What is the Definition of Necessity?

"What is sometimes given as the definition of philosophical Necessity, namely, 'That by which a thing cannot but be,' or 'whereby it cannot  be otherwise,' fails of being a proper explanation of it, on two accounts: First, the words can, or cannot, need explanation as much as the word Necessity; and the former may as well be explained by the latter, as the latter by the former. Thus, if any one asked us what we mean, when we say, a thing cannot but be, we might explain ourselves by saying, it must necessarily be so; as well as explain Necessity, by saying, it is that by which a thing cannot but be. And Secondly, this definition is liable to the fore-mentioned great inconvenience; the words cannot, or unable, are properly relative, and have relation to power exerted, or that may be exerted, in order to the thing spoken of; to which as I have now observed, the word Necessity, as used by philosophers, has no reference.
Philosophical Necessity is really nothing else than the full and fixed connexion between the things signified by the subject and predicate of a proposition, which affirms something to be true. When there is such a connexion then the thing affirmed in the proposition is necessary, in a philosophical sense; whether any opposition or contrary effort be supposed, or no. When the subject and predicate of the proposition, which affirms the existence of any thing, either substance, quality, act, or circumstance, have a full and certain connexion, then the existence or being of that thing is said to be necessary in a metaphysical sense. And in this sense I use the word necessity, in the following discourse, when I endeavor to prove that necessity is not inconsistent with liberty." - Jonathan Edwards, Freedom of the Will, Pg. 16 -17