Thread: Epistemological Relativism

And that is how I can tell you are just a poser, and don't actually know squat. You read it incorrectly, and if you knew the topic you wouldn't have done so. You weren't taught that basic arithmetic equations are called identities.

Identities are basically rules that work for all numbers, no one would ever call 2+2=4 an identity, because it isn't one. You just saw a loophole, a way out of looking like an idiot for saying it wasn't an equation and tried to use it. However you totally failed because it doesn't work the way you think it does.

You can try to twist things all you want, but no one is going to believe that you were taught that arithmetic problems are called identities. I would of just chalked it up to you making a simple mistake with words, since everyone makes mistakes, but then you kept arguing with me that it wasn't an equation but an identity. So obviously it isn't a mistake, you are just clueless.

Actually, asshole, 4 is a "constant function". That's how it is because it's usual to regard anything as a function so that an equation would be f(x) = g(x) and that would be an identity if f(x) = g(x) for all x. So 2 + 2 would be the constant function 2 added to itself and we have something like f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4.

Look up constant functions. And accept that you don't even know basic math or everything I've said would be comprehensible. You've just learned some algorithms. A computer could do anything you could...

And what about swearing that math is logical while refusing to acknowledge that it's not, formally, logical. So you have to go beyond math and logic to talk about them but then try to act like you talk with the authority of them both.

Who's weaseling?

Moron.

I still don't regard identities as equations (and 2 + 2 = 4 is most definitely an identity) and wikipedia supports me in claiming that many mathematicians don't.

You are either trying to be obnoxious, or you are really are totally clueless. I know what functions are, and I know everything you have been talking about on this thread. That is how I know you are totally wrong, and what you are saying doesn't make any sense.

You could write the problem as f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4, but that doesn't help your argument at all. Even written like that is still not an identity. Like I said identities are more like general rules, not specific equations, and that problem right there is a very specific equation.

And stop saying wiki backs you up, because it doesn't. We already know you suck at math, but you are proving that you suck at reading too. So let me educate you on reading.

Here is what wiki says, "Many mathematicians reserve the term equation exclusively for the second type, to signify an equality which is not an identity."

Okay you read that, but here is your problem. You didn't read what it was referring to when it said the "second type" of equation. So lets read what the second type of equation was.

"However, equations can also be correct for only certain values of the variables. In this case, they can be solved to find the values that satisfy the equality."

So here is your problem once again, f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4.

What?! Your equation is only correct for certain values of the variables? When f(x)=2 and when g(x)=4. I know you are a little slow, so read the post over five or six more times if you need to. Wikipedia actually says you are wrong, and that the problem is an equation, not an identity.

Originally Posted by Alric

You could write the problem as f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4, but that doesn't help your argument at all. Even written like that is still not an identity. Like I said identities are more like general rules, not specific equations, and that problem right there is a very specific equation.

LMAO. So cos²(x) + sin²(x) = 1 isn't an identity? Better inform all the trig teachers. It seems pretty specific to me. Or it at least removes the assertion that 2 + 2 = 4 can't be an identity because it's "a specific equation". Not that I think it's an equation but it is by your definition.

Pressed for time right now. For fun, I'll come back and correct the rest of the post later.

But will you at least admit that the statement that math is logical is neither a mathematical statement nor a logical one? You seem to be ignoring that and that's the primary point.

That is a trig identity because it works for all numbers. It isn't specific, but extremely general. If x is 5 it works. If x is 7 it works, if its 320, 76, 2, 5.4, 1/2, pi, 1,000, a million, it doesn't matter. That all work. I told you like five times, if something works for all numbers then it is an identity.

What is so hard to understand about this concept? If it is a general rule and you can plug anything into it and it remains true its an identity. If it only remains true with only a very specific variable then it is an equation.

Hence the trig identity which has an infinite amount of possible x's is an identity, when the formula you gave before that only had a single possible x, is an equation.

