'When Are Relations Neither True Nor False?
in [Math]
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From: Nam Nguyen on 20 Feb 2010 13:47 Frederick Williams wrote: > Nam Nguyen wrote: >> Frederick Williams wrote: >>> Nam Nguyen wrote: >>>> > My mistake, let's break that into 2 T's: T1 (with A1) and T2 (with A2). >>> But you now need to correct your: >>> >>> It's obvious in any model of T, the relation in which A1 is true is >>> a true relation, and the one in which A2 is true is a false relation. >>> >> Can you elaborate as to what is there to correct, after breaking T into >> T1 and T2? > > The thing that I quoted mentions T but you longer have T, you have T1 > and T2. > OK. So here it its. For T1, just replacing in my statement above "T" by "T1" and just drop all references about "A2" and "false" relation: It's obvious in any model of T1, the relation in which A1 is true is a true relation. For T2, do the same but treat "P2" as a _defined symbol_ of a language not containing "P2". The _definition_ of P2 now is: P2(x) <-> ~(x=x) For any consistent T2 (in FOL=), {} is a false relation for P2. A bit of word shuffling, but its' still within the definitions of true and false relations previously given in the thread.
From: Alan Smaill on 20 Feb 2010 13:58 Nam Nguyen <namducnguyen(a)shaw.ca> writes: > Alan Smaill wrote: > > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > > > >> Aatu Koskensilta wrote: > > > >>> "Philosophical" is not a term of derision. Musings about absolute > >>> undecidability are most assuredly philosophical. It seems you think I > >>> have said something about the validity of such musings. Why? > >>> > >> You summarily dismissed Calvin's appropriately mentioning of CH in this > >> thread topic, on the ground that it's philosophical, which I don't see > >> as justified at all. > > As Aatu just said, saying that something is philosophical is *not* > > dismissing it, summarily or otherwise. Why do you think it is? > > First of all that's not what Aatu said. What he said: > > "Philosophical" is not a term of derision. Correct. However, in the post you are replying to, you said: "You summarily dismissed Calvin's appropriately mentioning of CH in this thread topic, on the ground that it's philosophical, which I don't see as justified at all." My objection is that *you* claim that Aatu dismissed your comment on the grounds that it's philosophical. > I'm the one who said he "summarily dismissed Calvin's appropriately > mentioning of CH". Why stop the quote there? > And I said that based on a very short conversation > between him and Calvin. Iirc, Calvin had *only 1 short post* in this > thread: > > >> The 'continuum hypothesis' is neither true nor false, for example. > > to which Aatu had a terse response: > > >> This piece of philosophical reflection -- which stands in need of some > >> argument -- has no apparent relevance to Newberry's original post. > > If one responds for the very first time with a short _commandment-like_ > telling people their writing "has no apparent relevance to ..." _without_ > a courtesy of explaining to the writer then that's very dismissing > to me for no good reason (not to mention that it's rather rude). You may regard him as being rude. You may also be over-reacting, by taking the comment about philosophy as negative in itself. -- Alan Smaill
From: OP on 20 Feb 2010 15:22 Newberry wrote: > On Feb 19, 9:15 pm, OP <facetious_nickn...(a)hotmail.com> wrote: >> Newberry wrote: >> > On Feb 19, 7:30 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: >> >> >> Why then go on about such matters? >> >> > I do not have a clue. >> >> Well it's settled then. > > What gave you that peculiar idea? LOL
From: Nam Nguyen on 20 Feb 2010 18:28 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. 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_. And that, isn't only 1 incident in the thread. In arguing, examining what is or is not technically relevant to the thread discussions, _all of sudden_ AK again issued a _vague generalization_: "Thread titles are irrelevant." which I was surprised, knowing that millions of books, presentations, proceedings, would have titles being relevant to what was written, presented,... And what was AK's reaction to my surprise? In a short sentence: he found my "thought processes utterly unfathomable"! Again, short and commandment-like discrediting an opponent without bothering to give a slightest hint as to why! All this he wouldn't have time to clarify his discrediting people's ideas, or to make the conversations move forward constructively. Yet he found time in the "constructive" 'Sobbity-sob' "fun". I'm sorry Alan, I don't have any reason to change my mind (at this moment), after more than 2 such incidents in the same threads.
From: OP on 20 Feb 2010 19:23
Nam Nguyen wrote: [snip] > > And that, isn't only 1 incident in the thread. In arguing, examining what > is or is not technically relevant to the thread discussions, _all of sudden_ > AK again issued a _vague generalization_: > > "Thread titles are irrelevant." > > which I was surprised, knowing that millions of books, presentations, > proceedings, would have titles being relevant to what was written, > presented,... And what was AK's reaction to my surprise? In a short > sentence: he found my "thought processes utterly unfathomable"! > Again, short and commandment-like discrediting an opponent without > bothering to give a slightest hint as to why! [snip] I don't pretend to speak for the guy but I think it's very likely that when he said "thread titles are irrelevant" or words to that effect that he meant quite literally "thread titles," i.e., Usenet thread titles. Not book titles, not paper titles, etc., only Usenet thread titles. It's at least a fairly common notion on Usenet that because different Usenet readers display thread titles (i.e. "subject lines") in different ways, or not at all, they should not contain information that's vital to understanding the message they're announcing. People might argue about the merits of this claim, but I don't think there's much real ambiguity about the limited scope of what he was trying to convey. |