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Sorry, but I do not know another place to post this question.

Condition of possibility is an important philosophically philosophical concept. Naively, this concept could be formally defined this way:

$q$ is a condition of possibility of $p$ iff $\neg q$ implies $\neg p$

the latter being equivalent with $p$ implies $q$. When we write $\hookrightarrow$ for is a condition of possibility of and $\rightarrow$ for implies we get

$q \hookrightarrow p$ iff $p \rightarrow q$.

So, condition of possibility is something like co-implication.

My question is: While in category theory many concepts and co-concepts are treated as strongly related (= inter-definable) but each in its own right, and while in logic many concepts are treated as strongly related (= inter-definable) but each in its own right:

Why wasn't the - philosophically important - concept of condition of possibility found worthy of being named and treated in its own right in (formal) logic?

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# Condition of possibility = Co-Implication

Sorry, but I do not know another place to post this question.

Condition of possibility is an important philosophically concept. Naively, this concept could be formally defined this way:

$q$ is a condition of possibility of $p$ iff $\neg q$ implies $\neg p$

the latter being equivalent with $p$ implies $q$. When we write $\hookrightarrow$ for is a condition of possibility of and $\rightarrow$ for implies we get

$q \hookrightarrow p$ iff $p \rightarrow q$.

So, condition of possibility is something like co-implication.

My question is: While in category theory many concepts and co-concepts are treated as strongly related (= inter-definable) but each in its own right, and while in logic many concepts are treated as strongly related (= inter-definable) but each in its own right:

Why wasn't the - philosophically important - concept of condition of possibility found worthy of being named and treated in its own right in (formal) logic?