To answer that other question no. Obviously saying math is logical isn't a math statement, but I never claimed it was, because it has no math in it. It is however logical. You have not put forth anything to suggest that math isn't logical, and only stated it as your opinion. However, since you apparently don't know much about math, and your arguments are extremely chaotic, random and nonsensical, I don't really think your in a position to offer opinions on logic or math.

Originally Posted by Alric

That is a trig identity because it works for all numbers. It isn't specific, but extremely general. If x is 5 it works. If x is 7 it works, if its 320, 76, 2, 5.4, 1/2, pi, 1,000, a million, it doesn't matter. That all work. I told you like five times, if something works for all numbers then it is an identity.

We're not disagreeing that if something works for all inputs then it's an identity. That's basically the definition of an identity: it's true across it's entire range of input values, i.e. across its whole domain.

Now disregard constant functions and consider 2 + 2 = 4. Where are the independent variables? There are none. Hence its domain is the empty set and there is no value in it's domain for which it's false. Hence it's an identity. Remember the negation of "is true across it's domain" is "there exists one element in its domain for which it's false". There are no elements in its domain so there is no way in which there can be an element over which it's false.

To phrase this in terms of constant functions (which you already agreed to using) if f(x) = 2 and g(x) = 4 then regardless of the domain (i.e. the elements from which we choose x) then f(x) + f(x) = 2 + 2 = 4 = g(x). Hence any which way we choose x, the statement is true and we see that it's an identity.

So either by the definition of a constant function or by vacuous truth, 2 + 2 = 4 is an identity.

For elucidation, let's consider 1 = 0. The same considerations as above show that this is an equation by the definition supported by 'many mathematicians' as explained in the 'identities' heading of the 'equation' wiki article. In particular, by either vacuous truth or with constant functions, there is no way in which we can choose some dependent variable to make that true.

So you don't know what you're talking about.

You stepping beyond your intellectual means here is of little interest to me here (though I may use this later as an example of how the majority of people have no capacity for logical or original thought). If I am a poser then Xei (at least) would freely point it out and not rise above his station in doing so.

For the sake of amusement, could you prove that if A is a ring then choosing an element c of A and making the substitution X -> c induces a homomorphism A[X] -> A? Here A[X] is the ring of formal polynomials over A. If you understand everything I've said then surely you understand that. Unless you're the poser here. That's too trivial of a problem to be assigned in books. However it's a fact that needs to be referenced and hence stated. Therefore it's often stated in books but not proved. The author would simply assume that the student is reading the book with a pen and paper in hand and is hence ready to prove any such trivial statements if such cannot be done purely in mind. A simple sketch of the proof will suffice to show that you know what you're talking about. There's no need for the sort of formality that I usually prefer.

Originally Posted by Alric

To answer that other question no. Obviously saying math is logical isn't a math statement, but I never claimed it was, because it has no math in it. It is however logical. You have not put forth anything to suggest that math isn't logical, and only stated it as your opinion. However, since you apparently don't know much about math, and your arguments are extremely chaotic, random and nonsensical, I don't really think your in a position to offer opinions on logic or math.

Hmmm. I referenced the fact that logicism has, to the present date, failed. Can you support the fact that mathematics is logical or is that just your opinion as well? If the statement that mathematics is logical is just an opinion, then it certainly doesn't carry the weight of mathematics or logic behind it, does it? It's basically just the preconceived notions of someone that doesn't know much about math (at least not enough to solve the trivial posed problem) or logic, right?

For the sake of completeness, it's not quite true that 2 + 2 = 4 is false over Z/2Z, Z/3Z or Z/4Z for the simple fact that 4=0, 4=1 and 4=0 respectively over those rings. It is true that 2+2 = 1 and 0 over the specified rings however. You could have pointed out this discrepancy easily if you really know everything that I've been referencing.

punk

Sorry.

Plebeian punk.

