There's a footnote somewhere in Thomas Nagel's The View From Nowhere where he says, 'This is probably just Presocratic flailing about but...' then goes on to speculate about the possibility of a third type of 'substance', neither material nor mental which would somehow explain the mind-body connection. I like this. I like the idea of going 'back to the Presocratics'. It wouldn't be such a novelty.
Popper found in the Presocratic philosophers the perfect model for his favoured account of scientific inquiry (in Conjectures and Refutations). There's something very pure and clean about these old guys in their robes speculating about the ultimate, ultimate questions in complete ignorance of all that we know (or think we know) about the universe.
One debate in particular interests me, that between the Eleatic philosophers Parmenides and Melissus. According to Parmenides, the One concerning which no statement can be made that implies a negative can only exist in the present. If any temporal parts of the One exist in the past or future, then they are 'not now', contradicting the initial axiom that nothing can be thought or said that implies 'not' or negation.
Melissus wasn't impressed by this argument. His One is temporally infinite. The One has always existed and will always exist. For this reason, Melissus believed, the One must be spatially infinite, not finite as Parmenides held, because anything spatially finite is logically capable of growth or shrinkage, and anything that logically can shrink, can shrink to nothing, contradicting the necessary eternal existence of the One.
Why is this relevant? Because this very same debate is played out between two radically different conceptions of I. My subjective world necessarily exists only in the present moment. Yet, one could also argue for a conception of the self, according to which death can never happen because to die logically implies to be dead forever (Day 19). It is easy to extend the same argument to the past. The I which exists over time, is only intermittently conscious (because sometimes you sleep). There is no point so far back in finite time that I could not, logically, identify as a time when I existed (with suitable causal connection for genuine 'memory').
This is one of the main points of difference between Tibetan Buddhists, who hold that the self qua 'spark of consciousness' is capable of reincarnation, and Zen Buddhists, who hold that the spark of consciousness exists only in the present moment.
All we need to add to this is the master axiom that the world is other than I (Day zero). Now we have two alternate pairs, a momentary I confronting a momentary world, or an eternal I confronting an eternal world. Voila!