Hume here does not really seem to know what he is talking about. His view is that the difference between “memory” and “imagination” lies in the “superior force and vivacity” of the former. (AToHN, 1.3.5)
But surely, memory is merely a source of phantasms entertained by the imagination. The difference must be sought rather between abstract objects perfectly recalled and those fancifully created in the mind’s eye.
Once this is grasped, we can see that the difference between the two is in the level of detail of the phantasm being entertained. Assuming perfect memory, I may close my eyes and imagine a bowl of salad that looks exactly like the actual bowl in front of me. Since the modes of existence (real vs. ideal) of the two differ, there is no identity between the ideal and the real but a weaker relation of correspondence. (The image of the bowl is true.)
Now let me make one slight difference to the picture I am holding in my mind, viz., change the color of the bowl from tan to blue. Surely, there is little loss in the “force and vivacity” of the phantasm which for all that instantly changes from being of the “memory” to of the “imagination.” This disproves Hume’s theory. In addition, the two objects are equally detailed. Since they have different properties, they are not identical to each other.
Now let our imagination run wild and picture in the mind a “fat man in the doorway.” W.V. Quine asks, his words dripping with contempt:
Take, for instance, the possible fat man in the doorway; and, again, the possible bald man in the doorway. Are they the same possible man, or two possible men? How do we decide?
How many possible men are there in the doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? Are no two possible things alike? Is this the same as saying that it is impossible for two things to be alike?
Or, finally, is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another? (“On What There Is”)
Well, yes, the concept of quantitative or self-same identity is inapplicable to phantasms, because they hang in no time or place but in the mind’s eye; nor do they persist in being but upon the seer’s will. Further, we might be able to call two phantasms that look or sound or whatever the same qualitatively identical, but only if they were fully defined. Thus, all we know about the fat man in the doorway in the imagination is that it’s a man, fat, and has a doorway around him. Whether he is in addition bald is not specified. As a result, neither kind of identity applies to the Quine’s two men. They are neither the same nor different; yet surely, imagining things can make “sense” for a variety of purposes, such as graphic design or writing fiction or inventing a new machine or in a hundred other ways.
And now we can see that the main difference between phantasms that are recalled and those that are imagined is precisely the extent of their definition and description. Perfectly recalled things are full-featured qualitatively; imagined things rarely are. For example, in now imagining a non-existent “possible” entrée, I may be so focusing on its shape and color that I forget to “see” the surface it would need to rest on or the fork in it or the smell of its contents or most other things that might have been part of the experience, if it were real and could then be at least in principle faithfully recalled.