Using your logic, all equations(that actually exist as valid equations) are identities and clearly that is incorrect. In fact, that is exactly what you defined an equation as, since no equation would have a number within it's domain that is false. The definition of a domain, is all possible numbers that can be inputed into an equation. If some number is false, it can't be plugged into the equation and thus doesn't exist within it's domain.

In fact, 1=0 could be labeled an identity, because it has no domain and thus no varible within it's domain is false. So once again I proved by your own logic, your an idiot and totally wrong.

You seem to be missing the entire point of what identities are, and why they are seperated out as a subgroup. Which strongly suggests you are just arguing based on definitions you read some where, and not on actual knowledge of the subject.

The point of identities is that they are used as rules. There are identities that don't exist for all real numbers, and many have specific exceptions within them. However they are patterns that help people undersand and solve the different rules within math.

No person would think 2+2=4 is a special rule for solving math, and thus no person would ever call it an identity. For the sake of arguement, even if you did want to call it an identity, you would have known what I meant when I said equation, and you didn't seem to be aware of it at all.

For someone who claims to be very specific and precise you are using a lot of words in the wrong way, without having a solid grasp of what they mean. A person who needs to look up the words equation, and still doesn't grasp the concept is in no position to be trying to put others down.

We are just going in circles though. You keep making stupid arguments and then insult me, hoping that the insults will some how make your nonsense appear more valid, but then I point out the huge obvious flaws in what you are saying, and we go around and around.

My main point is that math follows set rules, and thus is logical and orderly, and that math doesn't arbitrarily changed based on peoples perspective. You can do that by actually following the rules and seeing that they do work.

So what does it mean for a number to be false? Or for a variable to be false? Would you care to clarify?

We are precisely going in circles because you have no idea what you're talking about.

What about the problem? I'll give you a few more posts and then solve it for you. Would you care to issue a challenge in algebra which is what we're talking about?

That it doesn't exist. There are no numbers within a domain that don't exist, because being within the domain implies that it does exist.

Also, the rule 2 + 2 = 4 is useful precisely when one has an expression including 2 + 2 that one would like to simplify. Don't let the point that it's trivial fool you.

One could say the same thing about cos²(x) + sin²(x) = 1. The point is to allow one to simplify expressions containing the left hand side of the identity down to 1 or to introduce the left hand side into an expression involving 1 in hopes that something will cancel.

You're seriously lost aren't you?

Go by math.stackexchange.com and ask if 2 + 2 = 4 is an identity. LMAO

The trig identities are useful as a rule because they help in a lot of situations. With 2+2=4 you would never memorize it as a special rule, you would just do the insanely easy addition.

Originally Posted by Alric

That it doesn't exist. There are no numbers within a domain that don't exist, because being within the domain implies that it does exist.

So the domain is empty (not "doesn't exist"). Hence the statement 2 + 2 = 4 is true for all elements of its domain vacuously. Like I said, find an element of its domain (either the empty set or any set that you want to define a constant function from) for which it's false. This is vacuous truth and is one of the more basic issue that beginning math students must grapple with. You're sure gung-ho about the virtues of math and logic for someone that doesn't understand it.

So is the statement that math is logical your opinion or a fact? It doesn't sound like you're using "logical" in a very logical manner. Normally if something is logical one would expect it to be provable using means from some system of logic.

Originally Posted by Alric

The trig identities are useful as a rule because they help in a lot of situations. With 2+2=4 you would never memorize it as a special rule, you would just do the insanely easy addition.

So an identity has to be something that you memorize as a special rule? Where does it say that on wikipedia or any other source?

You seem to be missing the point. If you make the claim that an identity is an equation where all the values within its domain exist, then by default all equations are then identities because domains are just numbers that exist for the given equation. That is the claim you made, and it is incorrect.

If you actually read the definitions of identities, and the wiki example is fine, you would see that it is speaking of the variables not the domain. If any number works then it is an identity.

