/sci/ - Science & Math

>>5217343
what were his arguments for it being subjective? Your friend sounds like an annoying smart ass

axioms are subjective.
everything based on axioms is objective.

>>5217343
>1 always equals 1.
Does it?
This is a serious question.

>>5217349
We didn't linger on it for long, but his statement was that math is absolutely subjective, and if I knew anything about the subject I wouldn't be able to disagree with that.

>>5217355
Tell him if he knew anything about logical fallacies, he wouldn't be able to disagree with how retarded is argument is.

>>5217350
Short answer: Yes.
Long answer: Yes, because the statement of 1 = 1, or x = x, is not a statement regarding the 1 or the x, but rather the statement defining what it means to be equal, or to have an equation. Further, you have to realize that math is a representation of our perception, and 1 = 1 is the trust that what we are experiencing is something outside of ourselves giving us stimulation, or even that we ourselves are giving us stimulation. This is hard to explain, but if 1 could ever not equal 1, we wouldn't be in this universe anymore.

If math were subjective, that would imply that different people could come to different conclusions regarding the same starting axioms.

Which is ridiculous.

about as real as biological differences between races.

>>5217372
This is why I come to /sci/
Cause every now and then, you stumble across something really neat.

>>5217347

I wouldn't call axioms subjective... maybe arbitrary in some very restricted way, but not subjective.

The word "subjective" evokes immense faggotry from dangerously pretentious people anyway.

>>5217347
Axioms are like the building blocks of objectivity, but I don't think they qualify as subjective themselves.

>>5217343
Considering that they are basically the definition of objectivity, I'd say they're pretty fucking objective.

It's a senseless question.

>>5217379
Still I think that if anything in mathematics is subjective, it is the axioms.
But by "subjective" in this case I understand as something disputable by some means. Of course most of known axioms are "obvious" and almost objective. But in group theory the problem is axiom of choice(at first glance also "obvious") which if we accept it can give some counterintuitive results.

tl;dr
Don't exaggerate "subjective"

Yes it is, as long as you're still in this universe, as someone here already pointed out.

>>5217418
Stop posting, or otherwise explain yourself.

>>5217431
It has no meaning.
Subjective: what subjects perceive.
Objective: what happens to the object.
It doesn't mean anything to say that a science is objective or subjective. Especially when it doesn't study the real world.

>>5217434
Mathematics is the purest method of observing the real world, and is the language of describing the world around us.
That's why the answer is that it's objective. It does not matter what the subject perceives, the object (not a physical object, but the solid system of numbers) always functions in the same way.
The definitions don't only apply to physical objects.

>>5217343
Mathematics is ENTIRELY objective.

When your friend makes a weird and nonsensical statement, ask him to explain himself. He might have a simple example or a reason for his statement.

Like, he confused the two terms, and you're wasting our time.

OP, do you know that, literally,

math = objectivity.

They're the same thing.

>>5217449
He wasn't confusing the terms, and he's usually a pretty smart fellow. One of the smarter people I know, for sure.

I just couldn't possibly understand how math could be subjective, and being that he is almost certainly more interested in mathematics than I am, I wanted to hear /sci/'s opinion.

Thanks for the discussion people.

math/logic are constructed by humans. they can't be objective.

>>5217482
No, they are observed by humans; we simply add the symbolism.
Math is the reality around us. Humanity only finds ways of describing it.

>>5217497

our perception is flawed, therefore so is math.

>>5217504
No; flaws in human perception to not boil down to flaws in basic mathematical principle.
1 always equals 1, period, objectively, without a doubt.

There are no right or wrong answers in math class. Every student is an individual with their own unique perception.

>>5217508
>without a doubt

because your perception is flawed.

>>5217517

And you're a unique little snowflake (:

>>5217519
It does not matter how you perceive a closed system, like math. There is no room for interpretation or subjectivity at all.

>>5217520
>There is no room for interpretation or subjectivity at all.

that's how you perceive it.

Objective, Liebniz and Newton both discovered calculus.

Math is defined over an arbitrary set of rules, the results of working over those rules are completely logical and exact.
I have no fucking idea what subjectivity and objectivity would mean in this context.

>>5217526
What is this Math with a big M that is a closed system? It's being built upon and discoursed on daily by people, albeit according to different sets of rules.

