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I read a discussion concerning the axiom schema of specification, which I yet take as saying that for every set and a class-defining condition, those elements of the set satisfying this condition extensionally comprise another set, given no antinomies are incurred therein.

First: Does my summary capture the semantic intention of the expression of the axiom in formal logic?

Second: Can you give me some insight into the significance of this statement, and explain why it is granted axiomatic status?


Additional Info:

Is it true that the axiom schema of specification is thought primarily to resolve the antinomies derivable from the Frege-an schema of unrestricted comprehension for classes, and more broadly as a tool with which to confide in the true existence of certain sets smaller than known sets as elements of which the elements of the former exist?

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    Not only this is a very very very long and ill-formatted post, but writing every few lines "excuse my ignorance" is making the readability much worse. Writing once is enough. You should remove the excessive apologies and perhaps add a summary of your post, i.e. what is the question?2012-06-23
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    1. Be concise and precise. 2. Don't apologize unless you did something wrong. Vacuous apologies annoy. 3. Using strange words and convoluted sentences shows a lack of language skills. 4. You should make clearer what your question is.2012-06-23
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    I removed all the apologies and inserted some paragraph breaks. I don't think there's much more I can do for this post. You need to drastically shorten it and simplify the language, or you aren't going to get any answers.2012-06-23
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    I made some more edits for clarity (everything above the line). The rest is up to you.2012-06-23
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    This post is at best [Mark V. Shaney](http://en.wikipedia.org/wiki/Mark_V_Shaney) and at worst very trollish.2012-06-24
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    the posting of this helplessly stupid question was rather regrettable, and I certainly can't see any one objecting to the question's removal from the site. Should I try to undertake such a removal, considering its inappropriateness and uselessness to other users of the site, and if so how might one go about such a task?-2012-06-24
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    Brenton, the question is not stupid. The problem is the way you chose to write it. I suggest you to edit it and make it clear and without thesr obfuscation. It is alright not to know.2012-06-25
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    I changed the title of the question for succinctness and to more definitely articulate the query. The protracted paragraphs I've deleted as they mostly constituted occasions of my ruminative prolixity, the which hasn’t any appropriate place here. I’ve also added the ‘soft-question’ tag meseemed due.-2012-06-25

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