You switched 'any number' with 'any number within the domain'. You can't do that, because they have different meanings. The wiki definition also specifically includes the word variables, which 2+2=4 has no variables. So how can you plug any number into a variable that doesn't exist? You can not. And even if you rewrite the equation, which you tried to do, the variables still did not accept any values except the specific ones you gave.

Originally Posted by Alric

You seem to be missing the point. If you make the claim that an identity is an equation where all the values within its domain exist, then by default all equations are then identities because domains are just numbers that exist for the given equation. That is the claim you made, and it is incorrect.

I didn't say that all values within the domain exist, I said that it's a mathematical statement which is true for all values within its domain. That's the claim I made and it's correct.

If you actually read the definitions of identities, and the wiki example is fine, you would see that it is speaking of the variables not the domain. If any number works then it is an identity.

A free variable is just an element of the domain. So to say that it's true on a specific domain or an a free variable that takes its values from that domain is the same.

You switched 'any number' with 'any number within the domain'. You can't do that, because they have different meanings.

Yes I can because 'any number' is just shorthand for 'any number within the domain'. Or really, any element. There's no need to restrict ourselves to numbers.

The wiki definition also specifically includes the word variables, which 2+2=4 has no variables. So how can you plug any number into a variable that doesn't exist? You can not. And even if you rewrite the equation, which you tried to do, the variables still did not accept any values except the specific ones you gave.

Here's the relevant quote:

Originally Posted by wiki

One use of equations is in mathematical identities, assertions that are true independent of the values of any variables contained within them.

Note the use of 'any'. So it's true that 2 + 2 = 4 is true regardless of the values of any variables contained in it. This is again the concept of 'vacuous' truth. Again, for it to not be true that 2 + 2 = 4 is true regardless of any variables, one would have to exhibit some variable contained in it and some value which that variable could assume that would make the statement false. But there is no way to do this because there are no variables in sight. Hence it's vacuously true that it's true for all values of all variables contained within it and is hence vacuously an identity.

Do you understand vacuous truth?

What about the problem? Like I said, it's an easy one if, as you claimed, you knew what I was talking about. It should be easy to back up. You're not a poser are you?

What about the important part? The statement that 'math is logical' is just your opinion, right?

To recap I called an equation, an equation. You insulted me and called me stupid for thinking an equation could actually be called an equation. You admit that it was an equation, but insulted me some more and in an attempt to save face for being wrong you made the claim that a lot of people wouldn't call it an equation. I disagreed, you posted a bunch of crap. I even admitted that it could technically be consider an identity but that is so pointless no one would ever call it such, we argued some more and here we are.

I think the real lesson here, is that I shouldn't bother trying to debate you when you are trying to act like a troll, and you were definitely acting like a troll when you personally insulted me for saying something you admitted to being true.

Any way I posted the question on that site, and got pretty much the answer that I expected to get. People said it is technically both, but that it isn't a very interesting example of either. So you can call both, or call it whatever you want, since no one cares. Problem solved.

As for the math logic issue, that is simple. Give an example of a illogical math problem that doesn't follow reason, yet is still correct. You claim math doesn't follow reason or logic, then there should be some reason you believe that and you can give an example.

Originally Posted by Alric

To recap I called an equation, an equation. You insulted me and called me stupid for thinking an equation could actually be called an equation. You admit that it was an equation, but insulted me some more and in an attempt to save face for being wrong you made the claim that a lot of people wouldn't call it an equation. I disagreed, you posted a bunch of crap. I even admitted that it could technically be consider an identity but that is so pointless no one would ever call it such, we argued some more and here we are.

That's a bad and biased recap. You called something an equation. I knew it to be an identity. According to the only definition I've actually run across in books (most consider it known) a statement with an equal sign in it is either a definition, an equation, or an identity. But this is already an identity. Hence it can't be an equation. An equation is something one solves.

