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Dear philosophy stack exchange,

I've been considering of late the problem of change as presented by Heraclities and Parmenides as well as the supposed solution to the problem by Aristotle himself. I began to wonder if it's the case that there has been other philosophical solutions to this problem of change? One's which do not invoke potentiality and actuality or dip into these two extremist views of either nothing being permanent but constantly changing or everything being permanent with change being but an illusion. Have there been other proposed solutions in other philosophical camps from antiquity to now?

Thank you for your consideration.

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  • There is eternalism in which one can talk about changes with time, but temporal change is not different ontologically from spatial change (like a color gradient, or a change in y-coordinate of a curve at different points along the x-axis). I'm not sure if this counts as what you meant by "everything being permanent with change being but an illusion" though, or if eternalism is compatible with Parmenides' ideas (I think he is sometimes read as denying all forms of internal differentiation in 'what is', not just temporal change).
    – Hypnosifl
    Dec 19 '19 at 22:03
  • The problem, as presented by Parmenides, is that only something self-identical can be or be thought, so the apparent change is incoherent. Aristotle denied that non-self-identical can not be (potentiality), but one can also deny that non-self-identical can not be thought. According to Papa-Grimaldi, this is the preferred solution (rather dissolution) today:"Hegelian logic is not a solution of the paradox but a dismissal of the logical coordinates that generate it... Mathematical solutions of Zeno’s paradoxes... are unconsciously Hegelian"
    – Conifold
    Dec 19 '19 at 23:20
  • The traditional solution has been to deny the metaphysical reality not just of change but of the things that change. Your solutions would reify one and deny the other, but this does not work. They have to both go for a workable view of change. This view would be that of Middle Way Buddhism or 'non-dualism'. .
    – user20253
    Jan 19 '20 at 10:31
  • @PeterJ - Why do you say "this does not work"? In the modern view of a universe obeying mathematical laws, one can have a mathematical model of "things that change", where each event in spacetime is represented by a mathematical proposition which is derivable from some set of axioms about initial conditions and laws of nature. In a mathematical Platonist view, wouldn't this mathematical structure exist "timelessly" in the world of mathematical forms? For that matter, in basic algebraic geometry there are non-temporal notions of change like the change in the y-value of a function as you vary x.
    – Hypnosifl
    Feb 18 '20 at 14:48
  • @Hypnosifl - You seem to be reifying the things that change. This does not work for reasons given by Kant and many others. What changes are appearances. When we look for a 'thing' that changes we cannot find it. Hence Realism is unverifiable. If the mathematical structure of the universe is eternal this would not be surprising to me, but it would have to be an idea inherent in Reality prior to space and time, not an extended object. If it is extended and eternal then so also is space and time, and this idea runs into problems. . .
    – user20253
    Feb 18 '20 at 19:26
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The underlying picture science currently uses, conceived of by Newton as 'fluxion' and institutionalized in the integral and differential calculus, really is not one of these three options. It discards the Aristotelian distinction between potentialities and actualities, and does not move backward into one of the two earlier positions.

Instead, it creates infinitely many infinitesimal-but-actual 'moments' that all things possess at every instant. Inertia is not a potential motion, it is an actual tendency toward motion, but not an actual motion. Likewise, ongoing changes to inertia created by the gravity of other objects as something moves through their fields of influence are actual tendencies to change the actual tendency toward motion.

This solution is intimately tied up with the idea of pervasive fields of effect which do not have observable instantaneous effects, but instead determine the derivatives, and through them cause observable change. This was a real break with Aristotle that actively bothered Newton.

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