Does math exist?

[Colanth]

Once again, Colanth nails it. I've made it a point to not post until after he does, just to look more astute by agreeing with him.  :-D

Just for that I'm instituting a new policy - I'm not posting until I see your response. Þ

[GurrenLagann]

Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

But that's not what it means to ask whether or not math exists. What is being asked is if there is a referrent in reality that mathematics refers to, or why does mathematics oftentimes seem so intertwined with reality (see geometry) if it does not exist?

I am in a room. I exist. The room exists. But does 'in' exist? Clearly 'in' is describing something actual, a relationship, but there is no apparent referrent, nor does such seem to make sense. But it clearly describes something, and I'm using English to describe it. I'm not sure if this comparison is really accurate (probably isn't), but I'll probably think of a better one later.  

[josephpalazzo]

Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

But that's not what it means to ask whether or not math exists. What is being asked is if there is a referrent in reality that mathematics refers to, or why does mathematics oftentimes seem so intertwined with reality (see geometry) if it does not exist?

I am in a room. I exist. The room exists. But does 'in' exist? Clearly 'in' is describing something actual, a relationship, but there is no apparent referrent, nor does such seem to make sense. But it clearly describes something, and I'm using English to describe it. I'm not sure if this comparison is really accurate (probably isn't), but I'll probably think of a better one later.  

Language can describe reality, but not all language reflects reality as it can be used to describe fantasy, like religion... :)

Similarly, math can describe reality, but not all math describes that.

[Colanth]

Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

But that's not what it means to ask whether or not math exists. What is being asked is if there is a referrent in reality that mathematics refers to, or why does mathematics oftentimes seem so intertwined with reality (see geometry) if it does not exist?

If you ask the wrong question, you get a meaningless answer.

I am in a room. I exist. The room exists. But does 'in' exist? Clearly 'in' is describing something actual, a relationship, but there is no apparent referrent, nor does such seem to make sense. But it clearly describes something, and I'm using English to describe it. I'm not sure if this comparison is really accurate (probably isn't), but I'll probably think of a better one later.

[/quote]You objectively exist.  The room objectively exists.  "in" exists as a descriptive word, but it doesn't objectively exist.

So "does math exist" is an incomplete question, since 'exist' is ambiguous.  Ask an unambiguous question and you can get an unambiguous answer.

[Hakurei Reimu]

You know, I think this entire argument is a disguised piece of Platonism trying to sneak in. A lot of people who assert "math exists" — especially if they're mathematicians — mean that there's this abstract object called a "two" out there that really exists. Of course this notion is wrong, because no single object can be a "two" — 'two' is what we label the notion and relationships between pairs of objects. We see a lot of pairs of objects, notice the underlying unity between them, and label that unifying relationship "two." We do similarly with "one" on singular objects, "three" on triplets, "four" on quadruples, and so on. We observe that combining a "one" group with a "two" group forms a "three" group, and so on, and label the entire mess of combining relationships "addition". Even if all humans disappeared and all mathematical knowledge destroyed, a singular object combined with a pair of objects will form a triplet of objects — the underlying fact is still there, even if the description does not.

I think that, despite your assertions to the contrary, Joseph, that you acknowledge this particular sense in which math is real, and not just a language. The physical laws that you teach your students and use to predict what will happen and test your theories are all highly mathematical in nature. The grounding the math has in reality doesn't merely anchor the mathematical descriptions, but allow you to predict what will happen to high accuracy. Math gives you not just descriptions, but tools to turn descriptions into predictions.

And no, the fact that mathematics can be used to describe completely imaginary situations is neither here nor there, as physics can be used to describe situations equally as imaginary and downright impossible, like gedanken experiments, or the imaginary physics of the Drive and the Field in Larry Niven's Mote in God's Eye world.

[Hijiri Byakuren]

It's all in your head. Math is a lie. We must abolish all science based upon this false mental construct.

[GurrenLagann]

Lol, I didn't notice the troll face at first. :p

[Saul the not so great!]

I was going to let this slide but..that Feynman quote is childish. I guess famous smart people can have bouts of "the stupid" like the rest of us mortals.