You were already being insulting by saying that everything I say is 100% wrong. Far from it.

So I pointed out your error with about the same level of insult. Maybe a little more just to punish your insolence. You persisted and I looked it up on wikipedia. I'm not in the habit of learning my math from them (I prefer textbooks) and they gave a stupid definition. We can discuss why an identity shouldn't be an equation later and I intend to post an answer to your question on math.stackexchange.com that argues as much. We'll see what the community decides. I love upvotes and downvotes. I intend to get a few of each.

I admitted not that it was an equation (again, who's distorting truth here) but that it could be considered an equation under an inferior definition. Surely an equation is something to be solved. That's the intuition that the definition should capture. For something to be solved, i.e. for the values on which it's true to be sorted out from the values on which it's false, there should be some non-trivial amount values for which it's not true.

The fact that wikipedia plainly stated that "many" mathematicians consider this to be the defining feature of an equation backs me up. So you tainted your "recap" by asserting that it was me and not wikipedia (with a reference backing it up) making that claim. Again, who's distorting reality here? I guess we both are because that's the way of things but who's actually trying not to?

So I got insulting after you botched understanding a simple statement. Or rather, I got honest. I told you what I really think. I stand by it too. You're an excellent example of how stupid people can stumble upon largely functioning world views by pure cultural osmosis. No rational thought required.

Or can't you understand that the definition of equation I learned with is just imposing a partition on the set of statements that you're used to calling equations? It's a simple definitional matter and I conceded it long ago.

We've been arguing about if it's an identity or not.

And that's only because you called me a poser. Poser. Where's the solution to that trivial problem that you'd be able to solve in a heart beat if you actually knew what I was talking about back when you claimed you did? Of course you just called it a bunch of crap so I guess you are a poser.

No matter, I never thought you were intelligent. You're good for explaining basic things to fundamentalists and new-agers that somebody else already explained to you. You get lost when you have to think. That's fine, most people do. I do deeply regret thinking of you as subhuman. We're all good at different things and we're all human (and you're no more of a monkey than I am) and it's okay that you can't think. Really if only one out of a hundred people can think, that's alright as long as the other ninety-nine people know who can think. That's the problem.

Also, where did you admit that technically it was an identity? Could you quote that? I think you're lying though I haven't checked since you made that claim.

Moreover, one doesn't consider x to not be X if x satisfies the definition of X because one doesn't find it interesting that x is X. One just doesn't use the fact. One doesn't say that it isn't. Which you did. Poser.

Who's saving face?

I think the real lesson here, is that I shouldn't bother trying to debate you when you are trying to act like a troll, and you were definitely acting like a troll when you personally insulted me for saying something you admitted to being true.

No I insulted you for not admitted that what I said was true. Even after I gave you the link, you still couldn't deal with the fact that there were two definitions. For you to have done that, you would have had to see that it was an identity but you didn't see that till you asked the question like I told you to.

And as I said you already insulted me. Everything I say is 100% wrong. I can't think of a worse insult than that.

The lesson here is that you should mind your p's and q's and stay within your station. Are you an artist? Then you should make art. Are you a plumber? Then you should plumb.

You are most definitely not a thinker and hence you should not attempt to think. Or you should at least take remedial thinking classes. Please don't vote. Unless you agree with me.

Originally Posted by Alric

Any way I posted the question on that site, and got pretty much the answer that I expected to get. People said it is technically both, but that it isn't a very interesting example of either. So you can call both, or call it whatever you want, since no one cares. Problem solved.

Hmmm. Both answerers have said it's an identity as I said and you denied. Did you expect to be wrong? I would understand if you did.

Originally Posted by Alric

As for the math logic issue, that is simple. Give an example of a illogical math problem that doesn't follow reason, yet is still correct. You claim math doesn't follow reason or logic, then there should be some reason you believe that and you can give an example.

