In <CdmdnXiAA4IeLr7MnZ2dnUVZ_gmdnZ2d@giganews.com>, on 02/19/2013 at 11:16 AM, fom <fomJUNK@nyms.net> said:
>They do. But, the nature of identity is treated casually.
By casually do you mean that they did not discuss ontology? IMHO that would be an issue in a philosophy course, but not in a logic course, where it's axioms and rules of inference that matter.
>I had written it in a format called WordPerfect
Ouch! Didn't the journal publish requirements for submissions?
>The second paper was submitted to "The Journal of Symbolic Logic". >I do not believe it had been reviewed at all. The day after >submission, I received a confirmation email. It addressed me as >"professor." I had been polite enough to inform them of their >error. Within 30 minutes I received an angry rejection about >wasting their time.
Are you sure that the issue was your lack of an academic position?
>Correct. My "stipulation of syntactic equality" is the same as your >"definition of notation".
The definition of notation gets you formal identities of 1.(0) and 0.(9) to two convergent series; it doesn't give you the proof that they converge to the same number.
>When I had been badly flamed quite some time ago, the flamer would >keep insisting that there was no problem with identity
Mathematical or philosophical? From a mathematical perspective all that matters is the axioms and the rules of inference.
>One has a set of symbols.
What do you mean by symbols? In normal usage the term refers to the inscriptions appearing in the axioms, not to the universe of discourse.
>One has a partition on that set of symbols.
See above. Are you referring to a theory or to a model of that theory?
>And, if one is claiming a homomorphism, then one is >looking at the uniqueness of an induced quotient topology on the >identification space/decomposition space/quotient space.
You have to start with a topology to have a quotient topology. There is no need to model theories on topological spaces.
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