# Verb tenses when writing the converse and contrapositive of an implication

Consider the statement "If you work hard then you will succeed". What is the right way of writing the converse and contrapositive of this statement? Should they be "If you will not succeed then you do not work hard." and "If you will succeed then you work hard." or "If you will not succeed then you did not work hard." and "If you will succeed then you worked hard."?

For the sake of math I don't think it matters.

Technically it is "If you work hard (in the present) then you will succeed (in the future)" and the contrapositive would be "If you will not succeed (in the future) then you do not work hard (in the present)".

But that makes for fairly unnatural and awkward english. We frequently talk of current causes having potential effect in the future, or present situations having being caused by conditions in the past, but we seldom talk about future known situations being caused by present (but unknown) causes. The rare exception might be a precautionary "If you are to fail to succeed, it is only because you do not work hard now".

I think it is understood that this statement applies for any time frame. If your grandfather worked hard in 1960 than he succeeded in 1970. If you grand daughter works hard in 2045, then she will succeed in 2055.

I think "If you do not succeed, then you didn't work hard" is the more natural statement. Although "If you will not succeed, then you do not work hard" is more technically accurate.

Consider the statement "If you work hard then you will succeed". What is the right way of writing the contrapositive? Should they be "If you will not succeed then you do not work hard" or "If you will not succeed then you did not work hard"?

While there is no inherent concept of time/tense in formulations and rules in classical logic (conditional-probability example), and logical if-then statements don't in general indicate causation, the above if-then statements are cause-and-effect statements, which consider the flow of time.

I think the appropriate contrapositive is "if you will not succeed, then you will not have worked hard", since the original antecedent is implicitly in the future tense and occurring before the original consequent.

Consider the statement "If you work hard then you will succeed". What is the right way of writing the converse? Should they be "If you will succeed then you work hard" or "If you will succeed then you worked hard"?

Similarly, I suggest "if you will succeed, then you will have worked hard".

I believe the converse would be “If you succeed then you worked hard.” and the contrapositive would be “If you don’t succeed, then you didn’t work hard.”. Also note that English is not a formal language. So time will have some effect on statements. While in Logic, when dealing with formal languages, time does not play any role. (You may see this a strong reason for the necessity of a rigorous language for Mathematics).