I've heard the following claim (in one form or another) here, and elsewhere in LSAT discussions: vacuous truths are a quirk of conditional logic that makes for an interesting philosophical discussion, but aren't really important for the LSAT. I think this is a mistake, and it has gotten a bit under my bonnet, so I thought I would post about it.

First, what is a vacuous truth? Typically it's described as a universal conditional statement, which we would represent in LAWGIC as A -> B, where the sufficient condition is contradictory or impossible, making the necessary condition irrelevant to the truth of the conditional. If pigs fly on their own power, then I have a 180 on the LSAT might be an example. Pigs do not fly on their own power, so I can put whatever I want in the necessary condition and the conditional will still be true. We can also think of this in terms of set logic, given an empty set, A, we can make a true statement A -> whatever we would like, because there are no elements in A.

Why do I think this concept is important on the LSAT? First of all, I grant that one does not have to think in this way in order to get a good score (even a 180) on the LSAT. People can have strong intuitive reasoning capabilities, and so grasp that saying "if I had a million dollars, I'd buy you a fur coat" doesn't mean much if one doesn't have a million dollars. Nevertheless, if we're to take a formal and rigorous approach to conditional logic, I think it is CRUCIAL to examine the formal representation behind that intuition, a truth table, for example, where we can list out all the possible combinations of having a million dollars and buying a fur coat (but not a real fur coat, that's cruel). This may not be understood as vacuous, as I'm sure many of us here will go into big law and at some point have a million dollars, but in the domain of right now, for me at least, I do not have a million liquid in any account, so in the domain of here and now, right now, I could say whatever I want about what I would do if I had a million dollars and be under no obligation whatsoever. So, lets examine the different cases. HM is I have a million dollars, BC is buy you a fur coat.

HM. BC. HM -> BC.

T. T. T.

T. F. F.

F. T. T.

F. F. T.

The conditional is satisfied in any case where one does not have a cool million, and in those cases where one does, only when one buys the requisite coat. That's what a conditional MEANS, and one must understand that to properly deploy them. If we're operating in a scenario where the conditional must be true (say it's a premise in a MBT question), we're limited to three rows of that table (the ones where the conditional is true, rows 1, 3, and 4). This is where we get modus ponens (assert the sufficient, conclude the necessary), and modus tollens (deny the necessary, conclude the sufficient is false). One MUST understand that the truth value of the necessary is irrelevant if the sufficient is false in order to do well on the LSAT, either formally or intuitively. This is precisely the concept of a vacuous truth. In a restricted domain, where nothing can satisfy the sufficient condition, the necessary can be whatever we want. That's where "the oldest mistake in the book" comes from (confusing the necessary condition for the sufficient condition).

Conceptually, understanding the empty set satisfies any conditional comes into play very clearly as an illustration of that oldest mistake in the book, for example, in PT 159.S1.Q21, which I won't spoil here, but might recommend for anyone questioning the relevance of the strongest form of a vacuous truth. To be clear on the lesson, I think it is pretty legible to moderately well prepared students that the stimulus is a necessary for sufficient error. But when you go hunting for the answer, you're left scratching your head UNLESS you understand that the reason necessary for sufficient is an error is because the conditional is satisfied in cases where the sufficient condition is an empty set.