Fw: ' possible' reply to Bruno Marchal

From: Lennart Nilsson <leonard.nilsson.domain.name.hidden>
Date: Fri, 23 Aug 2002 13:26:53 +0200

----- Original Message -----
From: terrysavage
To: avoid-l.domain.name.hidden
Sent: Tuesday, August 20, 2002 8:17 PM
Subject: ' possible' reply to Bruno Marchal


In an earlier note, (Re:Impossibilities,08/02/2002, 9:26) I made some dismissive comments about the terms 'possibility' and 'necessity'. For reasons I don't quite understand, these were forwarded to Bruno Marchal. Bruno, in turn, responded with views of his own, (via, Lennart Nilsson, Fw:Am I a Token or a Type, 08/06/2002, 8:07) and suggested (politely) that I was behind the times in the study of Modal Logic. He was right.

I then began a small effort to examine more recent work, having dismissed the whole topic in the middle of the last century (boy, that sounds odd). I read papers by Jennifer Davoren, John McCarthy, one of Bruno's papers available on the web,descriptions (and critiques) of Kripke's work, and a summary of the ideas of David Lewis.This is, by no means, an exhaustive study, but I think the comments below will show that it was sufficient for my purposes.

First, we need to distinguish between the uses of 'possibility' and 'necessity' within the propositional (sentential) calculus (PC), and then within quantification theory (QT). Within PC we also have to note the difference between the purely syntactic formulas (without interpretation) and those same formulas imbedded in a semantic metalanguage. Taken solely syntactially, introducing the Modal operators produces an extension to PC, the motivation for which is obscure. If, instead of calling the modal symbols (diamond and box) 'possibility' and 'necessity', we called them 'blark' and 'blog', nobody would take the excersize seriously, except to note that one can add arbitrary connectives (or functions) to one formalism and produce an extended one. Calling these arbitrary symbols 'necessity' and 'possibility' seems to me to be a ruse to sneak obscure philosophical concepts into a simple excersize for rewriting marks on paper.

A semantics for this excersize in rewriting can be introduced (a la Kripke) and undoubtedly generate some interesting (and perhaps) important results. None of these results, however, shed any light on the meanings of 'necessity' or 'possibility'. Moreover, the semantics has the odd characteristic of blurring what ought to be denotation rules for assigning references to the terms in the formalism. In the usual case one would have something of the sort, 'dog' denotes, severally, a bunch of furry quadrapeds. In the Kripke semantics, the only referents are the relations and classes of the formalism itself.

If we try to extend Modal Logic into QT, serious difficulties show up immediately. A striaghtforward interpretation results in the failure of Leibniz's Law of Identity. The Kripke solution for this is to postulate a model which ranges over multiple *possible* worlds. David Lewis, taking this to an extreme, maintains that these possible worlds somehow exist in parallel with our own world. I am reminded of Quine's despair at this kind of double-talk, which led him to give away the term 'exist'. It doesn't help me to understand the expression 'For some x, it's possible that Fx', by referring me to a set of possible worlds. The best advice re:Modal QT, comes from Jennifer Davoren 'One can also study predicate modal (or temporal) logics, extending predicate or first-order logics, but unless one has particularly good reasons, my advice is don't go there.' Lecture notes, ANU Summer School 2000, 'Non-classical Logic...'.

John McCarthy has attacked the problem in another way, summarized by the title of one of his short notes: 'Modality, SI!, Modal logic, NO!'. In this paper, and others, McCarthy attempts to extend ordinary logic by the addition of non-logical predicates, 'believe', know', 'want', 'intend', etc. These fall in the area I have previously called 'pragmatics' (filling out the tripartite study of language (syntax and semantics being, of course, the other two)). This approach avoids the objections to 'necessity' and 'possiblity' for two reasons. First, these pragmatic predicates are, in my view, less obscure than the modal ones and, second, they make explicit the fact that we are dealing with the users of the language and not some never-never-land where you don't refer to real stuff.

One final comment on Bruno's remarks. He says, ...when terms are confused and ambiguous, it is a motivation for axiomatizing them....If not, *new* sciences just cannot appear!' I have two responses:

          1. I have no interest in *new* sciences; I will leave that to Wolfram.
              We have enough trouble with the sciences we already have.

          2. There is a better alternative for terms that are confused and
              ambiguous - just throw them away.

terry savage
Received on Fri Aug 23 2002 - 05:00:22 PDT