huge <
hu...@operamail.com> writes:
> It is outside the range of the things the variables can refer to.
> It is outsede the universe of discourse of sentential logic.
>
> The second sentence is simply a factual restatement of the first.
If you say so. This is not standard terminology. You're of course free
to introduce any terminology you want, but can't reasonably expect
others to be familiar with your idiosyncratic usage.
It makes perfect sense to say the sentential variables -- p, q, r, s
and so on, as we meet in symbolic formulas such as p --> q, (p & ~q),
etc. -- have an intended range. They are to stand for declarative
sentences, so that questions, interjections, and such like, are ruled
out. (This is not put in terms of any "universe of discourse" anywhere
in the logical literature as far as I'm aware, but that's really neither
here nor there.)
Now, let's take a look at the use you wish to put this (perfectly
standard) observation:
It is considered a mistake in sentential logic to use quantificational
statements as premises in certain cases:
Holmes, if anyone can trap Moriarty.
Holmes cannot.
_________________________
No one can
...should not be attempted to be symbolized in sentential logic.
From the point of view of sentential logic this is an instance of the
argument (form):
p
q
--
r
obtained by letting p = "Holmes, if anyone can trap Moriarty", q =
"Holmes cannot" and r = "No one can". This argument (form) is not valid,
since there are instances -- obtained by substituting declarative
sentences for p, q and r -- whose premises are true but the conclusion
false. So your Holmesian argument is not valid by virtue of the truth
functional structure of the premises and the conclusion, but on other
grounds. And indeed, when we take into account the logical features of
such expressions as "no one", "anyone", and so on, bringing to bear the
machinery of quantificational logic, we find it is in virtue of these
that the argument is valid. This doesn't mean there's anything wrong in
formalizing the argument in sentential logic, which we might want to do
for instance to demonstrate the validity of this piece of reasoning is
not owing solely to the logical properties of sentential connectives
involved.
This has however nothing to do with the range of the sentential
variables, "the universe of discourse of sentential logic" in your
parlance, as we easily see by considering for example the following
argument
If Holmes is the greatest detective ever, he can trap Moriarty if
anyone can.
If Holmes can trap Moriarty if anyone can, it's not the case that no
one can.
Holmes is the greatest detective ever.
-----------------------------------------
It's not the case that no one can trap Moriarty.
which is valid, purely by virtue of the truth functional structure of
the sentences involved, an instance of
s --> p
p --> ~r
s
-----
~r.
You can't very well insist that some sentence one moment can't be the
value of a sentential variable and the next moment can.