Re: re: Tautology

[Carrol Cox]

Rod Hay wrote:

> After thinking better of my sarcastic tone to Carrol's message. Let me
> explain.

:-)

>
> A tautology is a statement that is true by definition. That is, it is
> always true.
>
> A = A is a tautology.

Yes, I'm aware of that. The example often used in writing classes etc
is "All black cats are cats." The trouble with A = A as an example is
that it doesn't bring out how tautologies may be hidden in apparently
postivie propositions. Perhaps you have to have taught freshman
composition to appreciate how easy that is. Many decades ago I
asked a freshman class to write a paper on "thoughtfulness." Almost
without exception all the papers boiled down to A = A. And the
trouble comes in part because such hidden tautologies (1) *seem*
true because they *are* true and (2) seem profound because the
source of the truth is hidden.

>
>
> A = B is not a tautology. That is, it might be false.
>
> Similarly all true statements are not tautologies. I.e., A = B might be
> true.

Yes.

> If all statements were tautologies, math and logic would be very easy.

How do you prove that a+b=b+a. I used to know but can't remember. Is
it a postulate or a theorem.

>
> Anything you write down would be true. No need to prove anything.

I'm many years away from this, but if I remember correctly some
mathematical expressions (in trig I think) were called "Identities" but
still had to be proved.

Also, I know "truisms" and "tautologies" are different things, though
the words are often used interchangeably in conversation. Truisms,
for one thing, can be false! That is, they are "true" only within the
limits of a given ideology (or world of common sense). But they
are apt to function like the hidden tautologies I speak of.

All social systems decay.
Capitalism is a social system.
Capitalism decays.

Doug did not say, "Capitalism does not decay [won't collapse]" He said
"Where have I heard that before?" I'll leave it to someone else to untangle

the exact logic implicit there (it's rather complex), but I think that
*some*
at least of what I.A. Richards would have called its emotive force came
from the clash of two concealed "tautologies": "All things decay" and
"Communists endlessly repeat slogans" or something like that. Both
(hidden) propositions *act* like tautologies, though I grant that a logic
text would not exactly support me here.

Carrol