'When Are Relations Neither True Nor False?
in [Math]
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From: Alan Smaill on 22 Feb 2010 08:12 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Alan Smaill wrote: > > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > > > >> Alan Smaill wrote: > >> > >>> You may regard him as being rude. > >>> You may also be over-reacting, by taking the comment about philosophy > >>> as negative in itself. > >> I don't think I've been overacting. > >> > >> There's nothing wrong with AP's "correcting mathematics" in the other > >> thread on the ground that it must be limited by the actual physical > >> universe, _as a philosophy_ (AP's philosophy). It's only in mathematical > >> reasoning context that it's ridiculous to claim mathematics is wrong > >> on the ground of such philosophy. > > If you believe that, then presumably you think that mathematicians > > like > > Brouwer or Poincare were ridiculous when they contested received > > mathematical opinion on whether every mathematical statement must be > > true or false; that's the sort of example presumably in > > the background here. > > > >> The point being is yes there's "Mathematical Philosophy" and there are cases > >> we have to take some _technical philosophical_ stand on mathematical issues, > >> but dismissing people's technical arguments, proposals,... on the ground of > >> being "philosophical" _without_ elaboration is at minimum double-talking: > >> after all dismissing here is really _discrediting_. > > Theer are two separate issues -- whether introducing philosophy > > is in itself being dismissive, and whether your point was treated seriously > > or not. It's only the first I was talking about. > > When Aatu says that the mention of philosophy is not dismissive, I > > see no reason to think he is lying to us. > > For the record I didn't accuse anyone as lying. I might have accused him > of being unfair in single-handedly deciding when relevancy exist or not > in technical conversations and in the process leaving people no fair chance > to defend or express their views; and he might believe he has his own valid > reasons to do so, and I might not agree with the reasons (and might still > protest them). But that's not the same as accusing him of lying. For the record, I didn't accuse you of lying. -- Alan Smaill
From: Nam Nguyen on 22 Feb 2010 10:01 Alan Smaill wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> Alan Smaill wrote: >>> Nam Nguyen <namducnguyen(a)shaw.ca> writes: >>> >>>> Alan Smaill wrote: >>>> >>>>> You may regard him as being rude. >>>>> You may also be over-reacting, by taking the comment about philosophy >>>>> as negative in itself. >>>> I don't think I've been overacting. >>>> >>>> There's nothing wrong with AP's "correcting mathematics" in the other >>>> thread on the ground that it must be limited by the actual physical >>>> universe, _as a philosophy_ (AP's philosophy). It's only in mathematical >>>> reasoning context that it's ridiculous to claim mathematics is wrong >>>> on the ground of such philosophy. >>> If you believe that, then presumably you think that mathematicians >>> like >>> Brouwer or Poincare were ridiculous when they contested received >>> mathematical opinion on whether every mathematical statement must be >>> true or false; that's the sort of example presumably in >>> the background here. >>> >>>> The point being is yes there's "Mathematical Philosophy" and there are cases >>>> we have to take some _technical philosophical_ stand on mathematical issues, >>>> but dismissing people's technical arguments, proposals,... on the ground of >>>> being "philosophical" _without_ elaboration is at minimum double-talking: >>>> after all dismissing here is really _discrediting_. >>> Theer are two separate issues -- whether introducing philosophy >>> is in itself being dismissive, and whether your point was treated seriously >>> or not. It's only the first I was talking about. >>> When Aatu says that the mention of philosophy is not dismissive, I >>> see no reason to think he is lying to us. >> For the record I didn't accuse anyone as lying. I might have accused him >> of being unfair in single-handedly deciding when relevancy exist or not >> in technical conversations and in the process leaving people no fair chance >> to defend or express their views; and he might believe he has his own valid >> reasons to do so, and I might not agree with the reasons (and might still >> protest them). But that's not the same as accusing him of lying. > > For the record, I didn't accuse you of lying. Why did you mention that word in the first place?
From: Alan Smaill on 22 Feb 2010 11:47 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Alan Smaill wrote: >> Nam Nguyen <namducnguyen(a)shaw.ca> writes: >> >>> Alan Smaill wrote: .... >>>> Theer are two separate issues -- whether introducing philosophy >>>> is in itself being dismissive, and whether your point was treated >>>> seriously or not. It's only the first I was talking about. >>>> When Aatu says that the mention of philosophy is not dismissive, I >>>> see no reason to think he is lying to us. >>> For the record I didn't accuse anyone as lying. I might have accused him >>> of being unfair in single-handedly deciding when relevancy exist or not >>> in technical conversations and in the process leaving people no fair chance >>> to defend or express their views; and he might believe he has his own valid >>> reasons to do so, and I might not agree with the reasons (and might still >>> protest them). But that's not the same as accusing him of lying. >> >> For the record, I didn't accuse you of lying. > > Why did you mention that word in the first place? To emphasise that I thought Aatu was speaking in good faith when he said the reference to philosophy was not meant as a dismissal. -- Alan Smaill
From: Nam Nguyen on 23 Feb 2010 02:00 Frederick Williams wrote: > This is one of those threads that causes me to think "would that the > contributors could find something more interesting to discuss." This thread to me is an interesting one in that (at least) its title suggests a way to generalize GIT into a more comprehensive statement about incompleteness in mathematical reasoning, through FOL.
From: Newberry on 23 Feb 2010 10:28
On Feb 22, 11:00 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Frederick Williams wrote: > > This is one of those threads that causes me to think "would that the > > contributors could find something more interesting to discuss." > > This thread to me is an interesting one in that (at least) its title > suggests a way to generalize GIT into a more comprehensive statement > about incompleteness in mathematical reasoning, through FOL. I do not know if I would call it generalization but it is something of that sort. Goedel's incompeteness theorem suggests that two valued logic is impossible. Furthermore Goedel's second theorem does not apply to theories with gaps. It is obvious where the gaps might be - in the so called "vacuously true" sentences. So again, if ~(Ex)[(x + n < 6) & (n = 8)] is neither true nor false for any n (according to the logic of presuppositions.) Am I right that ~(Ex)(Ey)[(x + y < 6) & (y = 8)] is neither true nor false? |