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mathematics discovered or invented?

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Arran
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20 Jan 2013, 4:55 am

BIDMAS is an invention.



ripped
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20 Jan 2013, 6:20 am

ruveyn wrote:
ripped wrote:

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


I guess I meant genes are naturally occurring - not manufactured at all.
I guess genetic engineering is different, but I meant patents on the naturally occurring genomes.



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20 Jan 2013, 11:08 am

ripped wrote:

I guess I meant genes are naturally occurring - not manufactured at all.
I guess genetic engineering is different, but I meant patents on the naturally occurring genomes.


What if they are artificially bred or selected. What if they are artificially mutated? Then they are produced by an artificial not normally occurring natural process which puts them in the same class as machines created from natural iron but fashioned in human designed ways.

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20 Jan 2013, 11:56 am

ruveyn wrote:
Any theorem can be proven in an infinite number of ways.

ruveyn


Actualy I've only proved 4 original theorems in my life and they're all related to this. One is that if a theorem (technical term in first order logic for those "statements" that can be proved from the axioms alone of the logic itself) depends only on the axioms of the logic itself, then there is only one way to prove it. The other one is the possible generalization to "stratements" that depend on hypothesis (technical therms for the actual axioms of a theory such as the axioms of the theory of groups): if the statement has two proofs and they depend on the same hypothesis to be proven, then the proofs are the same. This has as a consequence that in any theory with a finite number of axioms n, there are at most 2^n proofs for any statement.

The forth theorem is uninteresting.



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20 Jan 2013, 12:28 pm

ModusPonens wrote:
ruveyn wrote:
Any theorem can be proven in an infinite number of ways.

ruveyn


Actualy I've only proved 4 original theorems in my life and they're all related to this. One is that if a theorem (technical term in first order logic for those "statements" that can be proved from the axioms alone of the logic itself) depends only on the axioms of the logic itself, then there is only one way to prove it. The other one is the possible generalization to "stratements" that depend on hypothesis (technical therms for the actual axioms of a theory such as the axioms of the theory of groups): if the statement has two proofs and they depend on the same hypothesis to be proven, then the proofs are the same. This has as a consequence that in any theory with a finite number of axioms n, there are at most 2^n proofs for any statement.

The forth theorem is uninteresting.


In first order logic interpolate n formulae of the form p -> p where p is any wff. Each such proof is distinct depending on the place of interpolation and the multiplicity of the interpolation.

ruveyn



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20 Jan 2013, 1:09 pm

Could you expand, please? I don't know what interpolation of a formula means.



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20 Jan 2013, 9:06 pm

ruveyn wrote:
ripped wrote:

I guess I meant genes are naturally occurring - not manufactured at all.
I guess genetic engineering is different, but I meant patents on the naturally occurring genomes.


What if they are artificially bred or selected.
ruveyn


That's what I meant. Genes that do occur in nature. I don't think they should be patentable.



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20 Jan 2013, 11:34 pm

ruveyn wrote:
In first order logic interpolate n formulae of the form p -> p where p is any wff. Each such proof is distinct depending on the place of interpolation and the multiplicity of the interpolation.

ruveyn


It's interesting that you didn't respond to my question and also interesting is that when i google ""multiplicity of the interpolation" logic", the only page that comes up is this topic.

Are you trying to trick me?



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21 Jan 2013, 2:41 am

ModusPonens wrote:
ruveyn wrote:
In first order logic interpolate n formulae of the form p -> p where p is any wff. Each such proof is distinct depending on the place of interpolation and the multiplicity of the interpolation.

ruveyn


It's interesting that you didn't respond to my question and also interesting is that when i google ""multiplicity of the interpolation" logic", the only page that comes up is this topic.

Are you trying to trick me?


Its abstract math.



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21 Jan 2013, 12:34 pm

ModusPonens wrote:
ruveyn wrote:
In first order logic interpolate n formulae of the form p -> p where p is any wff. Each such proof is distinct depending on the place of interpolation and the multiplicity of the interpolation.

ruveyn


It's interesting that you didn't respond to my question and also interesting is that when i google ""multiplicity of the interpolation" logic", the only page that comes up is this topic.

Are you trying to trick me?


Not at all. I don't trick people when I am serious. I gave you an algorithm to generate an infinite number of distinct proof for a provable wff in fol.

ruveyn



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21 Jan 2013, 1:21 pm

Then explain how it works. The only interpolation I know is the Craig interpolation theorem, and it has nothing to do with my proof. Also, I suspect that your algorithm, if it's not BS, doesn't contradict my theorems, because different formulas of the form p=>p are different and so they don't have to have only one proof.

So please explain.



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22 Jan 2013, 11:38 am

In absence of explanation, I can conclude (among other things) that my theorems are correct. It would be strange that they were verified by a proof theory expert and didn't find any mistakes, while you, only having seen the verbal explanation of the theorems, could find a mistake in no time.