Christopher Menzel wrote:
> On May 5, 2007, at 10:13 AM, Waclaw Kusnierczyk wrote:
>> ...Pat says that logic is a theory of truth (or Truth?).
>
> No, he says that (classical first-order) logic includes a component
> (namely, model theory) that includes a theory of truth (namely,
> Tarski's). (01)
Let it be. This does not change much. (02)
This theory of truth is actually quite mundane -- it is a
> surprisingly simple and straightforward definition of truth as it
> pertains to formal languages and their interpretations that seems to
> capture much of what we have in mind by word "true" in the ordinary
> sense. It tells us nothing whatever about big-T Truth, assuming the
> big-T there is supposed to signify Something Profound. (03)
It was not me who first talked using 'Absoluteness', 'Logic', 'Truth',
and other scary terms. Yes, I guess 'Something Profound' is an equally
good scary term. (04)
>
>> So logic is a theory of Logic, but it is not Logic.
>
> Huh? What is this big-L Logic whereof you speak? (05)
See above. (What is this big-SP Something Profound whereof you speak?) (06)
>
>> If something is logically incoherent, it still does not prove, in
>> any way or sense, that it is also inconsistent with Logic.
>
> How would we know if you aren't telling us what Logic is? (07)
I assumed this to be more or less obvious (if it can be obvious at all)
from preceding posts. For now, let's say Logic is the way the real
world is. (08)
>> Same response to Chris: that your logic (*the* logic, if you
>> prefer) forces you to conclude that god is devil, and that this is
>> inconsistent, this does not prove (otherwise than in that logic)
>> that being god and devil at the same time is incoherent. Perhaps
>> stating this in logic (with appropriate assumptions) leads to
>> inconsistence, but that's all.
>>
>> I am not hereby defending the view that there is god, or any other
>> compatible or contradictory view, for that matter. My point is
>> that logic is a theory,
>
> This is sounding ominously like the claim that evolution is (just) a
> theory. (09)
And it isn't? (010)
>> and thus it is, in principle, as good as any other theory, in that
>> it may well be incorrect.
>
> Well, not if it *is* correct. (011)
As with any other theory. (012)
> So what do you mean exactly? That a
> logical theory, qua theory, is falsifiable? (013)
Depending on what you mean by falsifiable. Falsifiable by whom -- us?
Falsifiable by those who believe in logic? In a recent post, it was
claimed that God's existence is logically incoherent. If it would
suddenly become apparent that there is God, would not logic be
falsified, then? (Well, at least one of the assumptions these 'proofs'
for God's nonexistence are based on.) (014)
> But how would you
> falsify, say, the law of noncontradiction? How would you do that?
> Wouldn't you have to provide an argument that *assumes* that
> noncontradiction is valid? Or do you find arguments of the form
> "P&~P, therefore Q" rationally persuasive grounds for believing Q? (015)
If you ask me how I would use logic to falsify logic, then you won't get
an answer. What you seem to be saying is that there is no way to, e.g.,
falsify the law of noncontradiction. My point was that that we cannot
imagine something (e.g., a proof that the law of noncontradiction is
false) is not a proof that it does not exist. And I find it just as
relevant here. I have no such proof that you as me for. If I had, it
would be non-logical, and you would not consider it a proof, am I right? (016)
>
> There are, of course, logical systems in which certain classical
> principles do not hold across the board -- intuitionists, for
> example, reject excluded middle and paraconsistent logicians reject
> the general validity noncontradiction to accommodate paradox (though
> they do *not* accept the validity of the argument form above). So
> yes, there can be philosophical reasons for rejecting the general
> validity of certain classical principles. But these reasons are
> based upon a priori, philosophical views about the nature of the
> basic concepts of logic -- intutionists, notably, argue from a very
> distinctive (non-realist) philosophical position about truth and the
> nature of mathematics. But to think that logic, no matter which you
> prefer, is falsifiable in the way that, say, Newtonian Mechanics is,
> is simply a mistake. In logic we start with principles whose
> validity we accept a priori and we build our systems to reflect them
> after the fact. We do not derive them empirically by observation and
> test them with laboratory experiments. (017)
You take the a priori principles as valid on faith. You believe in
them. You have to believe in something; but this is faith, akin to
faith in God. (018)
>> That it it is unimaginable for us that there could be world in
>> which logic as we know it would not be an appropriate theory of
>> truth is closer to blindness than to omniscience.
>
> Well, *that* is certainly nothing more than an article of faith on
> your part, since you haven't provided the least reason to think there
> is actually something there to be seen. But if you want to believe
> there are worlds where every contradiction is true and people can
> truly believe six impossible things before breakfast, far be it from
> me to try to talk you out of it. :-) (019)
Chris, accepting that there *could* be such unimaginable (to us humans)
worlds is not the same as actually believing that there are such worlds.
If you forced me, I'd admit that I do not believe in God, and that I do
not believe in worlds such as those you mention, and that I do not want
to believe in them (unless someone convinces me that they are there).
But I take a sort of open world assumption here: that I do not believe
in all those things does not force me to believe in there not being such
things. I remain agnostic, and from this point of view, Ingvar's
argument that logical incoherence of God's existence [reformulate to
avoid unwanted ontological commitments] proves God's nonexistence is
simply unconvincing, and that's what I have been trying to say; *not*
that God exists and that logic is wrong. (020)
I believe that trying to talk someone deeply believing in logic out of
his faith has the same chance of success as trying to talk someone
deeply believing in God out of his faith. If one believes in God and
therefore takes logic as unacceptable (since it proves God does not
exist), then you can't successfully use logic to convince him he is
wrong. If someone believes in logic and therefore takes (putative)
God's existence as logically incoherent, then you can't successfully use
the existence of God to convince him that he is wrong. (021)
Let me stop here. (022)
vQ (023)
>
> -chris
>
>
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--
Wacek Kusnierczyk (025)
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Department of Information and Computer Science (IDI)
Norwegian University of Science and Technology (NTNU)
Sem Saelandsv. 7-9
7027 Trondheim
Norway (026)
tel. 0047 73591875
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