Re: The problematic connective

On Oct 14, 5:16 pm, John Jones <jonescard...@xxxxxxx> wrote:
Mitch wrote:
On Oct 13, 6:30 pm, John Jones <jonescard...@xxxxxxx> wrote:
Mitch wrote:
On Oct 12, 5:37 pm, John Jones <jonescard...@xxxxxxx> wrote:
Mitch wrote:
I'm surprised you're picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
I just picked on the first one I saw. The others will follow. But people
here have argued for 'p and q' from p and q. As does the texts I've
looked at.

Yes. They're all considering the things that could go in for p and q
to be of a certain kind.

I argued that the object or agency 'p and q' has NOT been
properly identified to assign a truth value to it, nor is it explained
how 'p and q' can be constructed from two other objects we know about,
p, and q.

If you restrict p and q appropriately, then 'p and q' follow from 'p
and 'q' pretty incontrovertibly. I fit makes you feel better, just
define 'p and q' the least possible inference from 'p' and 'q'.

The least possible inference is that 'p and q' is 'p', and 'q' but
written down in another way. That cannot be of any logical significance.

I think you've made a case by example that it is not entirely obvious,
if one is skeptical enough, that from 'p' and 'q' one should be able
to infer 'p and q'.


The other least possible inference is that 'p and q' is an object (or
statement etc)

or concept.

with a truth value; just as 'p' and 'q' are also objects
with truth values. But what sort of object is 'p and q'?
That's my point. 'P and q' is not identified as anything, yet it is
identified as an object. How? It is merely assumed that if there are two
truths then they, and their objects, can be 'conjunctioned'. This 'truth
conjunctioning' is not easily understood, in fact, I would say that it
is incomprehensible.

There's a difference between skepticism and not even trying.


If maths is made unambiguous by eliminating essential distinctions then
I wonder how far we can trust the project of disambiguation.

Uh...I don't know. Here again I don't know were you came up with
'eliminating essential distinctions'. I do think it practical to
remove ambiguities (it reduces the number of tracks of discussion).
Are you reading 'ambiguity' as an 'essential distinction'? (I don't)
What I think I mean by ambiguity is multiple interpretations.

I don't want to identify the task of removing ambiguity with the task of
of eliminating differences.

OK. Fine. But you're the one who brought up elimination of
differences, and I'm just trying to figure out what that really means
for you.

For example,
does 'not P' identify P-like objects or the absence of P and P-like objects?

Good point. Depends on the context. (if you're curious, your specific
case could be followed). But in each context, the mathematical 'not P'
is pretty well understood,

It is syntactically presented, but the translation of that syntax poses
problems.

Sure. Negation is not obvious.


Not-P can refer to the complete (necessary) absence of the
framework of P and P-like objects,

Oh. hm. maybe. that's one I've never heard before.


or refer to the absence of only P, or
refer to the presence of another object in the framework of P.

Usually, it's as simple as 'not p' means true if 'p' is false, and
vice versa. That is, in the cases where 'p' has a truth value, 'not p'
has the opposite truth value.

You might be confusing it with set-complement ('absence of only P'?),
which has a lot of algebraic similarities with logical not, and there
are interpretations where each can be implemented with the other.

As to 'framework', I think you're laying a lot of your own meaning
onto 'not'...er....or maybe you're really taking about one of the many
varieties of the English 'not' (and narrowmindedly, all I'm talking
about is the logical, stipulated version).

....
and maps well to ideas in our heads. A
particular piece of syntax may not mean much to you the individual,
but that doesn't mean it doesn't mean something coherent to others.

Yes, but I would have thought that the assumptions we make in everyday
life don't make an appearance in logic or maths.

I wouldn't go that far. I think there's -some- rationality in everyday
life.

In everyday life we are
immersed in contexts and frameworks and so are rarely at a loss to know
what it is we are talking about and their possibilities.

I wouldn't go that far here either. I think we're often at a loss (or
rather, many every day contexts are entertaining myths) but we get by
anyway.

But in maths and logic we are taken out of these contexts.

How about just a different context?

Mitch
.

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