'When Are Relations Neither True Nor False?
in [Math]
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From: Nam Nguyen on 15 Feb 2010 12:29 Nam Nguyen wrote: > 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". Also, you seem to too-easily label people's comments as "philosophical". Aren't there *technical* discussing contexts where a particular formula could be considered as being neither true nor false?
From: Aatu Koskensilta on 15 Feb 2010 12:42 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > "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". Just read Newberry's original post. Unless the suggestion is that the continuum hypothesis is "vacuous" in Newberry's sense -- and there's very little to recommend this idea -- the piece of philosophical reflection was entirely irrelevant. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 15 Feb 2010 12:45 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. > 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. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Nam Nguyen on 15 Feb 2010 12:46 Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> "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". > > Just read Newberry's original post. Unless the suggestion is that the > continuum hypothesis is "vacuous" in Newberry's sense -- and there's > very little to recommend this idea -- the piece of philosophical > reflection was entirely irrelevant. > I did read the post. But what's wrong with another poster posting comment very relevant to the thread? I meant is being vacuous in some sense is the only way to talk about when a relation might be neither true not false?
From: Aatu Koskensilta on 15 Feb 2010 12:52
Nam Nguyen <namducnguyen(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. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |