Counterfactual conditions

In this section it will be shown that basic temporal logic is not able to capture all aspects of everyday language or thinking. Often we contemplate on how thing might evolve or how things could have been if we had done otherwise in the past. We can say things like:

• If the weather is fine tomorrow, then I will go out fishing, else I will stay home and read.
• If I had asked for at raise yesterday, I would certain have had it.

When we evaluate a counterfactual conditional then we need to combine both temporal and alethic operators. One example of this the following example shows²⁵:

(A) If I had gone [then] I would have found happiness.

This sentence can be represented by its symbolic form:

132#132

Here 7#7 should be read ''I go`` and 133#133 should be read ''I find happiness``. The sentence above seems to express a common sense belief that many people holds; if they had acted differently that they actually did, things would have gone different. These types of propositions are called ``subjunctive conditionals'', ``counterfactual conditionals'' or just ``counterfactuals'' for short²⁶. The problem that propositional logic faces here is that these type of sentences seems to incorporate both temporal, alethic and - one might say that it also should incorporate epistemic - operators. The main problem is that the proposition is vacuous true due to the fact that the first premise is (de facto) false. Therefore it can be used to show anything because it is false. This allows us to add any logical variable to the proposition without changing the overall result. Because the `and' operator always will evaluate to false if one of the operands are false then we can add any other proposition. This can have some bizarre consequences like we could have:

134#134

Where 135#135 could be interpreted as ``I die''. So the sentence would sound like:

(A') If I had gone and had died [then] I would have found happiness.

This result is at best highly doubtful; most people would not accept the validity of (A'). An other (classical) example of counterfactual conditionals, where the temporal aspect is even more visible is from Jackson (1991, pp 6-7):

(B) If Lee Harvey Oswald did not kill Kennedy, then someone else did.

(B') If Lee Harvey Oswald had not killed Kennedy, then someone else would have.

Here we can see the two almost identical sentences (B) and (B'). But where most people would not accept the validity of the second sentence, almost anybody would accept the first at face value. In order for us to analyze propositions of the preceding types we need - among other things - a concept of a common past to avoid the possibility of changing the past and thereby changing the premises for the propositions in question. Furthermore we need to be able to distinguish between the actual future and possible ones - one thing basic temporal logic unable to do.