the theater where they belong.

[Anonymous No.15232346]

>>15232334
Define experience.
>Language is the map
Is experience not just a kind of map?
>so of course you cannot simulate the territory using the map alone
Your senses are presumably just a way of "simulating the territory".

[Anonymous No.15232347]

>>15232334
That isn't true; people use infinite sets for planning. The schedule of activities is as ordinary as the sun and trees, and you refuse to admit that people do not limit their projections of future activity to a specific time frame, they just assume that time will be unlimited.
>t. demanding royalty payments in fake internet style points right now for use of omitted period, pay up motherfucker!!!!

[Anonymous No.15232350]

>>15232334
Anytime you want to refer to a process that is going to involve activities that are repetitive and beyond your attention span, you will reach for infinite sets instinctively, and you should, because infinite sets will tell you what you want to know for the period of time where things are too boring for attention.
The whole point of proving things about infinite sets is to show that after a certain point, things aren't complicated, they're simple, you can grapple with the simple, and you can prove that things don't get too out of control.
Clearly you can give attention back to the process before an infinite amount of time has elapsed, but instead of specifically limiting yourself a priori to a limited horizon, you can just say
>okay, whenever I feel like it
>after all, I proved that everything is okay, the assembly line will be fine, the supply will be fine, the demand will be fine, &c.
>I didn't limit myself to a specific time frame
>I can relax

[Anonymous No.15232354]

>>15231015
>“This statement is false” would never be uttered by a human in real life,
And yet, here we are.

[Anonymous No.15232357]

>>15232346
>Define experience
Good question. We say that we are experiencing when we are awake, or when we are dreaming when we are asleep. When we take naps, everyone else has experience, whereas during that time frame we do not. If it weren’t for sleep and unconsciousness then we probably would not have been so aware of consciousness/experience. So we are just noticing the difference and creating those categories. To have an experience of something means I am somewhat familiar with it and can tell you about it by referring to my memory
>Is experience not just a kind of map?
what is the territory, then? You have no access to the “real world” without the map of experience. If you want me to clarify and say that language is the map of experience, as opposed to some objective reality, then I am happy to make that specification.

[Anonymous No.15232365]

>>15232357
>language is the map of experience, as opposed to some objective reality
So your words only mean something to you and when you try to communicate to anyone else they lose meaning?

[Anonymous No.15232367]

>>15232357
Go to a metaphysics board such as /lit/ or /his/ for
>muh consciousness
These topics aren't related to the OP
OP is math related
OP is not metaphysics

[Anonymous No.15232371]

>>15232365
this is linguistics and philosophy
it is not math
it is not science

[Anonymous No.15232382]

>>15232367
OP is metaphysics wrapped in a mathy wrapping paper.
Condemn the whole thread.

[Anonymous No.15232387]

>>15232365
My words are a reflection of my experience, yes. It just happens that people share common experiences and so our language refers to very similar things. People often assume that words or phrases can only have one objective meaning when they are actually completely dependent on the person speaking them. Sometimes you have to translate what they are saying into something that makes sense to you. For example, “life is meaningless and bad” really just means “I do not like living and would like to die.”

[Anonymous No.15232395]

>>15232387
Uniqueness makes this very complicated ain't it?

Welcome to reality son, in here we have to study things case by case, in the perfect scenario one scientist handles one sample

[Anonymous No.15232410]

>>15232395
Yes, no two things in the universe are equal, or else they would be the same object, or just one object. No two dogs are the same but they are much more similar to each other compared to other animals. Language is just the abstract categorization is patterns of experience, which is why I refuse to validate the term “infinite set” in a strictly formal mathematics. To me, “infinite” just means “incomprehensibly big.” By this understanding, even a finite amount could be considered infinite, because we would have no way of ever comprehending the amount. In other words, we could have no way of comparing it to other finite amounts, which just means that we haven’t yet counted it completely. So the natural numbers are finite but you can’t “just add one” because there is nothing to add and no one to add it

[Anonymous No.15232414]

>>15232382
bullshit
OP is trying to get you to think that rejecting Gödel implies rejecting Cantor
it has nothing to do with metaphysics
begone, future /lit/ or /his/ reader, begone!

[Anonymous No.15232417]

>>15232410
this is just insane garbage

[Anonymous No.15232421]

>>15232410
You're pretending that you can just ignore Cantor and his work by saying
>my solipsism is greater than all education philosophy since 1875
you are a fucking narcissist, motherfucker!!!

[Anonymous No.15232426]

>>15232410
>By this understanding, even a finite amount could be considered infinite
That's fine, but not in mathematics.
Go to /lit/ or /his/ to discuss this obviously metaphysical argument.
If you're going to refuse to read mathematical definitions of finite and infinity, fine.
Do it on a metaphysics board, dude!
You're just fucking with math nerds!
You're saying
>Oh, I don't like what the math nerds say.
Fine! Get the fuck out of here!
https://www.youtube.com/watch?v=fcrexKS8kxA

[Anonymous No.15232430]

>>15232414
Read OP's first paragraph.
It is clearly metaphysics.

OP's second paragraph spawned the whole circular definition discussion that went into linguistics and metaphysics.

[Anonymous No.15232438]

>>15232430
No, OP is trying to justify refusal to read the axiom of infinity.
That isn't metaphysics.
That's anti-mathematics.

