[Wittrs] [quickphilosophy] Re: 1.21 Continued

  • From: wittrsl@xxxxxxxxxxxxx
  • To: quickphilosophy@xxxxxxxxxxxxxxx
  • Date: Thu, 22 Jul 2010 16:18:20 -0000

1.21 Each can be the case or not be the case and all else stay the same.

Hacking on with my brush cutter....

19. One argument for the claim that elementary props must be mutually
independent is, roughly, that the ability to reason requires the
validity of propositional (in W's view, truth-functional) logic.  But
truth-functional logic requires that ll the tables be completable, which
they won't be if the ps and qs are not independent of each other.  E.g.,

[(p > q) . p] > q

means simply that for each value of p and q, the whole statement will be
true.  To wit:

p  |  q  |  p > q  | (p > q) . p  | [(p > q) . p] > q

T             T                 T                               T
T
T             F                 F                               F
T
F             T                 T                               F
T
F             F                 T                               F
T

But if p and q aren't independent some of the rows won't really make
sense or should be left blank.  Thus, if p were "x is red" and q were "x
is colored" there couldn't really be any row where p is T and q is F. 
The theory is that such a result would make propositional logic
impossible.  Ansc. puts it roughly this way: Either the theory of
truth-functions has no application, or there is a class of mutually
independent propositions.  But we apply propositional logic (i.e.
reason) constantly.  Thus, this class of independent, atomic
propositions must underlay nearly everything.  I note that W makes a
similar argument in "Some Remarks on Logical Form."

I'm not sure whether Ansc. realizes that that argument is fallacious,
but it seems so to me.  All truth functional reasoning requires is that
all the props in the table be independent of each other, not that each
be independent of ALL other props, whether in the table or not.

Ansc. also says that with atomic props brackets are never needed to
resolve ambiguities.  "The present king of France is bald" can be false
in 2 ways and must be clarified by the means of moving braces around. 
But no matter where you put braces "aRb" means the same thing if "a" and
"b" are simple names and "R" is similarly unanalyzable.  I think,
though, that the theory that "a is red" must be meaningless if "a" does
not refer is dependent on some sort of Russellian theory acquaintance,
which allows epistemological or psychological matters to seep back into
play.

I do think there's a sense in which determinacy requires
unanalyzability.  Take "Jones is a big shot."  Suppose it could be
analyzed into one of the following (where the little letters are taken
to be simple names):-

a is well known for being p
b is well known for being p
c is well known for being p
a is well known for being q
b is well known for being q
c is well known for being q

If that's right, it can hardly be denied that the sentence "Jones is a
big shot" is indeterminate, and this helps us understand why W claimed
that determinacy requires simples.  Consider again, however, all the
properties that Ansc. claimed atomic props must have:

(i) They're mutually independent; (ii) They're positive; (iii) There's
only one way for them to be true or false; (iv) There is in them no
distinction between an internal and an external negation [e.g., "The
present king of France is bald can be false in two ways."]; and (v) 
They
are concatenations of names (simple signs).  And,  presumably, all of
these features must follow from the very fact  that we can understand
language.

The fact that "a is all red at t" is inconsistent with "a is all green
at t" doesn't entail that either prop is indeterminate in the above
sense.

Also, the assertion regarding any prop that "there is only one way for
it to be false" seems to me to need further explanation.  "A is red and
square" may be said to have two ways of being false, I suppose, and, as
indicated above, "aRb" will have only one way of being false if some
sort of doctrine of acquaintance requires that it can only be understood
given certain psychological truths.  W says there are many ways in which
"the cat is on the mat" may be true/false.  But what about "A is bored"?
It seems to me that these sorts of complications are almost bound to
eventually drive one into some sort of "meaning is use" theory....

Walto





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