Are you saying negitive values didn't exist because they weren't discovered yet?

Or that America didn't exist in 1491, because it wasn't discovered yet?

Now, what makes your experiment superior to this one? What's significant about ancient times?

Also, there are differences between Egyptian, Chinese, and Greek maths that extend beyond what you're saying. You're reducing a philosophical discussion to a science experiment.

Mathematical sentences do not refer to real objects. I could lock myself in prison for 40 years and concentrate solely on mathematics and never have to test a thing with real objects. I'm still experiment, just not with anything real. (Math is a science, IMO).

The whole point of math is that they do not in themselves refer to real objects. They do not refer to anything.

Or put it another way. What's a widget? A placeholder. What's a placeholder? True. Therefore, what is a widget is valid and true.

You will never find a truer statement than "What's a unit?"

How about applying some simple calculas that deals with position,velocity and acceleration. Do the laws that we dicovered only apply when we apply them to an actual object in motion.

All three are advanced civilizations for ancient times. All are independent. Each civilization was unaware of the others. Don't know if this statement is true. Just don't see Greece mentioned in Genesis or Exodus.

Unfortunately, I don't know how independent they were either.

You tell me. You're the one positing that nonphysical "forms" of some kind exist in a "somewhere" you can't describe. I agree it's not grammatically well-formed. We're 2500 years beyond Plato and his naive ideas.

I can as easily say that I believe "truth" exists, or that there exists a "negative" and an "affirmative." Of course I don't - I think Platonism is all nonsense. But you're the one picking and choosing. If you want to consider it real, you get to - but if it's inconvenient, then you can claim it's nonsensical. Can you provide a rational distinction?

And I challenge your assertion that you can conceive of them being independent objects. All Platonists of all kinds claim to have some special independent knowledge of these supernatural "objects" they see - but I don't think they do. Plato believed that all chairs were just expressions of an essential "chairness," and he believe that he was "in contact" with this "chairness" - I believe that Plato's concept of "chairness" was actually derived from the chairs he interacted with, and that if Plato had never interacted with a chair, he would have no conception of "chairness." This is more an epistemological question than a subjective question.

If we perceive it all within a linguistic framework, as description rather than metaphysical "truth," then there is no contradiction. "Unit" is a label that human beings have devised because it's useful, just as "4" is a label that human beings have devised because it's useful.

I'm not comparing mathematicians and theists.

No, but I can say the same about language. But this is nowhere near analogous - I'm not talking about maths, I'm talking about mathematical realism. Mathematical realism hasn't been instrumental in the discovery of anything. And I do think it's very much the same as theism.

I think my responses in this post and this post answer these questions.

The laws that we invented don't apply to an actual object in motion. As you yourself noted above. And no, close doesn't count in metaphysics. That Newton managed to reasonably approximate motion - but still get it wrong - is not an indication that Newton identified metaphysical truth. On the contrary - metaphysical truth should be perfectly precise almost by definition.

Relativity theory and quantum theory may describe absolute truth, but I sure as hell don't think so. And given your above post, it seems you agree. So, by your own account, we have failed to identify any reality in our observations. What, then, is your justification for positing the reality of these constructs?

Well I try to be aware when I am using the Axiom of Choice, which is not often and I may well sometime have missed noting a use of it. I wouldn't have called it philosophical, though, though I can see how you could.

What I meant by what I said is that my doing mathematics is not really affected by the questions of whether, how, and to what extent mathematical objects are "out there", interesting though those questions are.

Very nice response. I not proposing we have discovered the absolute truth. Only models that aproximate truth close enough to be of use. Wait a sec., is it possible to discover 'un-truths". Ut oh, I'm starting to think I'm just digging myself in deeper.

Now you've got me started again. We don't discard 'untruths'. We let them ferment for a bit, then we compare them with other wines. See my post 'to be or not to be' to see how nutty my thinking is on this.

LOL..will do
A search under that gave me no results. Any help getting there?

Yeah, it's right on this page, I posted it yesterday... I actually got lolcatted by a troll or two. The search engine probably discarded every single word, FWIW. "To" "be" "or" "not" are all words discarded by search engines. Funny how s**t like that works.

I think that people have false epiphanies all the time. Not everyone's epiphany can be true. Yet we generally accept an epiphany as true, because it is one of the better feelings we get. Why crap on that?

Even after an epiphany, we don't forget the old ideas. The ideas that we hate the most are, and believe are the most untrue, are the ideas that are more likely to survive!

Madnak,

Are you leveling in this thread? I know it's bad form to ask but I really need to know.

Nobody has said the rules are arbitrary, the rules are chosen for the power as a syntax for formulated logic. But was it discovered?

No I don't think it was, if we presume to use the world today as an example: If there were no humans, there would be no mathematics.

Forgive my ignorance, what do you mean by leveling?

Put it this way, the moment you start saying that two points make a line as an absolute truth, is the moment I start drawing constellations and declaring them as an absolute truth.

As an absolute truth, it's completely unjustified! We invented metaphysics for the same reason we invented duct-tape. We can't have holes in our theory... so patch it up with duct-tape and hope nobody notices.

Here's a quote from the mathematician Quine, 1951, "commom sense is bankrupt for it left us in contradiction. Deprived of his tradition, the logician has resorted to myth making." (Set Theory and Its Phiosophy by Michael Potter 26)

Potter sees paradox's (such as the liar's paradox) as no real paradox at all, and should be expected from the axioms. So I should note that he is not terribly alarmed.

Using this definition of mathematics: Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, I would have to agree with you, with Plato's definition of knowledge; the overlapping of truth and belief. There's no beleif without humans, discarding the possibility of extraterrestrial. And this is where I went astray in this discussion. I believed mathematics as being axioms,laws ect. with or with out knowledge of them.

It's just an expression. He wants to know if madnak is serious with his assertions, or if he's going beyond his beliefs to make a point.

BTW: Thanks for your reply. Sometimes I don't know how to say what I mean. Denial, that makes complete sense. I probably should have thought a little more before posting that one.

Maybe a little. It's not lost on me that I'm shoving people into categories that don't necessarily apply, nor that my analogies could be toppled by a strong breeze. And I'm not actually sure what I believe on the subject.

But I'm not saying the opposite of what I mean. I like to think I'm making valid points, even though I'm toying with the semantics. This strikes me as a semantic question anyhow - what does it mean to "discover?" What does it mean to "invent?" What does it mean for mathematics to "exist?"

Now add a billion tomatoes to five tomatoes. Count how many tomatoes you have. Repeat on the surface of the moon and Jupiter.

I totaly agree for whatever it's worth, this is more a question of semantics.