Am I a crank?
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From: Virgil on 1 Sep 2006 19:54 In article <36chf2h05iio4drhfnla6i81agqkn6ns9r(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On 1 Sep 2006 12:21:38 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> > wrote: > > >Consider the example given above. It constitutes a > >definition of the phrase "John Doe" within the context > >of some legal process (let's say a trial). Are you prepared > >to declare that statement as true or false? > > I'm not prepared to deal with predicate combinations which are not > true, false, or ambiguous. Which means that Zick is only prepared to deal with declarative sentences, but not questions, exclamations, commands, requests, and a whole host of other forms other that declarative sentences. > > >Compare that to: "The defendant's name is John Doe." > >Do you agree that the defendant has a name, and that > >there are only two possibilities, that the name is John Doe > >or that it is not? > > This has exactly what bearing on my observation? If Zick declares himself unprepared to deal with questions, as he has done, what right does he think he has to ask them? > >Is it really "obvious" to you that "Let's call the defendant > >John Doe" must be either true or false? > > It's really obvious to me that you have no conception what you're > trying to reply to. "What" he is trying to reply to is apparently unqualified to be referred to as "whom", which makes "Lester Zick" a non-person, perhaps a 'bot, but of no real consequence.
From: Robert Israel on 1 Sep 2006 20:06 david petry wrote: > Chip Eastham wrote: > > Robert Israel wrote: > > > In article <1156822962.655075.212160(a)i3g2000cwc.googlegroups.com>, > > > david petry <david_lawrence_petry(a)yahoo.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. > > > > " Except that > > 1) in many cases we _can_ do better. > > 2) many perfectly plausible statements, supported by all kinds of > > heuristics, turn out to be wrong." > > > > Ironically this is a good heuristic argument that we can > > do better than a heuristic argument in many cases! > > Thus we should ordinarily try, which contrary to Petry's > > claim that mathematicians turn a blind eye to heuristics, > > leads to minutely careful evaluation of them. > > > FWIW, my claim was that mathematicians turn a blind eye to > probabilistic arguments. Nathan then changed that to "heuristic" > arguments, which may not be the same thing. Indeed. I was writing about heuristic arguments in general, not specifically probabilistic arguments in number theory. > Probabilistic arguments are part of the scientific method, but they > absolutely must be validated by experiment. If Robert Israel thinks > there are lots of examples of probabilistic arguments supported by > experimental evidence which nevertheless lead to wrong conclusions, I'd > like to see him name one such case. I don't know whether there are lots of these, but it seems that one case is the incompatibility of the Hardy and Littlewood conjecture pi(k) >= pi(n+k) - pi(n) for sufficiently large n and the prime k-tuples conjecture (see <http://www.utm.edu/staff/caldwell/preprints/Heuristics.pdf>). I am sure the number theorists in the group can supply more examples. Robert Israel israel(a)math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
From: Randy Poe on 1 Sep 2006 22:00 Lester Zick wrote: > On 1 Sep 2006 12:21:38 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> > wrote: > > > > >Lester Zick wrote: > >> On Fri, 01 Sep 2006 09:49:03 +0300, Aatu Koskensilta > >> <aatu.koskensilta(a)xortec.fi> wrote: > >> > >> >Lester Zick wrote: > >> >> On 31 Aug 2006 10:54:03 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > >> >> > >> >>> 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. > >> >> > >> >> Which really clears things up for us, Moe. > >> > > >> >MoeBlee's answer might be considered somewhat more obfuscated than > >> >necessary. We can rephrase it without reference to all this formal stuff > >> >and simply say that "let x be an even odd" is not a definition, it's > >> >just a shorter version "let x be a natural number and further assume > >> >that x is both even and odd" which is neither a proposition nor a > >> >definition. It's probably the beginning of a - relatively boring! - > >> >proof in which it is established that there is no natural that is both > >> >even and odd. > >> > > >> >Definitions in mathematics often appear in the following forms > >> > > >> > "An X such that P will be called a Q" > >> > "By a X we mean a Y" > >> > "When P(X,Y) we often say that X glurbles Y" > >> > ... > >> > > >> >One might quibble and say that a definition of that kind might be false > >> >if in fact no one will call an X such that P a Q; or if, in fact, the > >> >devious author doesn't