Leibniz offers as a reductio of materialism the idea that if materialism is true, one could have a mind whose functional parts are like the parts of a giant mill, and you could walk right through that giant mill, seeing big wheels of all sorts. But, he thinks, you'd never meet with consciousness.
Leibniz's argument has two parts:
- If materialism is true, a mind could be made of large gears (together with some source of kinetic energy, like a large water wheel).
- A mind could not be made of large gears (plus energy source).
- If materialism is true, functionalism is true.
- If functionalism is true, then any physical system that can do sufficiently complex computations can be a mind.
- A system of large gears (with an energy source) can do arbitrarily complex computations.
- Therefore, (1) holds.
Here's one approach. If a mind could be made of gears, so could a person. Imagine a person made of hard plastic gears. Moreover, every so often the gears are given a rest (maybe so they can cool off—we don't want them to melt)—a small clockwork contraption disconnects the energy source, and everything, except that clock, becomes motionless. Now, a person exists while asleep, and it's plausible that in the rest state, the person would still exist.
Scenario 1: The whole set of gears, but not the wake-up clock, is in a big closed box, and while the gear-person is in a rest state, a thin slow-set two-part epoxy is poured into the box. It turns out that the person could still function with the epoxy, because the source of energy is powerful enough to move the gears through the liquid. However, slowly, the epoxy sets. Within 24 hours, what we have in the box is basically a single solid chunk (if we like, we can imagine the gears were themselves made of the same kind of epoxy, and then maybe one can't even tell where the gears were—but Scenario 2 won't work in that case). A single solid chunk like that isn't a person. So, during the 24 hour epoxy curing process, the person gradually ceases to exist. If we believe there cannot be vague existence, then that's enough to yield absurdity: persons can't cease to exist gradually. But it would be absurd if some slight change in the set of the epoxy were to make the difference between existence and non-existence. But even if vague existence is possible, here there is something weird. We have a continuum between something with the kinds of non-occurrent mental states that a person has—states like knowing how to speak German and believing that naturalism is true—and something without them. Moreover, if the epoxy cures uniformly, all of these states fizzle out uniformly. Now, maybe, we could imagine a person ceasing to exist gradually by having mental abilities go away one by one, losing memories one by one, and so on. But here at any time at which we have a person, we have a person with the same full set of the non-occurrent mental states of a person, adn then eventually we have something with no mental states at all. That seems weird.
If one thinks that the person continues to exist when the epoxy cures, but simply is encased in epoxy, then one is going to have to say that a plain block of marble with an energy source can also be a person, but one encased in marble (one can make gears out of marble): there really is a Hermes in the stone. And that's absurd.
Scenario 2: The epoxy has a slightly different chemical composition from the gears. After the person has ceased to exist due to the epoxy having set, a chemical removes the epoxy, leaving the gears intact. And so we have a person again. If temporal gaps in existence are possible, this case doesn't add anything to the story. But suppose temporal gaps are impossible. Then we have something weird. For we can make an argument that the person after the removal of the epoxy is the same as the person before. Here's the argument. We can imagine a variant story. In order to clean out and cool the system, during the rest state, water is poured into the gearbox and frozen. Then it's melted and removed. Intuitively, the person should count as surviving that. But how is that different from the epoxy case when the epoxy is going to be removed? It's not—so after the removal of the epoxy, we have the same person, which contradicts the assumption that temporal gaps are impossible.