[Anonymous No.15232445]

>>15232430
Axiom of infinity says there is a I such that
>{} <- I
>if x <- I, then x U {x} <- I
and there is absolutely zero circularity here.
The whole point of OP is to try to get you to accept idiotic misunderstandings of Cantor's theory as if they were accurate.

[Anonymous No.15232447]

>>15232421
>You're pretending that you can just ignore Cantor and his work by saying
well.. why can’t I? The only that really matters is procuring good experiences, outcompeting other organisms, achieving your goals, etc. Math is a tool for that purpose. Infinite sets do not help me in the same way that they help you (by making you feel proud to understand something that is abstract and otherworldly), so I can ignore Cantor just fine. When he says that some infinite sets are bigger than others, all I can do is laugh. And yet I can translate this to something that I understand even in finitist terms. For example, the number of molecules is “infinite,” but the number of atoms is “more infinite.” I will not waste time trying to understand something that does not actually exist in my experience.

[Anonymous No.15232457]

>>15232445
Okay, fine. From a naive "I just opened p. 1 of Halmos and don't know what a derivative is" perspective, yes, there is a trivial circularity when you try to represent an infinite set using a finite amount of paper and ink.
The whole point of math proof culture is that you hit this barrier and realize it isn't going to work.
The whole point of math is getting over this trivial non-circularity that only appears to be a circularity for the first week of the first math class you take in college.

[Anonymous No.15232462]

>>15232445
sets of sets is nonsense (nonsets)

[Anonymous No.15232464]

>>15232447
>help
go to /lit/ or /his/ for pragmatism
math doesn't have to fit into your pragmatic philosophy like some metaphysical expansion card for your spiritual interconnect bus
take your nazi self-improvement rhetoric to /fit/

[Anonymous No.15232468]

>>15232462
This is anti-math
at least you're attacking Cantor directly and not trying to say that if you reject Gödel then you have to reject Cantor

[Anonymous No.15232477]

>>15232464
but your math is also pragmatism. You are trying to be intellectual without actually showing anything for it in the real world. At best it is only entertaining.

[Anonymous No.15232480]

>>15232447
I think you aren't realizing how useful a proof of the nonexistence of a bijection is. It's related to education philosophy culture, the same culture that actually took over Europe in the 20th century and actually caused WW I and WW II. It's an international language that can express meaning.
You aren't appreciating how this cuts across language barriers like a hot knife through butter.
There is a reason why it was called the foundational crisis.
The entire floor of European society gave way and the result was...the biggest events of the 20th century

[Anonymous No.15232481]

>>15232447
>well.. why can’t I?
Because proofs are true whether you understand them or not.

>Infinite sets do not help me in the same way that they help you
They do, since that are used in physics all the time.

>For example, the number of molecules is “infinite,” but the number of atoms is “more infinite.”
Wrong, they are both countable infinite, the same size. LOL. Dunning Kruger

[Anonymous No.15232482]

>>15232447
This is a fucking science board. If cantor says that some infinite sets are bigger than others you then go "Oh ok". Neither the number of atoms or molecules in the universe is infinite, at least to the best of our knowledge. Your entire post is garbage.

[Anonymous No.15232485]

>>15232477
>You are trying to be intellectual
I'm trying to avoid it, dipshit

[Anonymous No.15232487]

>>15232468
I’m not anti-math. Math is obviously extremely useful at solving problems in the real world. But all the argument over infinite sets and meta-mathematics etc. is a waste of time and intelligence. We invented math to solve problems, but now it has become a game that generates problems itself that need to be solved to satisfy the mathematician. They don’t actually relate to problems in the real world.

[Anonymous No.15232511]

>>15232481
>Because proofs are true whether you understand them or not
What does it mean for a proof to be true? It has to follow from the axioms. Every single step, every shaping and modification of the problem must refer to some axiom or law of logic. Supposing you COULD do this with Cantor’s proof, I would simply reject the axioms.
>They do, since that are used in physics all the time.
they’re unnecessary

[Anonymous No.15232512]

>>15232487
That's preposterous. Math is about creating problems in the real world. They're called math problems, and you have to solve them and turn them into the grader, who evaluates your problem solving skill.
Clearly this can't happen unless problems are created, math problems, math problems for math classes, math problems for math classes that can be solved by people who grade math homework.

[Anonymous No.15233300]

>>15232512
MATH
>HOMEWORK
FOR
>MATH
CLASSES
>THAT
CAN
>BE
SOLVED
>BY
PEOPLE
>WHO
SUBMIT
>MATH
HOMEWORK
>TO
PEOPLE
>WHO
GRADE
>MATH
HOMEWORK
https://www.youtube.com/watch?v=WDswiT87oo8

[Anonymous No.15233708]

>>15231188
TREE(Graham's Number)^-1

[Anonymous No.15233717]

-1
Proof:
-1 < TREE(Graham's Number)^-1

[Anonymous No.15234067]

>>15231188
Two. One is a unit, not a number.

[Anonymous No.15234076]

>>15231188
If there's no limit on word length, indeterminant. If 15 characters, threethreethree.

[Anonymous No.15234871]

>>15231015
you just need a trivalent logic system.
>true
>false
>retarded
the statement "this statement is false" is neither true nor false: it is retarded.

[Anonymous No.15234873]

>>15232113
after a while achilles will no longer be able to cut his distance in half due to his finite size and will need to either remain at rest or touch the finish line.