*Customer.* I’ll buy the car only if, if I buy the car, you’ll guarantee it.

*Salesman.* But let’s suppose that if you buy the car, then I’ll guarantee it; what then?

*Customer.* Then I’ll buy the car.

*Salesman.* Can I hold you to both the things you’ve just said?

*Customer.* Certainly.

*Salesman.* Then you are logically committed to buying the car anyhow, even if I don’t guarantee it.

*Customer.* What?!

*Salesman.* You say you’ll buy the car only on condition that if you buy the car I’ll guarantee it?

*Customer.* Yes, I do say that; I’m not a complete idiot!

*Salesman.* Well then: if you’ll buy the car, you’ll buy the car only if I guarantee it. Right?

*Customer.* Uh-huh.

*Salesman.* But in logic, “*p* only if *q*” is just a variant of “if *p* then *q*”; thus, “if *p*, then *p* only if *q*” is equivalent to “if *p*, then if *p* then *q*”—and that’s equivalent to “if *p*, then *q*”.

*Customer.* What on earth has that got to do with my buying the car?

*Salesman.* You said that if you’ll buy the car, then you’ll buy the car only if I’ll guarantee it. But that, you see, is logically equivalent to saying that if you’ll buy the car then I’ll guarantee it.

*Customer.* Never mind what is logically equivalent to what! **Will** you guarantee the car?

*Salesman.* I’m not saying anything about that just now. You said—remember?—that I can hold you to what **you’ve** said. And you’ve as good as said that if you’ll buy the car then I’ll guarantee it.

*Customer.* Well, yes, it looks as if I did say that.

*Salesman.* But you also said that, on condition that if you’ll buy the car that I’ll guarantee it, you undertake that you’ll buy the car.

*Customer.* Yes, I did.

*Salesman.* But you are logically committed, as we just saw, to saying that the condition that you stipulated is fulfilled: namely, that if you’ll buy the car than I’ll guarantee it.

*Customer.* — * — ? * ! *

*Salesman.* So you’ve just got to buy the car, guarantee or no guarantee.

*Customer.* But I said that I’ll buy the car only if you’ll guarantee it. So if I am going to buy the car—as you pretend to have proved I must—you’ve got to guarantee it.

*Salesman.* I don’t have to accept that. You said I could hold **you** to what **you** said: that’s all I’ve been doing. **I’m** not bound by what **you** said, obviously. So it’s a deal. I see you have your bank information there, Sir. Thank you very much, Sir. Please sign here.

#### Part II

*Professor.* Let’s suppose that *x* is the number of blocks; then, ...

*Student.* But Sir! Please, Sir! What if *x* **isn’t** the number of blocks?