'When Are Relations Neither True Nor False? [Logic]

Prev: geometry precisely defining ellipsis and how infinity is in the midsection #427 Correcting Math
Next: Accounting for Governmental and Nonprofit Entities, 15th Edition Earl Wilson McGraw Hill Test bank is available at affordable prices. Email me at allsolutionmanuals11[at]gmail.com if you need to buy this. All emails will be answered ASAP.

From: Newberry on 20 Feb 2010 22:08

On Feb 20, 10:15 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
> Nam Nguyen wrote:
> > Newberry wrote:
> >> On Feb 20, 9:42 am, Frederick Williams <frederick.willia...(a)tesco.net>
> >> wrote:
> >>> Nam Nguyen wrote:
>
> >>>> Frederick Williams wrote:
> >>>>> Aatu Koskensilta wrote:
> >>>>>> As usually understood it makes no sense to say of a relation that
> >>>>>> it is
> >>>>>> or is not true.
> >>>>> It seems ok to me to take "such and such a relation is false" to mean
> >>>>> that no objects in the domain of discourse have the relation to one
> >>>>> another. For example "x is the mother of y" could be called false in
> >>>>> the domain {Aatu, Fred}. Ok, you might say "not satisfiable" but so
> >>>>> what?
> >>>> For example, given a language L(P1,P2) where P1, P2 are 1-ary symbols,
> >>>> let's consider the following T:
> >>>> A1: P1(x) <-> x=x
> >>>> A2: P2(x) <-> ~P1(x)
> >>>> 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..
> >>>> Apparently, "satisfiable" isn't even an issue here.
> >>> This is one of those threads that causes me to think "would that the
> >>> contributors could find something more interesting to discuss."
>
> >> I also thought that we should have rather discussed the substance. But
> >> given all this and concurring that the terminology is less important,
> >> is there perhaps a better way to express my intent rather than "when
> >> are relations neither true nor false" to avoid any potential confusion?
>
> > First I've already corrected this particular post of mine with:
>
> > > My mistake, let's break that into 2 T's: T1 (with A1) and T2 (with A2).
>
> > As for your "original" intention, I also already made a guess and
> > suggested:
>
> > > (1) When is a relation R such that a particular formula F would
> > > be neither true nor false in it?
>
> > I think there's a huge _substance_ we could have for furthering the
> > discussion.
> > That's to say, as you've alluded to, if we really care for the
> > substance, instead of the "peripherals".
>
> One of the substances we could have from the question (1) is the possibility
> of formally classifying formulas of a particular groups: arithmetically
> truth-unassigned-able formulas.

What do you mean by that? Do you mean defining a class of Goedel
numbers of sentences that do not have a truth value? It is probably
possible, but we would be jumping ahead of ourselevs. First we need to
define the semantics i.e. a plausible explanation of why some
sentences (including arithmetic setences) are true, some false and
some neither.

>
> Anyone cares to constructively contribute to the classification. Even if just
> to say that's impossible and explain why it is so.- Hide quoted text -
>
> - Show quoted text -

From: Aatu Koskensilta on 21 Feb 2010 04:46

Frederick Williams <frederick.williams2(a)tesco.net> writes:

> It seems ok to me to take "such and such a relation is false" to mean
> that no objects in the domain of discourse have the relation to one
> another.

We can of course introduce whatever terminology we wish. There was
nothing profound or even particularly interesting to my trivial
observation.

--
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 21 Feb 2010 05:04

Nam Nguyen <namducnguyen(a)shaw.ca> writes:

> Nam Nguyen wrote:
>
>> Alan Smaill wrote:
>>
>> First of all that's not what Aatu said. What he said:
>>
>> "Philosophical" is not a term of derision.
>
> I might add: he said this to me, _after_ the fact (i.e. after he had
> dismissed Calvin's short and only note). For the record, I didn't
> "see" his caveat about 'derision' then. Without further information I
> had no choice but thinking his dismissing was based on the word
> "philosophical", which is a bad term about reasoning, without any
> qualifying caveat.

Calvin didn't present any reasoning, but this notion that
"philosophical" is a "bad term about reasoning" is merely
bizarre. "Philosophical", even without any qualifications, isn't a term
of derision. It's a description, not an evaluation. There's absolutely
first-rate philosophy and philosophical reasoning, and there's
fifth-rate philosophy and philosophical reasoning.

As for Calvin's comment, I took it to be philosophical because as a
mathematical claim, in classical mathematics or intuitionistic
mathematics, it is simply false, and because such comments are usually
intended to express various philosophical ideas -- you yourself
mentioned musings about absolute undecidability. This comment, about
which we can't really make much anything without further elucidation
from Calvin, I also didn't dismiss; I merely noted that it has no
apparent relevance to Newberry's original post. It may well be relevant,
for all I know, depending on what exactly Calvin had in mind, but its
relevance simply is not apparent.

As for thread titles, the question of their relevance is not a
"technical" question. It's a matter of convention, interpretation, and
so on. OP has already explained what I had in mind.

As for rudeness, we may well stipulate that I'm the most rude news
debater ever to walk this earth. In this capacity, I put forth it that
you're a tad overly sensitive, and prone to read into simple and
straightforward comments, observations, words stuff that simply isn't
there. Whatever thought processes led you to your peculiar surmise about
my opinion about the title of G�del's paper from a comment about thread
titles in news I still can't fathom.

--
Aatu Koskensilta (aatu.koskensilta(a)uta.fi)

"Wovon man nicht sprechan kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

From: Daryl McCullough on 21 Feb 2010 08:26

Nam Nguyen says...
>
>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.

It's hard to tell in a textual medium. Try saying "A horse! A horse!
My kingdom for a horse!" out loud.

--
Daryl McCullough
Ithaca, NY

From: Alan Smaill on 21 Feb 2010 14:29

Nam Nguyen <namducnguyen(a)shaw.ca> writes:

> 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.

If you believe that, then presumably you think that mathematicians like
Brouwer or Poincare were ridiculous when they contested received
mathematical opinion on whether every mathematical statement must be
true or false; that's the sort of example presumably in
the background here.

> 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_.

Theer are two separate issues -- whether introducing philosophy
is in itself being dismissive, and whether your point was treated seriously
or not. It's only the first I was talking about.

When Aatu says that the mention of philosophy is not dismissive,
I see no reason to think he is lying to us. At least that
aspect you may have taken the wrong way.

--
Alan Smaill