The reality is that the "self" is a corpus of work, not a moment. To go back to the quantum world analogy, it's the entire diffraction pattern, not one individual wave-particle duad.
Let's note his (in)famous comment in full:
“For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception…. If any one, upon serious and unprejudic'd reflection thinks he has a different notion of himself, I must confess I can reason no longer with him. All I can allow him is, that he may be in the right as well as I, and that we are essentially different in this particular. He may, perhaps, perceive something simple and continu'd, which he calls himself; tho' I am certain there is no such principle in me.”
The first thing I thought of when reading this again after hunting it up to get the exact quote?
The story about Hume being asked about the Problem of Induction by a lady, who wondered how he could fall asleep at night not knowing whether or not the sun would rise in the morning.
And, Hume essentially said, "I act as if."
Well, there's the hypocrisy part. Per what I said about the self being an ongoing corpus of work? Hume certainly did "act as if" in his personal life (other than when denying he wrote the Treatise). So, by his actions, if not his statement at the moment, he accepted the other side of the claim, not his own.
Of course, to further the petard-hoisting? The quote IS, as Hume students know ... from the Treatise! The book that Hume claimed he didn't write!
That said, the "bundle theory" behind this has its own additional problems. If all we can know about an object is a bundle of impressions, how can we know that that bundle of impressions is all we can know about it? To quote Hume against himself, the assumption that he makes could be called "divinity or school metaphysics" and another of his (in)famous quotes applied against himself:
“If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.”
Beyond that, Hume arguably stacked the deck, and for this we head back to quantum mechanics.
Maybe I can't see "particle X," but I can see the vapor trail left by its decay products and see if they match what's predicted. Likewise, maybe I can't see the self, but I can hear or see you state your political beliefs, your philosophical beliefs, your religious beliefs, your preferences in food and many other things.
These often do not stay rigid over a lifetime. The self of 20 years from now will likely not be the same as that of today, and the self of 20 years ago likely is not the same as the current one. (Example for me? As I write this, I think more and more that Hume needs to be shelved on the "overrated philosophers" list; 20 years ago, I couldn't conceive that.)
That said, the self of three months from now will likely be pretty close to the same as the self of today, close enough to be considered the same self, barring a Damascus Road moment. (Or a belief in p-zombies or something.)
The problem gets worse. Most of Hume's highlights in philosophy, such as the whole Problem of Induction, started in the Treatise. It's true that he reworked some of them in some degree in later works. Nonetheless, if we took Hume's fictive anonymity claims as face value real, we should throw out what, one-third of philosophical thought attributed to him? And, that would officially move him into my "overrated philosophers" list.
So, again, as with Kant, Hume, or an overestimation of Hume, has awakened me from dogmatic slumbers.
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