What is the difference between counterfactual condition and false condition?

Question

I encountered this problem while reading Terence Horgan's Essays on Paradoxes.According to David Lewis,

the counterfactual condition if P then Q is true iff either: 1. There are no possible worlds that P is true; 2. Some P-world at which Q is true is more similar, overall, to w than is any P-world at which Q is not true.

So I wonder if the false condition in mathematics is the same as the first condition of the counterfactual condition listed above?

Answer 1

In a nutshell, the issue is with the truth-functional definition of the conditional $\to$ :

$A \to B$ is TRUE when $A$ is FALSE.

When applied to statements like e.g. :

"If Oswald did not shoot Kennedy, then someone else did",

we are not satisfied to consider them TRUE, obly because we know that the antecedent is FALSE.

See Counterfactual Theories of Causation for more details :

The basic idea of counterfactual theories of causation is that the meaning of causal claims can be explained in terms of counterfactual conditionals of the form

“If A had not occurred, C would not have occurred”.

The best known counterfactual analysis of causation is David Lewis's theory. However, intense discussion over forty years has cast doubt on the adequacy of any simple analysis of singular causation in terms of counterfactuals.