Saturday, May 19, 2012

Possible worlds and possible worlds

I have trouble seeing philosophy as an intellectual discipline. The gist of my thinking is that 'philosophy' is a word which has changed its meaning quite dramatically over the centuries as various sciences have split off from it and I'm not sure that it has much meaning left.

If one has a theological view of the world, philosophy's position will not be threatened as it can resume (or continue) its traditional role as a secular complement to theological discourse. But if one denies that there are truths we can intuit or know by non-empirical, non-deductive means, then, arguably, there is no place for a non-scientific intellectual discipline (unless it be seen as an art form or as a kind of game).

Of course, the study of formal deductive systems, logical or mathematical, is non-empirical, but it is continuous with science.

All that is left of philosophy for someone who rejects claims to substantive intuitive knowledge of a religious or moral kind are reflections on the various intellectual disciplines (physical, social and historical sciences, mathematics, logic, etc.). Such meta-thinking is best carried out (I would presume) by the practitioners of the various intellectual disciplines rather than by outsiders (whether or not they are designated as 'philosophers').

I do recognize, however, that much pure and applied work in certain disciplines (logic, mathematics, psychology and linguistics come to mind) draws strongly on philosophical traditions of thought, and raises issues which previously have been addressed by philosophers. An example of such work is the attempt (drawing on theoretical work in logic and mathematics as well as linguistics) to model the processes of natural language.

Computational linguistics clearly has great practical and commercial importance at the moment, but it can also be seen as a project the relative success [or failure!] of which has implications for the way we see human language – and ourselves.

My reading of the current state of play is that the formal approaches which followed in the wake of Chomsky's early attempts to give an explicit analysis of the syntax of ordinary language have not delivered as expected, just as early work in the field of artificial intelligence produced very disappointing results. Both of these research projects underestimated the importance of contextual factors and real world knowledge which is inevitably a part of intelligent human functioning and communication. Formal systems need in some way to be integrated into this real world context, but, even if they are, it is still possible that many important aspects of language and communication will remain out of reach. I am thinking in particular of aspects of language use which depend on social awareness, a sense of the sorts of things that people with autism spectrum disorders have trouble dealing with, including subtleties of tone and style.

There is a huge body of theoretical work in the syntax and semantics of natural language which shows, if nothing else, that there are countless ways of conceptualizing and formalizing (at least aspects of) natural language. In the light of this profusion, the key question – it seems to me – is not which theoretical approaches are true (whatever that might mean) but which are useful.*

We may want to postulate possible worlds and use set theory to model the semantics of natural language, including complex noun phrases and verb tenses and auxiliaries. But sets and 'possible worlds' are only one way (albeit a possibly enlightening one) of representing the way, for example, words like 'must' or 'could' or 'should' work. No claim need be made that such possible worlds exist. They are merely useful fictions.

Physicists, of course, also talk about other possible worlds, parallel universes and so on, but they are making ontological claims. Their concern is primarily with how the world (or the multiverse) is rather than with formal systems, though they use formal systems to model the operations of nature (as linguists may use formal systems to model the operations of natural language).

But the possible worlds of logicians and linguists are – notwithstanding some outlandish claims by certain logicians – merely formal constructs, to be judged entirely by their usefulness. The other worlds of the physicist may well prove in fact to be 'out there' – to exist in the normal sense of the word, though they may be inaccessible to us.

I am aware that the question of what existence consists in is a traditional philosophical one, but is it a serious or potentially productive question? I think not. Most of the confusions can be resolved simply by accepting that we use words like 'exist' in various ways.

The one area which does seem to raise important issues is mathematics. Just as there are possible worlds and possible worlds (the 'worlds' of the logician and the worlds of the physicist), so there are formal systems and formal systems, and, as we move from, say, the first-order predicate calculus to formal systems which can encompass arithmetic we cross a kind of threshold. Mathematics needs to be clearly distinguished from logic. But this is a topic for another time.

* This is not to say that the exercise of trying to create formal representations of natural languages may not reveal interesting things about natural language and provide new, more concise, more explanatory ways of understanding aspects of the grammar of those languages than traditional grammars provided. But, although such rarefied goals are not pointless, nor are they the sorts of goals for which society is likely to provide support. Traditional grammarians were, after all, essentially pedagogues and their grammars were pedagogical aids.