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A counterfactual conditional, or subjunctive conditional, is a conditional (or "if-then") statement indicating what would be the case if its antecedent were true. This is to be contrasted with an indicative conditional, which indicates what is (in fact) the case if its antecedent is (in fact) true.
An example
The difference between indicative and counterfactual conditionals can be illustrated with a pair of examples:
- If Oswald did not shoot Kennedy, then someone else did.
- If Oswald had not shot Kennedy, then someone else would have.
The first sentence is an indicative conditional that is intuitively true. The second is a counterfactual conditional that is intuitively false (or at least not obviously true).
A counterfactual connective
In order to distinguish counterfactual conditionals from material conditionals, a new logical connective '>' is defined, where A > B can be interpreted as "If it were the case that A, then it would be the case that B."
The truth value of a material conditional, A → B, is determined by the truth values of A and B. This is not so for the counterfactual conditional A > B, for there are different situations agreeing on the truth values of A and B but which yield different evaluations of A > B. For example, if Keith is in Germany, the following two conditionals have both a false antecedent and a false consequent:
- if Keith were in Mexico then he would be in Africa.
- if Keith were in Mexico then he would be in North America.
Indeed, if Keith is in Germany, then all three conditions "Keith is in Mexico", "Keith is in Africa", and "Keith is in North America" are false. However, (1) is obviously false, while (2) is true.
Possible world semantics
Philosophers such as David Lewis and Robert Stalnaker modeled counterfactuals using the possible world semantics of modal logic. The semantics of a conditional A > B is based on considering the most similar (or "closest") situations in which A is true, and checking whether B is true in all of them. More formally:
For example:
- If the Braves had won, Keaton would've eaten his hat.
To evaluate this statement, consider a possible world where the Braves did win, and imagine that this world is otherwise as similar to the actual world as possible (so, for example, it is not a world ruled by Nazis). Then ask whether, in such a world, Keaton proceeded to eat his hat.
Other accounts
Counterfactual conditionals may also be evaluated using the so-called Ramsey test: A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.
Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only B is true in all such sets.
See also
References
- J. Bennett (2003). A Philosophical Guide to Conditionals, Oxford University Press.
- D. Bonevac (2003). Deduction, Introductory Symbolic Logic, 2nd edition, Blackwell Publishers.
- M. L. Ginsberg (1986). Counterfactuals. Artificial Intelligence, 30:35-79.
- D. Lewis (1973). Counterfactuals, Blackwell Publishers.
"Counterfactual conditional"