To those who equate math with the world around us, I find that idea retarded. Yes, math can be used to infer and model features of the world around us, but not necessarily so. It's mostly playing around with abstract rules that we formulated to begin with. That doesn't make it entirely subjective, however.

tl;dr, it's sort of both subjective and objective. It's the dichtonomy that's retarded. Mathematics is in constant dialogue with the real world as well as with people.

>>5217444
Thus why it's meaningless.
All sciences are interested in their subject, not their object (except sociology of science I guess).
It doesn't mean anything to says that a particular science is objective or subjective.

>>5217570
I meant the other way around.

The formulation of the OP begs the question if "objective" and "subjective" are sensible attributes in this regard.

I have to say that I'm annoyingly sceptic, and I basically don't believe in valid semantics for the real world. That being sad, here's my superfluous opinion on the subject:

My problem with calling mathematics objective is that what is considered true is at best that which people agree on to be true.
If e.g. everyone but you insists on "1=1 is wrong", what does it mean for you to be of the opinion that it's right?
Can you define truth without using the definiton of truth? Hint: no, you need a meta language, see Tarski. Hence truth is something people agree on.

Notice also that even if you accept this notion of truth, every conclusion you draw eventually relies on induction. Hence you need a basis for arguments and we can't single out a true one.

So here is the best I can do for you:
I personally accept (and by this I mean I take it as a base of reasoning, that doesn't mean it's granted in any way) that games like this "ask 100 strangers to take a look at the string XXXX and add tell them to add one X" will have a positive outcome, in the sense that they will manage to agree on the resulting string (this will be XXXXX).
In this sense I take the statement "If I add one X to XXXX I get XXXXX" to be 'true'.
Notice that this is basically a notion of computation, relies on others conciousness and moreover reduces mathematics to syntactic operations.
Some might consider this to be a somewhat cold point of view, but it doesn't take the fun away for me.

Here's a possible explanation:
>You're friend isn't very good at math.

>>5217570
>>5217571
New to thread.

I sense some equivocation.

>>5217576
Some people just like to argue over things. They pick some ridiculous stance to argue for and are happy when they get to use their creativity and learned debating techniques.

>>5217587
http://en.wikipedia.org/wiki/The_art_of_being_right

>>5217589
>It Applies in Theory, but Not in Practice
My fucking favorite one.

>>5217574
>begs the question
I think you mean "asks the question". They're different.
http://en.wikipedia.org/wiki/Begging_the_question

>My problem with calling mathematics objective is that what is considered true is at best that which people agree on to be true.
>considered true...people agree on to be true
>considered...people agree
You've changed the question by introducing a subjective element: consideration. What is considered true is different from what is actually true, which is the whole point of this thread. You've begged the question.

>If e.g. everyone but you insists on "1=1 is wrong", what does it mean for you to be of the opinion that it's right?
It means that everyone thinks differently than you. It doesn't follow from a variety of opinions that truth is based upon those opinions.

>Can you define truth without using the definiton of truth?
You are asking for both A&~A. You've broken an axiom. And now we end up at these posts:
>>5217379
>>5217384
>>5217372

There's more but I'll leave this here first.

>>5217616
I'm not sure if begging the question doesn't work here.

Regarding
>What is considered true is different from what is actually true
I don't know how to interpret this comparison under the premise that there is no sensible way of "actually true", this is what I argued for in my post. I don't believe in objective truth, and then nothing is "actually true".

>You are asking for both A&~A. You've broken an axiom. And now we end up at these posts
Well, again, in my post I state that I don't believe that there are semantics which are valid for the real world. Hence arguing about something, a human activity, never ends up in establishing any factual result on the subject, only "at best" change in opinions of the participants.
You can use "A&~A", or rather what you read into this string, as a tool for argumentation, but I don't feel the need to accept this and hence it will not convince me. I, and I think this goes for everyone, will not accept any conclusion because I see the necessity of the argument. If I change my mind then because I've convinced myself of it (supported by getting the necessary information for my opponent in discussion). We're just educating ourself.

I don't think that I've quotes "changed the question". I basically explicitly formulated my post as "a) I'm not sure to what extend the word objective can apply here, b) here is my opinion on the subject as a whole: c) I don't believe in objective truth, hence I don't see how anything (including mathematics) would be independend of peoples point of view - which would be necessary for mathematics"

Mathematical statements like "2+2=4" are context-dependent; they depend on which axioms you use. Subjective statements like "that painting is beautiful" are also context-dependent; they depend on which subject is relating his experience. Dependence on axioms and subjectivity are similar but not the same thing. Different mathematicians can choose to use the same axioms.

