Newsgroups: bit.listserv.politics
Date:         Fri, 24 Jul 1992 16:27:50 EDT
From:         Jamie <PL436000@BROWNVM.BITNET>
Subject:      Logical aside

Oh no. Now Gary's babbling, too.

Ahem.

> The key assumption here is that all statements can have either
> two values, true or false.

All statements CAN have either of two values, true or false. (I added
an "of" there, I hope you don't mind. Its wave packet just collapsed.)

> Boolean logic is certainly useful in computers, but is
> rather limited in facing questions of a more complex causal
> structure, such as political and social questions

Two valued logic, you mean. Boole doesn't have much to do with
the issue. There are many boolean logics.

What Gary is really concerned with is what's called "bivalence."
In certain contexts, it can be helpful and intelligible to say
that some statement is neither true nor false, that in effect
the function that assigns truth values to sentences is undefined
at some argument. SOME people think that might be related to
"quantum logic." I doubt it, myself.


From:         Travis Kidd <TKIDD@CLEMSON.BITNET>

>> There is no geometrical axiom that says this statement is
>> true. Axioms of geometry are about parallel lines, and so
>> forth.

>Axiom, law, rule, whatever....

No, the emphasis was on "geometrical."

[logic czar]
> If A is false, then the conditional CAN be proved true. Here is
> a proof:
>
> (1)   Not A.                             (By hypothesis)
> (2)   If not A, then (if A then B)       (Logically valid schema)
> (3)   If A, then B.                      (By modus ponens, from lines
>                                                       (1) and (2) )

[travis]
>Hmmmm....I don't quite follow #2.  It seems to me that you are usng a
>circular argument.  Show me that if not A, then (if A then B)...

It's what's called a "logically valid sentence."
That means that it comes out to be true no matter what truth
values you assign to its constituent parts (namely, the atomic
sentences represented by letters). This is essentially what
Evelyn was pointing out, though as you say, she used more
words.
In standard proof procedure, one is permitted to write
any logically valid sentence on any line. I availed myself.

A "circular argument" is one in which the conclusion sought is
used as a premise. I didn't do that.

>If not A, then there is no way to test if A then B,

Travis still misses the point.
"If A then B" is true whenever A is not true. So if you have
a test for A, and you find it is false, then you know that
"If A then B" is true.

For example, suppose I say,

"If Travis ever posts about logic again, then I will kill him."

Then Travis never does post about logic again. (We can always
fantasize.) So, what I said was correct.

>so there is no way
>to prove or disprove if A then B.  If it cannot be proven false, it is
>true.

This is the part that mystefies me the most.
Even if you were correct in what you said before, namely,
    if A is false then there is no way to test "If A then B,"
how would it follow that if something cannot be proven false,
it is true?

[logic czar]
>  "This statement can be proven false."
> There you go. A statement which cannot be proven false, yet
> it's false.

[travis]
>Surely you know that a logical statement never refers to itself...

That's silly, of course it can.

"Every English sentence contains a verb."

That is a sentence which refers to itself. And I bet EVERYONE
reading it knows exactly what it means. Is it illogical?

[travis]
>Statement:  This sentence has five words. is true.
>Converse: This sentence doesn't have five words. is also true.
>Logic would go out the window.

Those statements are not converses of each other.

Believe me, sentences can refer to themselves. There are lots
of books published about self-referential sentences (citations
available upon request--specify level of sophistication desired).
I can give you plenty of examples. Godel's proof of his First
Incompleteness Theorem shows how to MAKE sentences refer to themselves,
as long as the language contains vocabulary of arithmetic.

I know I should let this drop; it's just that I hate to
see the last word in public on the subject be misleading
to our poor, gullible readers.

Jamie the logic czar