JSH: Understanding prime gaps issue
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From: Mark Murray on 17 Jul 2010 09:58 On 17/07/2010 14:05, Aatu Koskensilta wrote: > Mark Murray<w.h.oami(a)example.com> writes: > >> Axioms are definitions. > > How is e.g. > > For every two sets A and B there is a set having exactly A and B as > elements. > > a definition? What does it define? Perhaps I should have said _like_ definitions. Very sloppy usage on my part. My point was that you don't _derive_ axioms, they are the starting points from which lemmas and theorems are derived. James has claimed a proof for his axiom, so I conclude that it is not an axiom (assuming that the purported proof is correct). M -- Mark "No Nickname" Murray Notable nebbish, extreme generalist.
From: Aatu Koskensilta on 17 Jul 2010 10:31 Mark Murray <w.h.oami(a)example.com> writes: > Perhaps I should have said _like_ definitions. Very sloppy usage on my > part. > > My point was that you don't _derive_ axioms, they are the starting > points from which lemmas and theorems are derived. Sure. Axioms and definitions are alike in this sense. In other respects they're very different. For example, if someone proves that an algorithm A terminates on all inputs invoking in the proof the axiom that there is a measurable cardinal, we can meaningfully ask whether we should conclude that A in fact terminates on all inputs. The analogous question makes no sense in case of a novel definition. In a word, we can argue about the acceptability of a proposed axiom, but not over a definition -- definitions are merely stipulations. > James has claimed a proof for his axiom, so I conclude that it is not > an axiom (assuming that the purported proof is correct). Based on my vague impressions -- I haven't really paid any attention to recent intriguing intricacies of Jamesiana -- James's axiom is not really a mathematical axiom at all. It is rather an informal principle we may or may not be able to squeeze some mathematics out of. Such principles don't have any definite mathematical consequences. They have an indefinite range of possible applications. A perhaps more familiar example from set theory is the reflection principle Whatever mathematical statement holds of the totality of all ordinals holds already of some set-sized initial segment of the totality. which also has no definite set of mathematical consequences, and which isn't even obviously consistent, but does lead, upon informal reflection, in the spirit of Kreisel's "informal rigour" perhaps, to various fruitful properly mathematical applications, principles, ideas. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: rossum on 17 Jul 2010 18:13 On Sat, 17 Jul 2010 07:44:04 -0700 (PDT), Chip Eastham <hardmath(a)gmail.com> wrote: >but only sort of information about their work as >one might find in a Time-Life book about math. James tends not to read books about maths, he reads Wikipedia and MathWorld. >It is not without basis that some >have tried to diagnose a narcissistic personality >disorder At one point James self-diagnosed himself with NPD. rossum
From: Chip Eastham on 17 Jul 2010 21:41 On Jul 17, 6:13 pm, rossum <rossu...(a)coldmail.com> wrote: > On Sat, 17 Jul 2010 07:44:04 -0700 (PDT), Chip Eastham > > <hardm...(a)gmail.com> wrote: > >but only sort of information about their work as > >one might find in a Time-Life book about math. > > James tends not to read books about maths, he reads Wikipedia and > MathWorld. > > >It is not without basis that some > >have tried to diagnose a narcissistic personality > >disorder > > At one point James self-diagnosed himself with NPD. > > rossum I almost commented that James seems to share a lot of personal information/admissions, another trait that on the face of it argues against classification as a troll. --c
From: JSH on 17 Jul 2010 22:00
On Jul 17, 3:13 pm, rossum <rossu...(a)coldmail.com> wrote: > On Sat, 17 Jul 2010 07:44:04 -0700 (PDT), Chip Eastham > > <hardm...(a)gmail.com> wrote: > >but only sort of information about their work as > >one might find in a Time-Life book about math. > > James tends not to read books about maths, he reads Wikipedia and > MathWorld. > > >It is not without basis that some > >have tried to diagnose a narcissistic personality > >disorder > > At one point James self-diagnosed himself with NPD. > > rossum I considered the possibility as a significant concern for myself. Turns out though that if I DO have NPD the prognosis is not good. People with the disorder are extremely resistant to treatment. What's interesting though was that I shifted mental illness accusations with my post! Over time the NPD accusation has come to dominate. In the past schizophrenia was often tossed out, until the movie "A Beautiful Mind", then for a while posters kind of drifted a bit as to the specifics of whatever mental illness I supposedly had! Till I gave them focus by putting NPD into the pot. James Harris |