It is after this manner that hope and fear arise from the different mixture of these opposite passions of grief and joy, and from their imperfect union and conjunction.
Upon the whole, contrary passions succeed each other alternately, when they arise from different objects: They mutually destroy each other, when they proceed from different parts of the same: And they subsist both of them and mingle together, when they are derived from the contrary and incompatible chances or possibilities, on which any one object depends.

The influence of the relations of ideas is plainly seen in this whole affair.

If the objects of the contrary passions be totally different, the passions are like two opposite liquors in different bottles, which have no influence on each other.

If the objects be intimately connected, the passions are like an alcali and an acid, which, being mingled, destroy each other.

If the relation be more imperfect, and consists in the contradictory views of the same object, the passions are like oil and vinegar, which, however mingled, never perfectly unite and incorporate.
As the hypothesis concerning hope and fear carries its own evidence along with it, we shall be the more concise in our proofs.