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From: mps@duke.cs.duke.edu (Michael P. Smith)
Newsgroups: sci.philosophy.tech
Subject: Re: Logic and Coercion
Message-ID: <10001@duke.cs.duke.edu>
Date: Wed, 5-Aug-87 00:30:40 EDT
Article-I.D.: duke.10001
Posted: Wed Aug  5 00:30:40 1987
Date-Received: Fri, 7-Aug-87 02:51:14 EDT
References: <9962@duke.cs.duke.edu> <7836@mimsy.UUCP>
Reply-To: mps@duke.UUCP (Michael P. Smith)
Organization: Duke University, Durham NC
Lines: 53
Keywords: basilisk
Summary: Explanations and proofs differ in epistemic direction

In article <7836@mimsy.UUCP> flink@mimsy.UUCP (Paul V Torek) writes:
>What is the difference between proof and explanation supposed to be?
>Presumably, not in logical form:  most of what I would commonly call
>explanations would take the form of modus ponens; and a proof can
>certainly have this form.

Proofs and explanations differ in *epistemic direction*.  (The phrase
and the following explanation come from Michael Dummett's "The
Justification of Deduction," although I doubt that he would claim to
be the originator of either.) Consider a proof and an explanation both
having the logical form of *modus ponens*:

		Proof:			Explanation:
	1.		A -> B			A' -> B'
	2.		A			A'
		       ---		       ---
	3.		B			B'

In a proof, the direction of *inference* coincides with that of
*logical consequence*.  That is, 1 & 2 are epistemically warranted
independently of the proof, and 3 inherits some of that warrant through
the proof.  Put simply, we know 1 and 2 in advance, we don't know 3 in
advance, and we come to know 3 by proving it from 1 and 2.

In an explanation, there may be no inference (in the sense of fixation
of belief) at all.  But often there is, and the direction of the
inference runs *counter* to that of the logical consequence involved.
That is, 3 will be better known than either 1 or 2, and these
logical premises will be warranted (or have their epistemic weight
increased) through providing an explanation of the known fact 3.

A stereotypical, if not necessarily typical, case involves subsumption
of an individual case under a general rule:

	1.	Anyone holding an emerald survives the glance of a basilisk.
	2.	I am holding an emerald.
	3.	So I survive the glance of a basilisk.

Before my confrontation with the basilisk, I may run through this bit
of reasoning to assure myself of the truth of its logical conclusion.
But we can imagine also this syllogism occurring to me after a chance
meeting with the beast, when the conclusion is evident, as a way of
confirming either of the premises.

For Charles Peirce, there were three types of inference possible above.
I may *deduce* 3 from 1 & 2.  By *induction*, I derive 2 from 1 & 3.
Finally, *abduction* allows one to ascend to general principles like 1
from particulars like 2 & 3.

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Michael P. Smith	ARPA:  mps@duke.cs.duke.edu
	"Tu ne me chercherais pas si tu ne m'avais trouve."	Pascal
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