Material conditional

I can’t pretend to have any special way of explaining the truth values of the material conditional, so I am only going to say which of the explanations I’ve seen works best for me. First, a list of some of the explanations and examples I’ve come across which are meant to throw some light on the workings of the material conditional:

- Use a conditional that expresses a promise, for example: If you get an A, you will pass the exam. What if I don't get an A? I didn't say you won't pass if you don't get an A, so the sentence is true, and I wouldn't have lied if you didn't get an A and didn't pass.

- The last two lines of the truth table are irrelevant anyway, because we do not deliberately use a conditional when we know that the antecedent is false. So we may as well make conditionals with false antecedents true.

- If x < 2 then x < 4. Substitute '5' for 'x'. What do you get? A true sentence, with a false antecedent and a false consequent.

- The majority of people, when asked, would say that a conditional is true as long as the consequent is true.

- Antecedent and consequent are deliberately unrelated and often absurd, as in this classic example: If the earth is flat, the moon is made of green cheese. Turning this conditional around by contraposition, which preserves its truth value, shows that it is true in fact: If the moon is not made of green cheese, then the earth is not flat.

The explanation I find most convincing is the one which exploits the distinction between what is asserted and what is implied, and is in fact similar to the first listed (conditional promise). For example:

(1) If it is after 5 pm, the shop is closed.

I can’t in the same breath say that if it is after 5 pm indeed, the shop is closed and is not closed. One of the statements must be false. If I accept that ‘the shop is closed’ is true, then ‘the shop is not closed’ is false. That’s the first two lines of the truth table done.

It’s a quarter to five and the shop is closed – is this true or false? I have never said in my original statement that if it is before 5 pm the shop is not closed. If you got that impression, you have overinterpreted what I have said. You have read too much into it. It could well be that the shop is closed before and after 5 pm. The sentences are not contradictory.

It’s a quarter to five and the shop is not closed – true or false? Again, there is nothing in this sentence that contradicts my original assertion. The sentence is true. You may think that this, the 4th line of the truth table, excludes the preceding situation, but we are not comparing these two! We are relating every line to the original assertion.