# [quickphilosophy] Re: 1.21 Continued

• From: wittrsl@xxxxxxxxxxxxx
• To: wittrsl@xxxxxxxxxxxxx
• Date: Thu, 22 Jul 2010 09:32:33 -0700 (PDT)

```
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

```