Truth Functionality and Counterfactual Conditionals

[Lucas Bennett]

In his book, Methods of Logic, W. V. Quine states that,

 “Whatever the proper analysis of the contrafactual conditional may be, we may be sure in advance that it cannot be truth-functional; for, obviously ordinary usage demands that some contrafactual conditionals with false antecedents and false consequents be true and that other contrafactual conditionals with false antecedents and false consequents be false.” 

(Quine uses the term “contrafactual;” current modal logicians substitute this for counterfactual, which I will use for this question). However, Quine does not provide an explicit analysis of this lack of truth functionality of counterfactual conditionals, and the examples that I can conjure up seem to similarly apply to material conditionals so that they no longer seem to be truth functional either. (Of course, by truth functional, I simply mean that the truth value of the whole statement is determined by the truth values of the constituent parts. In the material conditional, X –> Y, the truth value of this conditional is determined by the truth values of X and Y).

For example, suppose that Chris is currently in England. In this case, the following two counterfactual conditionals both have a false antecedent and a false consequent.

1. If Chris were in Toronto, then he would be in Algeria.

2. If Chris were in Toronto, then he would be in Canada.

Since Chris is in Mexico, then he cannot be in Toronto, Algeria, or Canada. If counterfactual conditionals were truth functional, then (1) and (2) would both be true (since a false antecedent and a false consequent result in a true conditional). However, it is obvious that (1) cannot be true, while (2) is true (Toronto is a city in Canada, so that, if Chris were in Toronto, then he would indeed be in Canada).

However, suppose that the same situation obtains in which Chris is in England, but we simply change the tense of these conditionals from the subjunctive into the present.

3. If Chris is in Toronto, then he is in Algeria.

4. If Chris is in Toronto, then he is in Canada.

But we have the exact same problem: Chris is in England, not Toronto, Algeria, or Canada, so both (3) and (4) have a false antecedent and a false consequent, meaning that both (3) and (4) should be true material conditionals. However, once again, (3) is clearly false, whereas (4) is clearly true.

I am certainly not one to contest against Quine, so I think I have clearly gone wrong somewhere, but I’m not sure where my reasoning is flawed (and I’m sure I’ll be smacking myself afterwards at how simple of a mistake I made). Any help would be much appreciated!