'When Are Relations Neither True Nor False?
in [Math]
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From: Marshall on 5 Mar 2010 13:41 On Mar 5, 10:44 am, MoeBlee <jazzm...(a)hotmail.com> wrote: > On Mar 4, 10:09 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > > > But for crying out loud, why on Earth would one want flip the semantics > > of "formalized" into "in-formalized"? > > Why on earth don't you just LISTEN to what people say to you? For me, Nam has mostly moved into the same category as AP. Totally pointless: devoid not merely of technical content, but even simple amusement. I hardly bother to read their posts anymore. Marshall
From: David Bernier on 5 Mar 2010 13:43 Newberry wrote: > On Mar 4, 11:56 pm, David Bernier <david...(a)videotron.ca> wrote: >> Newberry wrote: >>> On Mar 4, 9:23 am, David Bernier <david...(a)videotron.ca> wrote: >>>> Jesse F. Hughes wrote: >>>>> Newberry <newberr...(a)gmail.com> writes: >>>>>> On Mar 3, 9:37 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >>>>>>> Newberry <newberr...(a)gmail.com> writes: >>>>>>>> This is my main motivation: >>>>>>>> G�del's sentence has the same form as (3.1): >>>>>>>> ~(Ex)(Ey)(Pxy & Qy) (4.1) >>>>>>>> Pxy means that x is the proof of y, where x, y are G�del numbers of >>>>>>>> wffs or sequences of wffs. Q has been constructed such that only one y >>>>>>>> = m satisfies it, and m is the G�del number of (4.1). >>>>>>>> Assume that G�del's sentence (4.1) is not derivable, i.e. that >>>>>>>> ~(Ex)Pxm (4.2) >>>>>>>> is true. Then (4.1) is ~(T v F). Thus if G�del's sentence is not >>>>>>>> derivable it is neither true nor false. >>>>>>> So, you want to deny that Goedel's theorem is true. >>>>>> We better get this straigh first. No. I do not want to deny that >>>>>> Goedel's theorem is true. >>>>> Well, I'm sorry if I misrepresented your opinion, but you *just* >>>>> suggested that if (4.2) is true, then (4.1) is neither true nor false >>>>> and hence is not true. >>>> I read: >>>> [ Newberry:] >>>> " G�del's sentence has the same form as (3.1):" >>>> I've been wondering if there's a typo. there and if it ought to >>>> be numbered in the quote above (4.1) and not (3.1). >>> It is out of context. he whole story is here >>> http://www.scribd.com/doc/26833131/RelationsAndPresuppositions-2010-0.... >> There was a debate of some kind about "denoting", etc. between >> Bertrand Russell and Strawson, the author of the book you quote from. >> >> This is according to an article published by someone >> under the name _Nearly_Anonymous_ here: >> >> http://bookstove.com/non-fiction/the-russell-strawson-debate-a-useful... >> >> Strawson writes "[...] if its subject class is empty" . >> >> He seems to be saying something about expressions such as, say, >> "The current King of France" [there is no King of France today]. >> >> Either "The current King of France" is married, or (***) >> "The current King of France" is not married. >> >> For Russell, (***) would have been a fine sentence and a true one. >> But perhaps Strawson would have disagreed. >> >> David Bernier- Hide quoted text - > > As I mentioned there is entire literature on presuppositions. In fact > you have to be speacialized in it if you want to know all of it. It is > perhaps more popular among linguists than among logicians. Do you think that mathematical logicians and/or mathematicians should be concerned about the disputes between Strawson and Russell (a) When the suject matter is limited to mathematics, mathematical logic as taught today, or Goedel's theorems? (b) When the subject matter could be arbitrary? > Starwson indeed had disputes with Russell. Among other things he > criticized his theory of descriptions. > David Bernier