Yes here's the meat of it and again, here you're distorting my statement. I never said math wasn't reasonable, I said that math wasn't logical.

As for responding to your challenge, you'll have to formulate it properly. What is an illogical math problem? I would take an illogical statement to be an inference which violated whatever rules for inference were in place in whatever logical system was being employed.

At any rate, it's not even a valid challenge. Are all things logical until proven otherwise? If that was the case then surely the challenge would be valid and one would have to produce an example of an illogical mathematical theory.

The problem is that people can't even figure out how to phrase mathematics purely in terms of logic. One can surely apply logic to specific statements that occur in the process of engaging in mathematical proof but one can do the same in life. Does that make life logical?

It seems that the default assumption must be that things are not logical until proven otherwise.

Why can you not admit that your statement that math is logical is neither logical (i.e. taking place in a formal system of logic) nor mathematical and is just your opinion? Who's trying to save face? I have no problem admitting that it's a valid opinion but over my dead body will I watch a religious zealot (even one of my preferred religion) tarnish the name of mathematics by attempting to make non mathematical statements with the force of mathematics.

But okay. For the sake of argument, I'll take your challenge in a colloquial manner and just show you this: banach-tarki. This is a well known result and is known to far more people than can understand even the intuition behind its proof.

It is, in the sense which you use the word logical, totally illogical.

It works because of the Axiom of Choice.

Was mathematics logical in the sense that you mean it mathematicians would long ago have considered this to be a proof by contradiction that the Axiom of Choice is false.

But it's not logical in the sense which you seem to mean it.

If you mean it in some other sense, then what is that sense if not that it can be stated entirely within some logical system, i.e. that it can be reduced to logic as I had first assumed you meant?

Oh yeah, that's just a bunch of crap.

Do you like Budweiser too?

I am not going to get into that debate again, anyone can read the thread and come up with their own conclusion on weather or not normal people call that an equation or not.

What I will say, is that I never said you were 100% wrong(at least not about the stuff you said originally). I was speaking in general that people can't just make up math rules, and it was in response to Omnis saying people can make up their own rules and that saying a foot isn't 12 inches isn't objectively wrong. Yet a foot is a unit of measurement and saying a foot is say 42 inches would be 100% incorrect. Your context argument doesn't even work here, since you are talking inches and feet which implies a specific context and measurement.

As for distorting what you said, no I didn't. I defined logical multiple times as following reason. There are multiple ways to define logic and I was quiet specific in saying when I said logical I was using it in the general sense of saying math uses reason and has structure. For the challenge, I was just asking for something that doesn't follow the rules of math, and can't be explained is a reasonable fashion.

Banach-tarki doesn't fit that. It may not seem intuitive at first glance but a person can explain why it happens without any weird unexplained things happening. It is entirely reasonable.

Originally Posted by PhilosopherStoned

First off, is it 2.000 as a real number or 2 as an integer?

2 + 2 = 1 is a true statement. Taken modulo 3.

That isn't just 2+2. You are adding to the equation.

Originally Posted by PhilosopherStoned

You should check out logicism. Essentially you are making a religious claim.

tl;dr: math has not been logically reduced to logic.

Everything is based off logic so you saying that math has not been reduced to logic is erroneous. Whether you are a Kantian or a Thomistic you either impose logic upon the reality around you or receive it from the reality around you. In either case logic is at work in your surrounding environment.

Originally Posted by PhilosopherStoned

There is no such thing as a logical mind either.

More on point though, your assertion that it doesn't exist (i.e. "no such thing") is itself based on the assumption that the only way for something to exist is if we can percieve it, understand it, or interact with it. This assumption isn't even necessary for rational materialism to function as one of the most distinguished of a number of possible models of reality. However, there's no way to have it be The One True Way though without this assumption.

In this reality, the only things that do exist are those that can be perceived, understood or interacted with. It does not necessarily have to be all three at the same time. You can perceive something and not understand it etc.