>>5217343

>thinks 1 is always equal to 1

>>5217350 : no, it doesn't

That which has reference and meaning must have being - I'm sure we can all agree to something so simple. If I can speak of and designate a meaningful singular object in the universe, it must be.

With this in mind, any being must have some place in a spatio-temporal context. If 1 has being, then it also must be the case that being oneness must have being, for being 1 cannot be non-being, for if it were we wouldn't be able to speak of it. This suggests that there lays an infinite regression of oneness which is needed to justify the being of 1. 1 thus, must not be equal to 1, but be equal to the inter-relationships among numbers as a whole; for 1 alone cannot be if it is equal to itself, and thus must be equal to not-1; or those numbers which are not 1.

>>5217343
do you even axioms?

>>5217616
Modern usage

Many English speakers use "begs the question" to mean "raises the question," or "impels the question," and follow that phrase with the question raised,[17]

English is a fluid language, the usage was correct

http://arxiv.org/abs/1108.4223

QED

>>5217642
I'm simplifying but it seems like you are saying one of two things:
>It is objectively true that there is no objectivity.
This is a contradiction.
>It is subjectively true (I believe it is true) that there is no objectivity.
This is coherent but leaves you with no epistemic justification for believing anything, only a instrumental one.

Here's a similar problem. Below are two propositions. Which has the better direction of explanation?
>It's true because I believe it's true.
>I believe it's true because it's true.
Or maybe you want to say:
>I believe it's true because I believe it's true.
A tautology that begs the question.

Or another:
>Apples are good.
>I like apples.
In the former, the speaker expresses his opinion of apples but in the latter, the speaker expresses the fact of his opinion of apples.

>>5217679
the fuck?

>>5217679
It's like you really think your babble makes any sense at all.
What you just said would get you laughed out of any institution. You sound like a college dropout on acid.

>If 1 has being, then it also must be the case that being oneness must have being, for being 1 cannot be non-being, for if it were we wouldn't be able to speak of it.
It exists as an idea within an unchanging system of interaction.

Do you know that even discussing 'equality' in your argument means that 1 must equal 1, because the equation 1=1 is the reality upon which equality relies?

If one didn't equal one, you couldn't even make an equation to begin with, or grasp the concept of equality at all.

>>5217684
>Many English speakers use "begs the question" to mean "raises the question," or "impels the question," and follow that phrase with the question raised,[17]
You forgot the very next sentence:
>Philosophers and many grammarians deem such usage incorrect.[18][19]

Do you really want to take the side of colloquial English?

>>5217720

You're mistaking your own subjective incomprehensibility for objective incomprehensibility; what authority are you on what an institution most desires to see anyway?

Let me explain it in layman's terms:

The statement 1 = 1 relies on the belief that being 1 must necessarily be 1; this statement in itself relies on the being of the being of oneness ad infinitum, thus resulting in an infinite regression of terms requiring justification for prior terms. The statement 1 = 1 alone is thus not a justifiable statement unless 1 is considered as a relationship among numbers of different relational values. 1 is not equal to 1, but it's equal to not-that-which-isn't-one.

my god...was it that difficult to fathom?

This is a semantics difference. Colloquially, objective means that there actually is a right answer. Philosophically, objective can mean having to do with the object, things outside the subject or mind. Math is purely subjective in that its goal is only of the mind, not the physical world. Physics is math applied objectively.

>>5217704
It's the second one of your statement. I think there is no "godgiven" justification to believe anything. Discussion is a vehicle for people which ends up in them making the next move.
If one comes to expect that in my XXXX game, the result of the experiment will be XXXXX then this suggest to him to do something on that premise. The premise being that XXXXX will be the result. People collect expectations and this somehow makes them do something based on it. This is pretty instrumental, if you want to use that word. Pragmatic too.


not so relevant side note:
Also your conclusion
>This is a contradiction.
is based on semantics. You translate the englisch sentence into "A&~A" and imply "A&~A" is false.
Under this light, you might call the sentence a contradiction, but even if we have established this this is the case (even if we have now established that under this light it would be a consequence that we can call it a contradiction) that is still not an interesting argument. I don't consider contradiction in this sense to be a bad thing.
This reminds me of that debate
http://en.wikipedia.org/wiki/Brouwer%E2%80%93Hilbert_controversy
even if back then, they were not as radical.
It might be not particular meaningful to discuss these things with someone who rejects the necessarity for there to be a base of logical implication in the real world (=e.g. me).

so guys, this is a story about subjective axioms.

