Meaning, Presuppositions, Truth-relevance, Goedel's Theorem andthe Liar Paradox
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From: Newberry on 12 Aug 2010 23:25 On Aug 12, 9:54 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Newberry <newberr...(a)gmail.com> writes: > >> > Wow! We are making a lot of progress. (Actually it is ~(T v F) > >> > regardless if Qm is true.) > > >> No, we're not. > > > It is disappointing. You need to read chapter 2.2. > > Oh, I recall (now) your odd beliefs about vacuity. I just think > they're unmotivated. > > Take a simple deductive rule: v-elimination, that is: > > |- P v Q |- ~Q > --------------- > |- P. > > It seems to me that this rule is very hard to understand, given your > ideas. As soon as I prove that P is true, P v Q is neither true nor > false ... despite the fact that I have (by assumption) proved P v Q > prior to deducing P. I suppose I have to retroactively judge that my > purported proof of P v Q was not a proof after all, since P v Q is not > true. Truth-relevant logic is not classicl logic, and this rule is probably not compatible with it. > > -- > Jesse F. Hughes > "[I]f gravel cannot make itself into an animal in a year, how could it > do it in a million years? The animal would be dead before it got > alive." --The Creation Evolution Encyclopedia
From: Newberry on 13 Aug 2010 10:27
On Aug 13, 6:00 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Newberry <newberr...(a)gmail.com> writes: > > On Aug 12, 9:54 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > >> Newberry <newberr...(a)gmail.com> writes: > >> >> > Wow! We are making a lot of progress. (Actually it is ~(T v F) > >> >> > regardless if Qm is true.) > > >> >> No, we're not. > > >> > It is disappointing. You need to read chapter 2.2. > > >> Oh, I recall (now) your odd beliefs about vacuity. I just think > >> they're unmotivated. > > >> Take a simple deductive rule: v-elimination, that is: > > >> |- P v Q |- ~Q > >> --------------- > >> |- P. > > >> It seems to me that this rule is very hard to understand, given your > >> ideas. As soon as I prove that P is true, P v Q is neither true nor > >> false ... despite the fact that I have (by assumption) proved P v Q > >> prior to deducing P. I suppose I have to retroactively judge that my > >> purported proof of P v Q was not a proof after all, since P v Q is not > >> true. > > > Truth-relevant logic is not classicl logic, and this rule is probably > > not compatible with it. > > I think you need to reconsider this judgment. The same reasoning > applies to, for instance, Modus Ponens. > > If P -> Q is provable and P is provable, then Q is provable and hence > Q is necessarily true. But if Q is necessarily true, then P -> Q is > vacuously true (right?) and hence neither true nor false. > > Similarly for Modus Tollens. > > So, it seems as if MP and MT are not rules of your truth-relevant > logic. Does that seem right to you? Theorem: The rule of modus ponens is compatible with TR: |- A, |- A -> B ----------------- |- B Proof: A -> B is equivalent to. ~A v B. A and ~A v B are t-relevant by hypothesis. ~A is false. Assume B is not t-r. Then there exist a variable q such that q = U and B = T (for all possible valuations of B.) Then ~A v B = T contrary to the assumption. This is the case even if q is relevant in A. Then for q = U, A can take either U or T. But in either case ~A v B = T. Hence q is not relevant in ~A v B. QED. http://www.scribd.com/doc/32296467/System-TR All ideas in that paper are due to Richard Diaz, all inadequacies including but not limited to distortions, omissions and errors ar due to X.Y. Newberry. > > -- > Jesse F. Hughes > "[M]oving towards development meetings for new release class viewer 5.0 > and since [I]'m the only developer, easy to schedule." > --James S. Harris tweets on code development- Hide quoted text - > > - Show quoted text - |