Terminology:
Will: that by which the mind chooses anything (1.1).
Act of will: act of choosing. JE identifies volition with the prevailing act of the soul; what other writers call “voluntary.”
Determined: under some influence to a fixed object.
Thesis: it is that motive which, as it stands in the view of the mind, is the strongest that determines the will (I.).
Necessity of consequence: while JE plays fast and loose sometimes with terms, what he says makes sense, nonetheless. There is also a weaker type of necessity, accidental necessity.
Part 1
Thesis: a man never wills anythiing contrary to his (greatest apparent) desire (section 1).
Section 2: Determination of the WIll
A will is determined when its choice is directed to a fixed object. Motive is that which excites the mind to volition. For Edwards “understanding” is the whole faculty of perception.
Section 3: Necessity
A thing is necessary when it cannot be otherwise. Necessity is a fixed connection between things (e.g., the subject and predicate of a proposition). Contingency is when something has no previous connection.
Section 4: Moral Necessity and Inability
Moral necessity is the certainty of the will itself. Edwards’ argument seems to be that it is impossible for the will to act contrary to its greatest inclination. This impossibility is the moral inability.
Moral inability is the want or defect of an inclination. Being able is not the same thing as being willing. I can have the faculty/capacity to do x, yet never actualize it.
Section 5: Concerning the Notion of Liberty and Agency
Liberty is the power to do as one pleases. It doesn’t belong under the category of “Will,” but agency. Agents are free, wills are not.
Logical Investigations 