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Paradoxes are arguments designed to provoke rather than persuade and philosophers who propose them rarely accept their conclusions. So here is a brand new paradox of my own invention for you to think about.
(1) Dying, i.e. the transition from being alive to being dead, is a discontinuous change.
While it is often hard to identify the precise moment in time at which someone dies, and perhaps dying itself takes a period of time, it seems to be an a priori truth that we cannot represent dying in terms of the continuous change of some variable. To see this, suppose we could and call the variable ‘liveliness’. Then dying would be a continuous decrease in liveliness until its value was so low the person was dead. What would be that value? Surely it must be zero: whatever the property is which makes for being alive, being dead consists in a total lack of it. You can perhaps be more or less alive, but however little alive you are, you are not dead at all. So dying is a discontinuous change, from possessing some liveliness to possessing none at all.
(2) There are no discontinuous changes in nature.
It seems to be the case that all natural changes, that is, all changes studied by the natural sciences, consist in continuous change of some variable such as mass, energy or velocity. Let’s accept that for now.
These two premises entail the paradoxical conclusion:
(3) No one has ever died.
Now the simplest way out would be to deny premise (2), but that is not so easy. Not because (2) is undeniable, but because it is contingent and a matter of empirical discovery. Perhaps quantizing effects in current physics show that (2) is false, but the problem (2) presents is that it makes the question of whether anyone has ever died or not depend upon fine details of theoretical physics, and that just seems plain wrong.
Furthermore, death plays a rather major role in several widespread religions and it would be surprising – and a little uncomfortable – to discover that the coherence of those religions depends upon whether light quantizes or not.
Another way of seeing the paradox is to combine (1) and the denial of (3): this seems to prove something about physics which we should not be able to prove from an a priori claim like (1). So perhaps we should deny that (1) is a priori? Unfortunately, that is not plausible, because our reasons for thinking (1) is true look like they are conceptual: anyone who properly grasps the concept of dying will think that it is a discontinuous change.
So the paradox is genuine. That does not mean there are not solutions to it, but we need to do some philosophy to find them.
Tom Stoneham is Head of Philosophy at the University of York.