# Conditionals and logic

When second and third conditional sentences are used, are they logical?

If he won the lottery, he would buy a new car.

The reality is he is not buying a new car. So we can safely say he hasn't won the lottery, right?

If he had gone to the event, he would have returned home late last night.

The reality is he returned home early last night. So we can safely say he didn't go to the event, right?

• Grammar isn't mathematical logic. Why do you assume the speaker is telling you the truth? I might have gone to the event, left early and returned home early, but I wanted you to think I didn't go to the event. Jan 29 '20 at 10:13
• Yes, you are right. But I mean, if we believe truths are told, we can safely get the answers I provided, right? Jan 29 '20 at 15:42
• Context is everything. By their nature, conditional statements are contingent, and their consequents are matters of opinion, not truths. In the context of logical deduction, you're right, as in "If he had fired the weapon, his hands would be covered with gunshot residue." In other contexts, not so much. Applying formal logic to grammar would lead one to deduce that when Mick sings "I can't get no satisfaction," he really means he's satisfied. Jan 30 '20 at 2:14
• It's hard to tell whether your nervousness about the logic of your essays is warranted without reading the essays. I'd say as a general rule, that you'll have to marshal evidence to make your conditionals follow formal logical rules. This is a matter of semantics and not grammar. So you could say, "If he'd won the lottery, we can be sure he would have bought a new car" and then give the reasons that we know this: it's all he talked about, he'd signed a contract contingent on his winning, or whatever. Jan 30 '20 at 3:01
• It makes sense, although I don't know how you'd confirm it. The contrapositive is "If people want to look good, then they want attention from others." Do you think that's universally true? Traditional formal logic is based on two truth values. The best you can do for human behavior is make probabilistic statements, which rely on a range of values in the interval [0,1]. Jan 31 '20 at 2:59

No, at least no more in English than in any other language.

If he won the lottery, he would buy a new car.

This speaks of a possible future event (winning the lottery) and a claimed consequence (buying a new car). It doesn't describe the past. We can't logically infer anything from the fact that he has, or hasn't bought a new car.

If you gave me a slice of cake, I would eat it.

I'm not currently eating cake, but I can't infer that you have never given me cake in the past.

Now practically we can use general knowledge of human behaviour and make educated guesses:

The second sentence talks about past actions ("had gone" and "would have") So if we assume the whole sentence is true, then we can deduce that "He came home early, so he didn't go to the event". However there is no special fact of English grammar being applied here. All languages can make similar statements, and all natural languages unsuitable for formal logical proofs.

Technically no, because would can also be a "will in the past".

If he won the lottery, he would buy a new car.

This can also mean something like Each time he would win the lottery, he would then buy a new car. It's not likely given the context but possible.

• Thank you for your answer. If we focus only on the present meaning of the second conditional example, we can make the conclusion like I mentioned, right? Also, if we focus only on the past meaning of the third conditional example, we can also make the conclusion like I mentioned, right? Jan 30 '20 at 2:11