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Encyclopedia > Counterfactual conditional

A counterfactual conditional (sometimes called a subjunctive conditional) is a logical conditional statement whose antecedent is (ordinarily) taken to be contrary to fact by those who utter it. Contrast the following statements:

(1) If Keith didn't touch the hot stove, then it didn't burn him.

(2) If Keith hadn't touched the hot stove, it wouldn't have burned him.

Someone uttering (1) would not ordinarily take "Keith didn't touch the hot stove" to be false, but someone uttering (2) would.

Counterfactual conditionals cannot be modeled using the material conditional, because any material conditional with a false antecedent is automatically true. For example,

(3) If the Nazis had won WWII, the world would not have become a very different place.

would be modeled with the material conditional as

(4) The Nazis won WWII -> The world did not become a very different place.

where -> represents the material conditional. (4) is true (by the truth table for ->), while (3) is clearly false. Because of this problem (and others like it), philosophers such as David Lewis and Robert Stalnaker have tried to devise ways of formally modelling counterfactuals using the possible world semantics of modal logic. Essentially, one can define a symbol []-> so that:

(5) A []-> B is true at a world w if, in all the worlds closest to w where A is true, B is also true.

Consider

(6) If the braves had won, Keaton would've eaten his hat.

To evaluate (6), 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.

Classically, an important work on counterfactuals is

Counterfactuals, by David Lewis, 1973 (Blackwell Publishers)

For a good introduction, see the chapter on counterfactuals in the excellent

Deduction, Introductory Symbolic Logic, 2nd edition, by Daniel Bonevac, 2003 (Blackwell Publishers).

For a very well written philosophical discussion of conditionals, see

A Philosophical Guide to Conditionals, by Jonathan Bennett, 2003 (Oxford).

Results from FactBites:

 Counterfactual conditional - encyclopedia article about Counterfactual conditional. (623 words) Differently from logical conditional In propositional calculus, or logical calculus in mathematics, the logical conditional is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). In particular, logical conditionals are always true whenever their antecedent is true, while an if-then statement in a natural language can be false in that case. A Philosophical Guide to Conditionals, by Jonathan Bennett Jonathan F. Bennett (born 1930, New Zealand) is a British philosopher of language and metaphysics, and a historian of early modern philosophy.
 Counterfactual Theories of Causation (7207 words) The basic idea of counterfactual theories of causation is that the meaning of a singular causal claim of the form "Event c caused event e" can be explained in terms of counterfactual conditionals of the form "If c had not occurred, e would not have occurred". The chief obstacle in empiricists' minds to explaining causation in terms of counterfactuals was the obscurity of counterfactuals themselves, owing chiefly to their reference to unactualised possibilities. Counterfactual dependence is not transitive, so it can happen that three actual events c, d and e are such that d would not have occurred without c, and e would not have occurrred without d, but e would still have occurred without c.
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