'When Are Relations Neither True Nor False?
in [Math]
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From: Nam Nguyen on 15 Feb 2010 13:01 Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Also, you seem to too-easily label people's comments as >> "philosophical". > > How should we understand > > The continuum hypothesis is neither true nor false. > > if not as a philosophical claim? As a mathematical claim in classical > mathematics it is trivially false. In constructing a model if you, for argument sake, _incompletely_ define a relation, say, symbolized by '<', as: {e0,e1), (e1,e3), ...} Then although you can determine the truth value of some formulas, isn't it true some other formulas would be in the category of being neither true nor false in this incomplete model, technically speaking? Similarly did *you* have a complete definition of an instance of ZF model where one could see CH as true, or false? > >> Aren't there *technical* discussing contexts where a particular formula >> could be considered as being neither true nor false? > > Sure. For example, when discussing Kripke's theory of truth we may > observe that some sentences, e.g. the liar, are neither true nor false > according to his construction. What's your reason then to dismiss the possibility that CH being not LEM conforming as "philosophical"?
From: Jesse F. Hughes on 15 Feb 2010 19:38 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Aatu Koskensilta wrote: >> calvin <crice5(a)windstream.net> writes: >> >>> The 'continuum hypothesis' is neither true nor false, >>> for example. >> >> This piece of philosophical reflection -- which stands in need of some >> argument -- has no apparent relevance to Newberry's original post. >> > > "In need of some argument", yes I'd agree. But not sure about this > post has no relevance to Newberry's original post, when the title > of the thread is "When Are Relations Neither True Nor False". Perhaps you'll have a better idea of what's relevant if you read the body of Newberry's post, rather than just the subject. > -- "Your knowledge is the power that promote good thought, how then can you have good thought without powerful knowledge or how can you have powerful knowledge without learning or how can you learn without a teacher and how can a teacher teach if he or she has not learned the subject." --CA Alternative High School
From: Nam Nguyen on 15 Feb 2010 20:26 Jesse F. Hughes wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Aatu Koskensilta wrote: >>> calvin <crice5(a)windstream.net> writes: >>> >>>> The 'continuum hypothesis' is neither true nor false, >>>> for example. >>> This piece of philosophical reflection -- which stands in need of some >>> argument -- has no apparent relevance to Newberry's original post. >>> >> "In need of some argument", yes I'd agree. But not sure about this >> post has no relevance to Newberry's original post, when the title >> of the thread is "When Are Relations Neither True Nor False". > > Perhaps you'll have a better idea of what's relevant if you read the > body of Newberry's post, rather than just the subject. > I read both but that has never changed my comment on AK's _dismissing assertion_. Are you saying that posting something very relevant to subject of the thread would be a miserably irrelevant posting, especially after only a few exchanges between you and the op it seemed apparent that that's a dead-end to have a relation that's neither true nor false? Iirc, at the end of his very first post, Newberry had an _unqualified_ invitation: "Comments appreciated."
From: spudnik on 15 Feb 2010 23:05 all of Russell's paradoxes are illinguistic, which might be discerned from when he "lost it," after Godel's incompleteness thing; not as bad as Korbyzinski's pidgen, E-prime, though! thus: one soes not have to ape "global" warming (from computerized simuacra & wholly selective reporting), to see that the climate is changing very rapidly, in the Anthropocene. > The lesson of climategate and now the IPCC's shoddy sourcing is that the > claims of the global warming lobby need far more rigorous scrutiny. thus: wow, neat problem; don't tell me what it is, but did you solve it? > >http://sites.google.com/site/tommy1729/home/eggs-probl thuis quoth: Simultaneously, EU Commission advisor Alberto Giovannini, who led the group that set up the technical transition from national currencies to the euro, is quoted in today's Italian daily Il Sole 24 Ore stating unabashedly: "History teaches us that empires are more efficient and achieve great prosperity, because the imperial model is successful with an extended geography." Although much attention has been mis-focused on Greece, LaRouche has emphasized that the epicenter of the European crisis is not Greece but Spain, and its Banco Santander. For example, of total German bank exposure in the eurozone of some 540 billion euros, Greek debt accounts for only 43 billion, or 8% of the total. Spain, by contrast, amounts to 240 billion euros, or 44% of the total. http://larouchepub.com/pr_lar/2010/lar_pac/100210lar_no_banco_bailout.html thus: yeah, massless rocks o'light, built a hugely impenetrable bosonic wall around EinsteinoNewtonianism! thus: the photographic record that I saw, in some rather eclectic compendium of Einsteinmania, seemed to show quite an effect, I must say; not that the usual interpretation is correct, though. Nude Scientist said: > > "Enter another piece of luck for Einstein. We now know that the light- > > bending effect was actually too small for Eddington to have discerned --Another Flower for Einstein: http://www.21stcenturysciencetech.com/articles/spring01/Electrodynamics.html --les OEuvres! http://wlym.com --Stop Cheeny, Ricw & the ICC in Sudan; no more Anglo-american quagmires! http://larouchepub.com/pr/2010/100204rice
From: Newberry on 15 Feb 2010 23:35
On Feb 15, 9:52 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Nam Nguyen <namducngu...(a)shaw.ca> writes: > > But what's wrong with another poster posting comment very relevant to > > the thread? > > Relevant how? Claims like "the continuum hypothesis is neither true nor > false" are usually used to express various philosophical ideas about set > theory, often prompted by set theoretic independence results. Such > things have no apparent relation to Newberry's logical fiddling. > > > I meant is being vacuous in some sense is the only way to talk about > > when a relation might be neither true not false? > > As usually understood it makes no sense to say of a relation that it is > or is not true. What do you mean by "as usually understood"? Does the logic of presuppositions fall in the category "as usually understood"? > > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |