Re: The problematic connective



John Jones wrote:
herbzet wrote:
Mitch wrote:
John Jones wrote:

I was arguing that you can't argue for 'p and q' from 'p' and 'q', let
alone assign a truth value to it.

Right. We all got that from the beginning. And everyone else is saying
that that is old news, that p and q aren't arbitrary statements for
one to infer from 'p' and 'q' to get 'p and q'. both p and q can't
have modals, or different contexts for interpretation, or other
ambiguities.

I'm surprised you're picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?

... I thought I responded to this post but I can't see my post.

Yes, you responded to Mitch's post on Monday; I'm about 24 hours
behind you. Your post was news:gd0i50$jnk$1@xxxxxxxx .

Then I responded to Mitch's comment (just above) on Tuesday.

Er...yes, I will take a look at those others soon.

Stick with "and" till you beat it death, is my advice. You
can't get much more fundamental than that, and "not".

Me talking to Mitch:

It is precisely because 'and' is *less* problematic than 'or' or
'if then' that it is the place for a really fundamental critique
of (symbolic?) logic.

I think that 'and' in logic is a mysterious operation or power that
allows two truths to be reduced to one truth. How is that possible? It
breaks the link between truth and the object of truth.

I don't know what you mean by "the object of truth"; a wild guess
is that you might mean the object that bears or possesses truth.

It says that two
true objects are one true object. But what object is that?

A proposition.

About the only thing that is about as un-problematic as 'and'
in logic is 'not', which I assume JJ will get around to in due
course.

It is worth noting, John, that 'and' and 'not', when taken as
primitive, are a sufficient basis for defining all the other
propositional operators -- '(inclusive) or', '(exclusive) or',
'if then', 'if and only if', etc.

(A propositional operator takes propositions as arguments and
returns a proposition as a value.

It looks to me like an argument is a value.

This does not contradict my assertion in any way.

'P' is not an argument or a
value but a presentation of P. If I append or operate upon it with 'not'
as in not-P, or if/then, as in 'if P' then these are arguments and
values; in the sense that it must be either true or false. But 'P' per
se is not true/false or argument/value.

If P is something that can be true or false, what else could it be
but a proposition?

If P is a proposition, and 'P' is the presentation of P, I wouldn't
necessarily expect 'P' to be true or false, though I would expect
P to be true or false.

It's unclear from what you wrote just above whether you mean to
assert that by "not-P" whether you consider the propositional
operator 'not' as operating on P or 'P'.

Witt says (somewhere in
Tractatus) that they might be better regarded as taking truth-
values as arguments and returning a truth-value as a value
(I'll look it up).

I have to kind of retract this -- I mis-remembered it. Having discussed
an elementary proposition

4.21 The simplist kind of proposition, an elementary proposition,
assets the existence of a state of affairs.

4.22 An elementary proposition consists of names. It is a nexus,
a concantenation, of names.

4.23 It is only in the nexus of an elementary proposition that
a name occurs in a proposition.

he then says

5 A proposition is a truth-function of elementary propositions.
(An elementary proposition is a truth-function of itself.)

5.01 Elementary propositions are the truth-arguments of propositions.

and develops from there.

(Pears, McGuinness translation)

From an algebraic point of view, the [operators] of a Boolean algebra
could take as arguments and values propositions, truth-values, or
any one of many other sorts of things, e.g., switches (open or closed),
sets of points in a plane, etc.)

--
hz
.

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