Axioms, as you know, are based on logic. Logic is based on preferred state of condition.
So let me ask you:

To you left is a hole of fire. If you choose it and jump in it you will die, but before you die, you will BURN.
To your right is a pool filled with ocean water, just the right temperature to relax and invite some ladies to have fun.

Your logic picks the pool. Your logic is subjective. It's not fair to the hole of fire.

Axioms are based on logic. Axioms are subjective.

Do your best to tear these ideas apart. tell me why they aren't feasible and what would be a better alternative.

>>5217350
The equivalence relation is reflective, and we defined the equivalence relation.

>inb4 this devolves into "All maths is just abstraction"

>>5217751
btw. in the second paragraph I'm refering especially to Brouwers paper "The untrustworthiness of the principles of logic" and his problem with the law of the excluded middle. I call this mild, as he only rejects the primary position of the so called classical logic.
Nowadays, I'd even call

http://en.wikipedia.org/wiki/Paraconsistent_logic

classical.
If you take a modern stance, drop the set perspective and consider more general topoi ("modern", well these category theoretical ideas are also already from the 60's now), then you get an infinite number of "logics" - their consistency suggests to me that one should extend Brouwers dismissal to reject any logics irl. I.e. drop any "final meta language", take human action and interaction as primary thing and consider math to be what people who call them self mathematicans do - writing down strings of symbols and getting money for publishing them.

Math is objective by the nature of its conceptualization. Ultimately all concepts used in math derive from observations of reality, there are just levels and levels of abstracting involved with mathematics.

We get the concept of length from observing an existent, i.e a stick. We see that a rock too has length, but a different length. Therefore we can say things have length, and that they can exist in some finite quantity and still be attributed to a concept. When one thinks of a stick or a rock, one does not have a specific length (or any other measurement) in mind with that concept, just an implicit understanding that it has those dimensions in some quantity. You can even define a relationship between the dimensions of the stick and rock (i.e multiple things).

Sounds like algebra or geometry, right? 2x = x + x is true for any quantity, not just a specific quantity.

Abstract =/= subjective. "Subjective mathematics" is a contradiction in terms, as any form of math not rooted in reality will be insane and useless with regards to any real world problem solving, insights into logic, or any other thing we use math for. It would not be math, it would be the scribblings of a deranged person.

>>5217683
so believing in the axiom of choice is not subjective?

>>5217794
Interesting stuff. I saved the links for future reading.
>It might be not particular meaningful to discuss these things with someone who rejects the necessarity...
You're probably right, though this ironically means nothing for you.

>Emma Stone
At least we can agree on something.

>>5217890
>not stating your axioms

>>5217642
>>5217751
>>5217794
I like you. Are you a mathematician ?

Mathematical objects and construction are objective, the meaning we give to them and the interpretations and use we make of them are subjective.

>entire field developed off of logic, abstractions and based on proofs
>must be subjective
Math is true regardless of what language you speak or whether or not your father raped you at night.

Hey, OP, I created this boards.4chan.org/sci/res/5216663 thread faster than you ! its not fair !

>>5217938
nope.

Q: have you been participating in this thread?

>>5218325
no i wasnt

so what is ur major then ?

>>5217343
There are degrees of subjectivity and objectivity and most non-philosophers of maths find a hard time expressing their real views. Are mathematical truths absolute truths? I don't know how one could answer such a question without providing a teleological explanation. Are they completely subjective in the sense that they are meaningless and reflect no truths of the world? They could be, however, one must then answer the question why we have such predictive sciences whose foundations rest on areas of mathematics like real analysis. In conclusion, this is not at all an easy question and it will take you years to even become competent enough to propose a theory of your own. I suggest reading some literature on the subject.

>>5217728
>Implying words and definitions aren't added to dictionaries and phrase books on a regular basis

The usage was correct, just because some people are stuck in the past doesn't change that fact

String theory showing us the perfectness and objectivity of mathematical truths

>>5218678
string theory is a big jumble of shit. it's not elegant and it doesn't work. it's about as objective as taking all the sickers off a scrambled rubix cube and putting the stickers back to default

>>5218687
Do you have any idea what you are talking about, or any education whatsoever, or are you just a pseudointellectual laymen trying to sound smart?

>>5218713
ST-fags are as quick as light

>>5218455
I studied physics to a masters