Beyond Incompleteness
in [Logic]
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From: Marshall on 29 Jun 2010 11:18 On Jun 28, 6:29 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > On Jun 27, 3:23 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > >> Charlie-Boo <shymath...(a)gmail.com> writes: > >> > Yes. That is the first conclusion in Godel's 1st Incompleteness > >> > Theorem based on Soundness in the introduction to the 1931 paper. > > >> > The second conclusion was that not all sentences are provable or > >> > refutable ("incompleteness".) The theorem based on w-consistency in > >> > the body of the paper came next, then the 2nd theorem. Later was > >> > Rosser's and Smullyan's versions. > > >> > Then C-B showed how to shrink all of these proofs to one short English > >> > sentence, in at least two different ways, as well as how to generate > >> > proofs from simple properties of 3 specific sets of wffs. > > >> Yes, CBL is a great advance in logic. I've always said so. > > >> Congrats! > > > Thanks. And BTW do you know what would be cool? If sarcasm were > > replaced by specific valid mathematical points. > > Some time in the past, I tried to make sense of CBL. I couldn't do it. > As far as I recall, each application of CBL required certain axioms that > contained the meat of the mathematical insight of the original proofs. I could never even figure out the syntax. I tried asking various questions to get a clearer understanding, and while I often got responses, I never got answers to my questions. Eventually I gave up. It's pretty clear that Charlie's approach to syntax is "if it feels good, do it." Consider the "Wouldnt It be Cool if These Were Equivalent?" thread. Marshall
From: Charlie-Boo on 29 Jun 2010 13:20 On Jun 29, 11:18 am, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jun 28, 6:29 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > > > > > > Charlie-Boo <shymath...(a)gmail.com> writes: > > > On Jun 27, 3:23 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > >> Charlie-Boo <shymath...(a)gmail.com> writes: > > >> > Yes. That is the first conclusion in Godel's 1st Incompleteness > > >> > Theorem based on Soundness in the introduction to the 1931 paper. > > > >> > The second conclusion was that not all sentences are provable or > > >> > refutable ("incompleteness".) The theorem based on w-consistency in > > >> > the body of the paper came next, then the 2nd theorem. Later was > > >> > Rosser's and Smullyan's versions. > > > >> > Then C-B showed how to shrink all of these proofs to one short English > > >> > sentence, in at least two different ways, as well as how to generate > > >> > proofs from simple properties of 3 specific sets of wffs. > > > >> Yes, CBL is a great advance in logic. I've always said so. > > > >> Congrats! > > > > Thanks. And BTW do you know what would be cool? If sarcasm were > > > replaced by specific valid mathematical points. > > > Some time in the past, I tried to make sense of CBL. I couldn't do it. > > As far as I recall, each application of CBL required certain axioms that > > contained the meat of the mathematical insight of the original proofs. > > I could never even figure out the syntax. I tried asking various > questions to get a clearer understanding, and while I often > got responses, I never got answers to my questions. Eventually > I gave up. It would be nice if you substantiated what you say. I spend inordinate amounts of time whenever anyone asks about CBL. One reader posted dozens of times challenging it. I answered every quesion - many more than once. > It's pretty clear that Charlie's approach to syntax is "if it > feels good, do it." Consider the "Wouldnt It be Cool if > These Were Equivalent?" thread. That is not CBL, BTW. I thought it would be obvious what they meant. Really, what do you think they mean? 1. |- (allX)P(X) 2. (allX) |- P(X) 3. ~ |- (existsX)~P(X) Don't you naturally read them left-to-right, "|-" is "This is provable:", (allx) is "For all x" etc.? C-B > Marshall- Hide quoted text - > > - Show quoted text -
From: Chip Eastham on 29 Jun 2010 17:03 On Jun 29, 5:21 am, Charlie-Boo <shymath...(a)gmail.com> wrote: > Should you say something you cannot - and will not - defend? Should you ask something if you will disregard the answer? regards, chip
From: Marshall on 29 Jun 2010 18:09 On Jun 29, 10:20 am, Charlie-Boo <shymath...(a)gmail.com> wrote: > On Jun 29, 11:18 am, Marshall <marshall.spi...(a)gmail.com> wrote: > > On Jun 28, 6:29 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > > > Some time in the past, I tried to make sense of CBL. I couldn't do it. > > > As far as I recall, each application of CBL required certain axioms that > > > contained the meat of the mathematical insight of the original proofs.. > > > I could never even figure out the syntax. I tried asking various > > questions to get a clearer understanding, and while I often > > got responses, I never got answers to my questions. Eventually > > I gave up. > > It would be nice if you substantiated what you say. Here's an example thread: http://groups.google.com/group/sci.logic/browse_frm/thread/b53fad4b8336b67/97b8bc827624e8a?hl=en&q=cbl+group:sci.logic+author:marshall.spight%40gmail.com#097b8bc827624e8a I sent you various emails, and made various posts on sci.logic, trying to figure out even simple things like what characters you were trying to use. I never got that question answered. Again note that I do not say you never responded; you did in fact often respond. But you *were* pretty consistent about not answering direct questions. Searching for that thread caused me to revisit some threads from 2008 which reminded me of just how difficult it is to have a conversation with you. > I spend > inordinate amounts of time whenever anyone asks about CBL. One reader > posted dozens of times challenging it. I answered every quesion - > many more than once. I believe you think you thought you answered my questions. > > It's pretty clear that Charlie's approach to syntax is "if it > > feels good, do it." Consider the "Wouldnt It be Cool if > > These Were Equivalent?" thread. > > That is not CBL, BTW. I know that. > I thought it would be obvious what they meant. > Really, what do you think they mean? What they indicate to me is that you don't understand much about formal language, since 2 and 3 both contain obvious syntax errors. Since you're making up your own syntax, (even if it is reminiscent of existing syntax) it's up to you to say what they mean. If I try to force meaning on them on a best-guess basis, I get three different ways of saying the same thing. Clearly they don't mean to me what they mean to you. > 1. |- (allX)P(X) > 2. (allX) |- P(X) > 3. ~ |- (existsX)~P(X) > > Don't you naturally read them left-to-right, "|-" is "This is > provable:", (allx) is "For all x" etc.? That doesn't help. Marshall
From: Charlie-Boo on 29 Jun 2010 22:23
On Jun 29, 5:03 pm, Chip Eastham <hardm...(a)gmail.com> wrote: > On Jun 29, 5:21 am, Charlie-Boo <shymath...(a)gmail.com> wrote: > > > Should you say something you cannot - and will not - defend? > > Should you ask something if you will disregard the answer? > > regards, chip Can you ever know what will happen? How? C-B |