You can't define anything precisely. If we attempt to, we get into the paralysis of thought that comes to philosophers, one saying to the other: "You don't know what you're talking about!" The second one says: "What do you mean by 'talking'? What do you mean by 'you'? What do you mean by 'know'?"
-- Richard Feynman

First off, precision isn't all or nothing it comes in degrees. This is a prime example of the black and white fallacy.
Secondly, there is much to be criticized when it comes to how philosophy has been done traditionally like philosophers wanting perfect necessary and sufficient conditions for just about every important idea, but asking for clarification of problems isn't one of them. It's basic problem solving 101: define the terms of the problem or question before you even try to answer or solve it. Why? Because some "problems" aren't even real problems. Many unanswerable questions are unsolvable because they are so ill defined. Also how the hell are you going to solve a problem you don't even understand?
By the way: If someone claims, "God exists" is it so "unreasonable" to ask the speaker what is meant by "god" and "exists?"

That's all I wanted to add.

[stromboli]

Once again, Colanth nails it. I've made it a point to not post until after he does, just to look more astute by agreeing with him.  :-D

Just for that I'm instituting a new policy - I'm not posting until I see your response. Þ

We're gonna be circling the campfire with uncooked hot dogs, in that case.

[Colanth]

So?  You never ate an uncooked hot dog?  They're good.

[frosty]

This thread reminds me of a guy I knew years back that insisted that there was a special meaning to numbers, and the numbers 1333 in particular. He said he saw it by looking through (or past) pictures and imagery, he saw it on public business signs, he even saw it by adding up numbers as frivolous as the license plates of a car on TV. He believed that the government was trying to force this number into the public so it could counter-act the alien coalition that also is trying to send humanity the number 1333 to save them from ultimate destruction.

I still remember him flipping out when I told him that numbers only have a "spiritual", mental/psychological or emotional impact when you assign that value to them. If you do not assign such values, they are void and without such properties. He got very mad and was in a hysterical breakdown and almost crashed the car. I feel bad for his parents and all the problems he caused them but then again but it is their fault for enabling him and never doing anything to discipline him or get him proper mental help that he needed.

Yep.

[Sulaco]

But math is purely a human construct - a language.

I disagree.

As with any universal law, principle or force, our recognition of it doesn't suddenly give rise to its' existence. We merely attribute a word and definition to something we recognise as either a part of reality, or as a concept in opposition to something that exists in reality.

If we take the color red, it exists as the color that it is because we exist to define it, but the spectrum of light that gives rise to what we interpret and label as 'red' exists whether we're around to recognise it or not.

[josephpalazzo]

But math is purely a human construct - a language.

I disagree.

As with any universal law or force, our recognition of it doesn't suddenly give rise to its' existence. We merely attribute a word and definition to something we recognise as either a part of reality, or as a concept in opposition to something that exists in reality.

If we take the color red, it exists as the color that it is because we exist to define it, but the spectrum of light that gives rise to what we interpret and label as 'red' exists whether we're around to recognise it or not.

There are 5 sheep over there only means: over there, there is a sheep, and then another one, and another one, and another one, and one more. That we group them under the symbol 5 is just a mental construct. All math are mental construct. Now, like language, it is a tool our minds can use to understand the universe.

[Sulaco]

There are 5 sheep over there only means: over there, there is a sheep, and then another one, and another one, and another one, and one more. That we group them under the symbol 5 is just a mental construct. All math are mental construct. Now, like language, it is a tool our minds can use to understand the universe.

I define mathematics as a principle, rather then a language or mental construct, as universal laws and forces outside of human interaction or interpretation follows mathematical principles (which we then observe, analyze, predict, etc, and communicte using symbols to define them, such as numbers and equations).

To put it another way; do we call a spectrum of light that is beyond our capability of processing, color? (for example ultraviolet light). Or a frequency of sound beyond human capability of hearing, sound?

[Plu]

If we define it as a principle, it should follow that there is only one way to do it; which is the way that it is.

Yet we can define many ways to do the exact same thing, and what we call current math is merely one of them that happens to work fairly well (but is still rough, contradictionary and incomplete in various areas)

We can define colors in many ways, but there is only one wave-length spectrum. We can also define our maths in many ways; but there doesn't seem to be any natural construct that we map it to. That's why we have fields like abstract mathematics that don't even describe real things anymore but still work.