Saturday, June 30, 2012

Semantics of indicative and counterfactual conditionals

To: Mark S.
From: Geoffrey Klempner
Subject: Semantics of indicative and counterfactual conditionals
Date: 27 November 2007 12:51

Dear Mark,

Thank you for your email of 17 November, with your University of London Logic essay in response to the question, 'Should we treat indicative and counterfactual conditionals differently? Justify your answer.'

This is a model answer. I have no doubt that if you were able to reproduce something like this in an exam you would get a first class mark.

Firstly, this is a horrible question. You are being tempted to offer (and defend) theories of indicative and counterfactual conditionals, which would take you way beyond the scope of the question. You have managed to avoid this, by sticking to the logic of the question:

1. If indicative conditionals are truth functional then indicative and counterfactual conditionals should be treated differently.

2. If indicative conditionals are not truth functional, then indicative and counterfactual conditionals should be treated in the same way only if there is a unifying theory that explains both.

3. Indicative conditionals are not truth functional.

4. The two unifying theories proposed (by Davis and Edgington) both fail in the face of counterexamples.

5. Therefore, in the absence of a third proposal for a unifying theory, indicative and counterfactual conditionals should be treated differently.

As it happens, Dorothy Edgington was my tutor when I was an undergraduate at Birkbeck during 1972-6. She marked and commented on an essay I wrote on counterfactuals for my Oxford graduate application where I argued for a novel treatment of counterfactuals, which basically involved defending Mackie's account against David Lewises objections in 'Counterfactuals' by turning Mackie's account upside down. Instead of starting with the actual world and considering what changes need to be made if we hypothesise the antecedent of the counterfactual, we just start with the antecedent and build up a world (or, rather, a range of alternative worlds) from that. (To this day, I don't know whether the theory could be made to work or not: Dorothy had a number of pertinent objections!)

Your counterexample to Grice is a thinly disguised version of the two paradoxes of material implication put in the form of a disjunction:

Either if P then not-P or if not-P then P.

If P is false then the first disjunct is true, if true then the second disjunct is true.

I'm not convinced. However, I accept that it is a good ad hominem argument against Grice's theory of conversational implicatures.

My question would be, what does it mean to say that when 'we' assert indicative conditionals 'we' do not mean them to be understood truth functionally? Who is 'we'?

Suppose I told you that whenever I use indicative conditionals, *I* wish them to be understood truth functionally. I've used a number of indicative conditionals (e.g. 2. above). Are you confused? There is no reason to be. The point of having a sign for conditional statements 'P -> Q' in *my* language is that there is a way to learn that such a conditional is true *in some other manner* than using introduction rules for propositional calculus (e.g. from Q you can infer P -> Q). If there wasn't a way to do this, then any time I asserted P -> Q I would have to know that either P is false or that Q is true.

That is where the causal or logical connection comes in. It has nothing to do with 'conversational implication' but simply with grounds. The ground for asserting a proposition P are not equivalent to the truth conditions for P. Truth conditions are tied to consequences. Human knowledge is expanded by means of indicative conditionals because of the possibility of using the elimination rules modus ponens and modus tolens.

Frege somewhere gives the example, 'If the sun has not gone down then it is very cloudy.' The ground for the assertion of this conditional is that it is late and it has gone dark. Either of the two hypotheses, 'The sun has gone down', 'It is very cloudy' would explain what we see, but there is no other connection asserted or implied between the two propositions.

However, I said I was talking about 'my' language. I would regard this question in a Quinian spirit as one of 'regimentation', avoiding completely the muddy question of what the average speaker thinks or means by indicative conditionals. The only question is what is the best, most elegant way to explain how indicative conditionals could *possibly* have a point, a use.

As for the so-called paradoxes of material implication, this is just a case of 'baroque', i.e. irrelevant consequences of the use of a particular system of representation. It is 'language going on holiday' to use Wittgenstein's phrase. We don't need to be protected against this (as if the only theory that is acceptable is one that makes it impossible to say anything pointless or stupid). We just need to be proficient in using this particular linguistic tool, to be au fait with the logic of our language.

Of course, it still leaves open all the interesting questions about how we evaluate the grounds for indicative conditionals, and whether indeed there can be a single philosophical 'theory' that explains all this. I don't think there is one, because what one is asking is a theory that would encompass all forms of reasoning, causal reasoning, probabilistic reasoning, inference to the best explanation etc. etc.

I'm sure that if Edgington was reading this she would probably pick my argument full of holes. You do need to be aware (maybe you are already) that Edgington has much more to say about indicative conditionals, which links the issue of conditionals to probability theory. However, you have certainly said enough to answer the question.

All the best,

Geoffrey