Topics Logic

Question If the sentence "q because p" is true, must the sentence "If p then q" also be true? For example, "the streets are wet because it is raining," and the sentence "if it is raining, then the streets are wet." Are there any counter-examples where "q because p" could be true while "If p then q" could be false?

Accepted:
December 20, 2012

Comments

Suppose that "q because p" is true. I would say that it follows that both q and p have to be true. But, in that case, "if p then q" is also true (assuming that the English "if...then..." expression is interpreted as the material conditional). However, "if q then p" is also true! So, there doesn't seem to be much of an interesting connection between the causal sentence and the conditional sentence.

I agree with my co-panelist: "q because p" implies that "q" and "p" are both true. And on more than one reading of "if.. then" sentences, it will follow that "if p than q" as well as "if q then p" are true. It may be worth noting, though: not everyone agrees that when "p" and "q" are both true, so are "if p then q" and "if q then p." There's a different sort of point that may be relevant to your worry. Suppose Peter's smoking caused his emphysema. We can't conclude that if Petra smokes, she'll develop emphysema. Causes needn't be fail-proof. A bit more formally:

Qa because Pa

(which says, more or less that a has property Q because a has property P) doesn't allow us to conclude

∀x(If Px then Qx)

(that is, for every thing x, if x has property P then x has property Q.) The truth of a "because" statement doesn't require the truth of a generalized "if...then" statement.