'When Are Relations Neither True Nor False?
in [Math]
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From: Newberry on 27 Feb 2010 12:41 On Feb 27, 6:56 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Newberry <newberr...(a)gmail.com> writes: > > For what I know ordinary mathematics may well go on by using "there > > are no counterexamples to GC less than 27." But if you want to do any > > work in the foundations of mathematics you need higher precision. > > In ordinary mathematical language and reasoning there is no distinction > between "there are no counterexamples to GC less than 27" and "it's not > true that there are counterexamples to GC less than 27" and thus nothing > to be highly precise about. We can of course introduce whatever ideas > and semantics we want on which such a distinction can be understood, but > in the wider scheme of things such novelties have any interest only in > so far as we can relate them in some informative manner to our actual > mathematical experience and reasoning. > > To take another example, consider Priest's suggestion that there are > true arithmetical contradictions, of the form "there is a natural n such > that P(n) and not-P(n)" with P a decidable predicate. He also defines a > non-standard semantics (essentially, just a bit of standard mathematics) > on which we can make sense of this. However, absent some account of how > this semantics relates to our actual mathematical reasoning about > naturals, the idea, that number theorists might one day solve, say, the > Goldbach conjecture by showing that there is an even natural greater > than two that can't be expressed as the sum of two primes but can be > expressed as the sum of two primes, remains baffling and entirely > vacuous. The same is true of your various musings and logical fiddling. The ideas of Graham Priest are absurd. Please do not compare me with him. > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Jesse F. Hughes on 27 Feb 2010 12:51 Newberry <newberryxy(a)gmail.com> writes: > On Feb 27, 4:40 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Newberry <newberr...(a)gmail.com> writes: >> > For what I know ordinary mathematics may well go on by using "there >> > are no counterexamples to GC less than 27." But if you want to do >> > any work in the foundations of mathematics you need higher >> > precision. >> >> So you say, yet curiously folks who *do* work in the foundations of >> mathematics do *not* seem to share your view. >> >> Honestly, this is a Quixotic battle you're waging, as far as I can >> tell. Good luck with it. > > Do you have anything to say about the substance? Nothing I haven't said before. You claim There is no counterexample to GC that is less than 27. (*) is possibly meaningless, although It is not true that there is a counterexample to GC that is less (**) than 27. is meaningful and true. I simply cannot see why you think this makes a lick of sense. Whether GC is true or not, (*) is both meaningful and true because (1) I know what it means and (2) it is trivial to prove that it is true. Any further discussion will, I'm sure, amount to repeating these same trivial observations. -- Jesse F. Hughes | "There's no other star but one star | and you want it to make light, | but it's not making light." | -- A blues tune by Quincy P. Hughes
From: Jesse F. Hughes on 27 Feb 2010 13:00 Newberry <newberryxy(a)gmail.com> writes: > People noticed long time ago (beginning with Strawson himself) that > some sentences with empty subjects feel false and some of them just > feel ..., well, empty. There is a lot of literature trying to explain > the different intuitions. I recommed this highly interesting paper > http://semanticsarchive.net/Archive/zAzNjllO/von.fintel.kof.pdf > I do not know if von Fintel's theory is directly applicable tp your > example. A quick glance at the paper suggests that it's about definite descriptions and hence has nothing much to do with our conversation. Even if I do accept that certain sentences involving definite descriptions without referent are neither true nor false (and I'm not saying that I accept this), it does not follow that sentences of the form (Ax)(Px -> Qx) are meaningless unless (Ex)Px and (Ex)~Qx are true. -- Jesse F. Hughes "Liberals have hijacked science for long enough. Now it's our turn." -- From the cover of "The Politically Incorrect Guide to Science"
From: Newberry on 27 Feb 2010 13:56 On Feb 27, 10:00 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Newberry <newberr...(a)gmail.com> writes: > > People noticed long time ago (beginning with Strawson himself) that > > some sentences with empty subjects feel false and some of them just > > feel ..., well, empty. There is a lot of literature trying to explain > > the different intuitions. I recommed this highly interesting paper > >http://semanticsarchive.net/Archive/zAzNjllO/von.fintel.kof.pdf > > I do not know if von Fintel's theory is directly applicable tp your > > example. > > A quick glance at the paper suggests that it's about definite > descriptions and hence has nothing much to do with our conversation. First of all the paper is primarily about presuppositions. The subtitle is "Presuppositions and Truth-Value Intuitions." Strawson's example is "all John's children are asleep" when John has no children. You can also try a similar paper by Peter Lasersohn, "Existence Presuppositions and Background Knowledge." He discusses the sentence "All American kings lived in New York." > Even if I do accept that certain sentences involving definite > descriptions without referent are neither true nor false (and I'm not > saying that I accept this), it does not follow that sentences of the > form > > (Ax)(Px -> Qx) > > are meaningless unless (Ex)Px and (Ex)~Qx are true. > Clarification. The theory of presuppositions teaches that the above sentences are neither true nor false. That a proper subset of such sentences are meaningless is my addition. In fact Strawson's main problem was to explain why an apparently meaningful sentence "All Jonh's children are asleep" is neither true nor false. I would be happy to supply you my paper on this topic. Strawson also did NOT include the secong condition (Ex)~Qx.
From: Jesse F. Hughes on 27 Feb 2010 14:55
Newberry <newberryxy(a)gmail.com> writes: > On Feb 27, 10:00 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Even if I do accept that certain sentences involving definite >> descriptions without referent are neither true nor false (and I'm not >> saying that I accept this), it does not follow that sentences of the >> form >> >> (Ax)(Px -> Qx) >> >> are meaningless unless (Ex)Px and (Ex)~Qx are true. >> > Clarification. The theory of presuppositions teaches that the above > sentences are neither true nor false. That a proper subset of such > sentences are meaningless is my addition. In fact Strawson's main > problem was to explain why an apparently meaningful sentence "All > Jonh's children are asleep" is neither true nor false. I would be > happy to supply you my paper on this topic. > > Strawson also did NOT include the secong condition (Ex)~Qx. But (Ax)(Px -> Qx) is equivalent to (Ax)(~Qx -> ~Px) -- right? Let's call those formulas (1) and (2), resp. Suppose (Ex)Px and ~(Ex)~Qx, i.e., (Ax)Qx. Then (2) is (according to what you've told me) neither true nor false. I surely assumed that (1) is similarly neither true nor false under the same conditions. (I also thought that you'd said something similar previously.) -- Jesse F. Hughes "And I will dream that I live underground and people will say, 'How did you get there?' "'I just live there,' I will tell them." -- Quincy P. Hughes, Age 4 |