mathematics discovered or invented?

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IChris, Have you ever heard of the Sokal affair? Wiki it.

Trencher93, if you are an ultra-finitist, I prefer not to continue my discussion with you. Ultrafinitism is the agoraphobia of the philosophy of mathematics. You may be safe, but you can't experience anything from the wonderful outside world.

Just because I've never heard the word ultrafinewhatever before doesn't mean they don't exist!

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

Okay, so I'm not one of those. No, what I was doing was making fun of the idea of cultural relativism being applied to mathematics. I was taking the extreme position that not only aren't prime numbers infinite, but they're scarce, so we better ration them before we run out, in an attempt to show how cultural relativism doesn't really apply to math.

But having another cognitive apparatus means that irrational numbers and so may not be experienced and at the same time ghosts or God may be experienced. With a cognitive relativity approach we cannot dismiss either of them as something which does not exist; but must accept they both as either facts or, like Kant would say, features of our perceptions.

Someone asked me before about it; seems like a standard argument from positivists. But the Sokal affair based it's sarcasm of postmodernism and I am against postmodernism. Postmodernism believes that all thingumbobs are socially constructed, I believe that there exist a natural world which is not constructed and that social constructions only is a mean to structure it.

http://www.wrongplanet.net/postt191979.html

This thread may include some comments relevant to this topic.

Absolutely

So what is it exactly about mathematics that is culturaly dependent? Notation?

The concepts, invented in many different cultures, seem to apply to reality with great acuracy. And different cultures, if exposed to mathematics, would learn it. Just because there isn't a word for infinite in a language doesn't mean the concept can't be learned or that there is no thing which is infinite.

Trencher93, I didn't understand your joke when I wrote my previous post. Yes, we may run out of primes one day! Just as we cannot walk the lenght of the diagonal of a square.

It may still be hard to learn if presented as something real. A similar story is pictured by a native american professor (Waters, 2002) who tried to learn the native american students logic. The only way the student learned it and did not fail their exam was when the professor told them that it was something which was not applied to reality but to computers only. The students was not able to understand that the logic, by which the western cultures take for given, could be applied to reality.

Source: Waters, A. (2002). Language Matters - A Metaphysic of NonDiscreet NonBinary Dualism. APA Newsletter on American Indians in Philosophy 1(2), 5-14.

In what culture does two plus two not equal four?

Both discovered or invented depending on how it is presented to the world. If a mathematician devised something like Simpson's rule or the quadratic formula today then published a paper about it then it classes as a discovery which also means that it cannot be patented. If the same mathematician decided to express the same thing in the form of a computer program and managed to obtain a software patent on it then it classes as an invention.

Some countries do not allow software to be patented on the basis that it is effectively patenting mathematics which has historically been exempt from patents.

The -algorithm- underlying the software cannot be patented under current law, since by definition it is a mathematical artifact. However if one writes the patented algorithm in a different language or modifies it slightly than any patent law restrictions can be bypassed.

ruveyn

Is it not a compelling argument that the creation of a computer program is a manufactured entity in its own right?
If Pythagoras theorem was in my lines of code why should that mean I am disqualified for applying for a patent?

You might be able to patent the -program- but you could not patent the -algorithm- on which the program is based because an algorithm is a mathematical principle. You can patent designs, you can patent bendable breakable objects but the law does not permit patenting algorithms, mathematical theorems or physical laws. If you do find an algorithm (say for fast factoring of large integers) your only chance of exclusivity is to keep it a trade secret. Which means if someone else discovers it also, you cannot sue.

ruveyn

I have not read about such a specific case, so I can not answer. But as some cultures relay on something more like a fuzzy logic, the case may possibly be that two plus two do not equal four but a degree of four. In addition in some cultures this only picture an idea which give no meaning to experience and is so probably ignored.

If only the legal community placed the same rigor on gene patents.

Genes are particular material substances. They are not abstract principles. Just because we -call- a gene information (which is abstract) does not mean it is abstract. But since the gene is a pattern it falls under the same classification as written material which is either hand written, typed or physically recorded. I think genes might be protected under the same rules as materials created by authors and playwrights.

Copyright can be a very tricky dicey thing as legal things go.

It just occurred to me that while a theorem is not patentable, a -proof- for the theorem might be copyrightable as is any other literary production. In other words you can't charge for the final step of a proof, but you could for the whole proof. But soft! Any theorem can be proven in an infinite number of ways.


ruveyn

ruveyn