really mean a Y by X; or if "we" will not, in > >> >fact, often say that X glurbles Y when P(X,Y); and so forth. However, > >> >such objections ignore the role claims such as above have in > >> >mathematical language, acting as they do essentially as stipulations, > >> >analogously as one might say "let's call whoever it was who committed > >> >this heinous crime 'John Doe'". > >> > >> Is a stipulation a statement? Is a definition a statement? Is a > >> theorem a statement? Then my question remains as to what the > >> difference is between or among statements such that one can be true or > >> false and others not? Obviously the answer is that there is no such > >> difference. > > > >"Obviously"? > > Obviously. > > >Consider the example given above. It constitutes a > >definition of the phrase "John Doe" within the context > >of some legal process (let's say a trial). Are you prepared > >to declare that statement as true or false? > > I'm not prepared to deal with predicate combinations which are not > true, false, or ambiguous. > > >Compare that to: "The defendant's name is John Doe." > >Do you agree that the defendant has a name, and that > >there are only two possibilities, that the name is John Doe > >or that it is not? > > This has exactly what bearing on my observation? Let's walk through this again slowly. You claim that there is no difference ("obviously") between definitions and factual propositions which can be either true or false. Then I offer a definition, and a factual proposition. And you ask what this has to do with the discussion of the difference between definitions and factual propositions. You know, I'm just going to leave that as an exercise to you... what could an example of a declaration and a factual proposition have to do with a discussion of the difference between declarations and factual propositions? Hmmm, think, think, think... - Randy
From: fernando revilla on 1 Sep 2006 18:27 > > Chip Eastham wrote: > > Robert Israel wrote: > > > In article > <1156822962.655075.212160(a)i3g2000cwc.googlegroups.com> > , > > > david petry <david_lawrence_petry(a)yahoo.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. > > > > " Except that > > 1) in many cases we _can_ do better. > > 2) many perfectly plausible statements, supported > by all kinds of > > heuristics, turn out to be wrong." > > > > Ironically this is a good heuristic argument that > we can > > do better than a heuristic argument in many cases! > > Thus we should ordinarily try, which contrary to > Petry's > > claim that mathematicians turn a blind eye to > heuristics, > > leads to minutely careful evaluation of them. > > > FWIW, my claim was that mathematicians turn a blind > eye to > probabilistic arguments. Nathan then changed that to > "heuristic" > arguments, which may not be the same thing. > > Probabilistic arguments are part of the scientific > method, but they > absolutely must be validated by experiment. If > Robert Israel thinks > there are lots of examples of probabilistic arguments > supported by > experimental evidence which nevertheless lead to > wrong conclusions, I'd > like to see him name one such case. > I can not imagine a fuction that it is continuous in an closed interval and not differentiable for all the points of the interval. However such a function does exist. Mathematics are wonderful !. Heuristic lies ! Fernando
From: Dik T. Winter on 1 Sep 2006 22:43
In article <9ebb9$44f84202$82a1e228$24060(a)news1.tudelft.nl> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > Jesse F. Hughes wrote: > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > > > >>Dik T. Winter wrote: > >> > >>>In article <1157052981.177594.80970(a)p79g2000cwp.googlegroups.com> > >>>Han.deBruijn(a)DTO.TUDelft.NL writes: > >>>... > >>> > Is that so? Lately, I found that if you have ten apples and five > >>> > people, then you can give everybody two apples. I checked > >>> > this with the axioms of arithmetic and found that 10 / 5 = 2. > >>>Interesting. What are the axioms of arithmetic? > >> > >>Have no idea. But I'm sure that 10 / 5 = 2 can be derived from them. > > > > I thought you "checked this with the axioms of arithmetic". How could > > you do that if you have no idea what the axioms are? > > Oh, come on, Jesse! I checked this with arithmetic. Arithmetic is based > upon axioms. So I checked it with the axioms of arithmetic. No ? What axioms is arithmetic based on? Your "Is that so" above was a reply to: > By that argument, it will do no harm to throw out every axiom of every > set theory or geometry theory or any other mathematical theory since > none of them refer to anything that exists in the "real world". So what axioms referring to anything that exists in the "real world" is your arithmetic based on? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ |