Talk:Axiom schema

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Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Stub Class	Mid Priority	Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Maybe Start-Class: more structure and explanation would help. Geometry guy 02:05, 15 June 2007 (UTC)

I think this entry needs to reference the inference rule of Uniform Substitution (which doesn't yet have an entry). Uniform subsitution, in sketch: given wff X, in which variable y is free, and another wff Y, we can create a new wff X\[y/Y\] in which every occurrence of y is replaced with Y. 'Uniform' indicates that every y has been replaced with the same wff. The inference rule of Uniform Substitution is: if X is a theorem, and Y a wff, then X\[y/y\] is also a theorem. If Uniform Substitution exists as a given or derivable inference rule in a deductive system, then a great many axiom schemata can be dispensed with (though, given how general the definition in this entry is, not necessarily all). Thoughts?

I have just rewritten this entry, unintentionally doing so without implementing your suggestion. I have no quarrel with what you say, but I do find it very hard to be very precise about substitution rules. I wrote the substitution rules in Laws of Form. I have read that even Alonzo Church himself had trouble getting substitution right in his early formulations of the predicate calculus.132.181.160.42 05:33, 8 August 2006 (UTC)

[edit] "Loss of 'elegance'"?

"(...) can be finitely axiomatized, but only with some loss of elegance."

What the fuck is that supposed to mean?

Who gives a fuck about elegance, as long as it makes sense?

That's not fucking relevant.

Isn't anybody else out there tired of the use of "elegance" as though it was a relevant mathematical attribute?

I really think assessing the matter of "elegance" of certain mathematics shouldn't have place in Wikipedia articles.

I am a little extra pissed off because I am just coming from complex number, which full of this "elegant" this and "elegant" that shit.

The fact that "elegant" is slang for the mathematical community doesn't make any less slang of it. Talking about about "elegance" of mathematics isn't any different from talking about it's "coolness".

The fact that you are so angry for no reason and appear to be not only a person of severely limited understanding but also one who is unwilling to understand, detracts from your credibility. Michael Hardy 21:07, 16 March 2007 (UTC)

I don't need credibility, I am not trying to get a loan or running for a public office. It's just a matter of common fucking sense, and it's out there for everyone to see, independent of my "credibility". "Loss of elegance"? Are you fucking kidding me? That's outright ridiculous. I don't give a shit if you think mathematics is some form of art in which aesthetic concepts are intrinsic and important, it isn't. It simply isn't. Mathematics is a formal science, and that's it. Beauty has nothing to do with it's investigation (bear in mind I am not talking about mathematicians' personal motives and inspirations in their study, that's a whole other story), and aesthetic concepts shouldn't contaminate the articles, slightly POVing into this aesthetic view of mathematics, as if the "loss of elegance" was going to cripple mathematics from it's "beauty" (as if this was a relevant criterion for it's study). —The preceding unsigned comment was added by 200.164.220.194 (talk) 23:42, 16 March 2007 (UTC).