From: "Tobin Nellhaus" <nellhaus-AT-gwi.net>
Subject: BHA: Re: logic and tautology
Date: Thu, 8 May 1997 21:24:17 -0400


Doug, you may be right that applying the concept of closure to logic, maths
etc is a category mistake.  But I think it's at least fair to say that the
latter have something strongly *analogous* to closure.  For example, you
write that "In a closed causal system a finite number of generative
mechanisms operate in isolation without outside interference."  Well, the
syllogism, inference from an if-then clause, and similar logical structures
do operate without external interventions (the structure of the syllogism
isn't, say, valid every day but Thursdays, or everywhere except the big
shopping mall in Edmonton), and generally one can't arbitrarily introduce new
logical procedures except on the basis of (e.g., as proved by) previous ones.

> 	What would be the causal generative mechanisms operating in logic,
> mathematics, or language?

If a conclusion is the product of an analysis, might one not say that one's
premises and logical operations "caused" the conclusions?  (Causation is,
after all, a process of production, even if of something so basic as motion
toward the ground.)  I am not saying that "language speaks us" (although to a
degree that's true): my point is that we frequently find that someone's
assumptions--say, of the absence of ontological depth--forces them into
particular analytical positions.  But it's not the assumption itself that
accomplishes this, but the exercise of logic upon them.  Thus a scientist may
believe in God, but if she doesn't follow up the implications of that for her
science (or for that matter, any other practice), what of it?

We need also to remember that reasons and meanings are causes, hence language
(whether as formal logic, poetry, expletives, or whathaveyou) has causal
mechanisms.  If that's so, then it should indeed be proper to speak of the
possibility of closure in logic, math, and language, since these *are* causal
systems.

---
Tobin Nellhaus
nellhaus-AT-gwi.net
"Faith requires us to be materialists without flinching": C.S. Peirce



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