From: Newberry on 6 Mar 2010 00:03 On Mar 5, 10:43 am, David Bernier <david...(a)videotron.ca> wrote: > Newberry wrote: > > On Mar 4, 11:56 pm, David Bernier <david...(a)videotron.ca> wrote: > >> Newberry wrote: > >>> On Mar 4, 9:23 am, David Bernier <david...(a)videotron.ca> wrote: > >>>> Jesse F. Hughes wrote: > >>>>> Newberry <newberr...(a)gmail.com> writes: > >>>>>> On Mar 3, 9:37 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > >>>>>>> Newberry <newberr...(a)gmail.com> writes: > >>>>>>>> This is my main motivation: > >>>>>>>> Gödel's sentence has the same form as (3.1): > >>>>>>>> ~(Ex)(Ey)(Pxy & Qy) (4.1) > >>>>>>>> Pxy means that x is the proof of y, where x, y are Gödel numbers of > >>>>>>>> wffs or sequences of wffs. Q has been constructed such that only one y > >>>>>>>> = m satisfies it, and m is the Gödel number of (4.1). > >>>>>>>> Assume that Gödel's sentence (4.1) is not derivable, i.e. that > >>>>>>>> ~(Ex)Pxm (4.2) > >>>>>>>> is true. Then (4.1) is ~(T v F). Thus if Gödel's sentence is not > >>>>>>>> derivable it is neither true nor false. > >>>>>>> So, you want to deny that Goedel's theorem is true. > >>>>>> We better get this straigh first. No. I do not want to deny that > >>>>>> Goedel's theorem is true. > >>>>> Well, I'm sorry if I misrepresented your opinion, but you *just* > >>>>> suggested that if (4.2) is true, then (4.1) is neither true nor false > >>>>> and hence is not true. > >>>> I read: > >>>> [ Newberry:] > >>>> " Gödel's sentence has the same form as (3.1):" > >>>> I've been wondering if there's a typo. there and if it ought to > >>>> be numbered in the quote above (4.1) and not (3.1). > >>> It is out of context. he whole story is here > >>>http://www.scribd.com/doc/26833131/RelationsAndPresuppositions-2010-0..... > >> There was a debate of some kind about "denoting", etc. between > >> Bertrand Russell and Strawson, the author of the book you quote from. > > >> This is according to an article published by someone > >> under the name _Nearly_Anonymous_ here: > > >>http://bookstove.com/non-fiction/the-russell-strawson-debate-a-useful.... > > >> Strawson writes "[...] if its subject class is empty" . > > >> He seems to be saying something about expressions such as, say, > >> "The current King of France" [there is no King of France today]. > > >> Either "The current King of France" is married, or (***) > >> "The current King of France" is not married. > > >> For Russell, (***) would have been a fine sentence and a true one. > >> But perhaps Strawson would have disagreed. > > >> David Bernier- Hide quoted text - > > > As I mentioned there is entire literature on presuppositions. In fact > > you have to be speacialized in it if you want to know all of it. It is > > perhaps more popular among linguists than among logicians. > > Do you think that mathematical logicians and/or mathematicians > should be concerned about the disputes between > Strawson and Russell Yes. It is up to them how wide they want to make the scope. > (a) When the suject matter is limited to mathematics, > mathematical logic as taught today, or Goedel's theorems? > > (b) When the subject matter could be arbitrary? > > > Starwson indeed had disputes with Russell. Among other things he > > criticized his theory of descriptions. > > David Bernier- Hide quoted text - > > - Show quoted text -
From: Aatu Koskensilta on 6 Mar 2010 05:24 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > I think you meant the passage I had earlier said: > >>> if there's a formal system where what he asserted is a theorem, then >>> his proof is a formal proof. If not then his proof isn't. It's >>> that's straight forward which doesn't require explanation on thing >>> such as "ordinary mathematical proof", as you said. > > Why is that definition of a _formal proof_ "bizarre and pointless"? This has already been explained. It is bizarre and pointless because according to it pretty much any and every piece of reasoning, however vague or informal, however cogent or inane, is a formal proof. > But for crying out loud, why on Earth would one want flip the > semantics of "formalized" into "in-formalized"? What on earth are you talking about? -- 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 6 Mar 2010 05:26
Newberry <newberryxy(a)gmail.com> writes: > But in any case why is quoting G�del's original statement pointless > obscurantism? The notation and terminology of G�del's original statement is impenetrable to anyone who doesn't have the paper in front of them. There's no reason not to state it in standard terminology and notation. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |