When explaining the distinction between essential and accidental properties bachelors are often used. The idea of essential properties is this:
The distinction between essential versus accidental properties has been characterized in various ways, but it is currently most commonly understood in modal terms along these lines: an essential property of an object is a property that it must have while an accidental property of an object is one that it happens to have but that it could lack. (SEP)
So, bachelors have the essential property of being unmarried. This is because a married bachelor is a contradiction. This is because the concept of being a bachelor implies the concept of being unmarried. Implication with concepts works just as one might intuitively think that it does; very similar to that of propositions (or whatever truth carrier that you like), but see Swartz & Bradley (1979) for a deeper explanation using possible worlds semantics.
So, since we’re good analytics, we shall invoke the power of formalization.
A. For any person, it is impossible that (the person is a bachelor and the person is married).
∀x¬◊(Bx∧Mx)
That’s all fine and dandy. But it seems then that essential properties are just a matter of semantics, of language, and has nothing to do with the bachelor at all. Based on some idea of essential properties and bachelors and so on, we might say that:
B. Bachelors can’t be married.
But then, how do we formalize this?
∀xBx→¬◊Mx
Going with some very literal interpretation we may get the above, but surely the proposition that that wff expresses is false. Let’s translate it to LAE1
For any person, if that person is a bachelor, then it is not the case that it is possibly the case that the person is married.
So, a bachelor can’t even marry. But this is wrong. Bachelors can and do marry. The only thing is that the concept of being a bachelor and that of being married cannot at the same time be instantiated in the same person. Nothing else. There is no contradiction in saying:
I was a bachelor for many years, but then I married Jane. Gosh she is so wonderful, blahblahblah…
We may reduce this tale to something like:
Bert the Bachelor was a bachelor at time t1, but then later he married and stopped being a bachelor.
Which we may formalize as something like:
Bbt1∧Mbt2∧t1≠t2
1Logically Aided English