Am I a crank?
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From: Lester Zick on 31 Aug 2006 13:18 On 31 Aug 2006 18:47:17 +0300, Phil Carmody <thefatphil_demunged(a)yahoo.co.uk> wrote: >schoenfeld.one(a)gmail.com writes: >> Definitions can be false too (i.e. "Let x be an even odd"). > >Nonsense. It appears you are unaware of the use of the word >'vacuous' in mathematics. Probably due to the matching state >of your brain cavity. So definitions in modern math are not true? ~v~~
From: Lester Zick on 31 Aug 2006 13:19 On Wed, 30 Aug 2006 22:02:24 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <bn4cf213is70kjhmu35h9e7945hc3bb36i(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Wed, 30 Aug 2006 13:43:02 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >In article <r7kbf2tlc70iqjm2rp4ktprl1o3uui79jf(a)4ax.com>, >> > Lester Zick <dontbother(a)nowhere.net> wrote: >> > >> > >> >> >Hello Crackpot. >> >> >> >> Crackpot=disagreer. Quite mathematical. >> > >> >Crackpots are those who disagree not only without supporting evidence >> >but despite contrary evidence. >> > >> >Like Zick. >> >> Like exactly what contrary evidence do you mean, sport? Your opinions >> and assumptions of what's true and false? Or in your case I guess I >> should say your opinion of what's not true and not false? > >Zick claims that mathematicians claim their axioms to be true. >What evidence does he have of this claim? >Like most of his claims here, none! Actually Zick claims that modern mathematikers claim their axioms are not true. ~v~~
From: Lester Zick on 31 Aug 2006 13:22 On Thu, 31 Aug 2006 06:14:02 EDT, "T.H. Ray" <thray123(a)aol.com> wrote: >> >> Nathan wrote: >> > david petry wrote: >> > >> > > It could be argued that since the mathematics >> community does expend a >> > > great deal of energy in the search for formal >> proofs of conjectures >> > > having ridiculously high probabilities of being >> true, and often turns a >> > > blind eye to the probabilistic arguments, the >> mathematics community >> > > itself engages in crank-like behavior. >> > >> > I have read many heuristic arguments advanced by >> mathematicians to >> > suggest what *might* be true, especially in number >> theory. I disagree >> > that the community "often turns a blind eye" to >> such. It's just that >> > these still leave the actual question unanswered. >> >> It all depends on what the "actual" question is. If >> mathematics is >> thought of as a science having the purpose of >> explaining why we observe >> the phenomena that we do observe, then the heuristic >> argument really >> does answer the "actual" question. There's >> absolutely no reason to >> believe that we can do better than a heuristic >> argument in many cases. >> > > >What makes you think that mathematicians assign any >value at all to what one personally believes? And what makes you think anyone assigns any value to what anyone believes about modern mathematics? ~v~~
From: MoeBlee on 31 Aug 2006 13:45 Lester Zick wrote: > So how exactly do definitions differ from propositions? A common approach for formal languages is that definitions are definitional axioms, which differ from non-definitional axioms as definitional axioms satisfy the criteria of eliminability and non-creativity, which is to say that defintional axioms provide that any formula using the defined term has an equivalent formula not using the defined term (i.e., the definitional axiom only provides for abbreviation) and the definitional axiom does not provide for theorems couched without the defined term that are not theorems without the definitional axiom anyway. For a mere understanding of such formal systems, it is not necessary to determine what are propositions, but rather what are formulas and what are sentences. However, in an informal understanding of such formal systems, of course, such definitional axioms are regarded as propositions. But they are a special kind of proposition in the way I just described: they provide merely for abbreviation. In the most strict technical sense, definitional axioms are true in some models and false in other models. However, though that is, very strictly speaking, true, it is also extremely pedantic to dwell upon. Since definitions are not substantive (in the sense that they are only abbreviatory), we regarded them as stipulative rather than amenable to evaluation for truth and falsehood, which evaluation would allow ourselves to lose sight of the abbreviatory role of definitions and get us bogged down in extreme pedanticism that is, for working purposes, irrelevent to the abbreviatory and stipulative nature of defintions. For example, whether we define '@' (as, say, the typographic shape to represent the 3rd 2-place function symbol of the formal language) or we define '#" (as, say, the typographic shape to represent the 4th 2-place function symbol of the language) to denote the binary operation of a group is not important. It is stipulative and virtually beyond all reasonableness to argue about as being correct or incorrect or true or false. MoeBlee
From: MoeBlee on 31 Aug 2006 13:54
schoenfeld.one(a)gmail.com wrote: > Definitions can be false too (i.e. "Let x be an even odd"). That's not a definition. That's just a rendering of an open formula whose existential closure is not a member of such theories as PA. MoeBlee |