Identity theory can be traced back to the mid sixteen hundreds, when Descartes argued that there is a distinction between physical things (res extensa) and mental things (res cogitans). Descartes argued that physical things and mental things must be ontologically distinct from one another because each has properties that the other not only does not have – but can not possibly have.
A thought, for example, can not be hard or soft, nor can it be square and two metres extended in space; but a table can be. Likewise, a table can not intend something, or wish for something or feel anything.
But then we encounter the problem of causation. We want to say that mental events can cause physical events (I intend to put my keys in the door; and then I put my keys in the door: my arms moves towards the keyhole and puts the key inside the lock). But physics is supposed to be a closed system: only physical things can cause other physical things. Only the wind can cause a leaf to fly in to the air, for example. But it seems like mental things (thoughts) do cause physical things – actions, like putting my keys inside the lock to open the door, or pouring a glass of water for me to drink.
One way to get around this problem is to say that mental things are physical things. Some neuroscientists have identified the feeling of pain as a ‘c-fibre’ in the brain. Each time we experience pain, what we are experiencing is a c-fibre firing in the brain. Pain is c-fibre firing, in the same way that a=a, and I am me.
This is where Leibniz’ laws of identity come in to play. Leibniz’ law of indiscernibles states that if a and b share all of the same properties, then a=b. Conversely, if a has a property (or properties) that b doesn’t share, then a and b are not identical. So how does this fit in to the argument at hand? Well, as we saw earlier, mental things do have different properties to physical things. According to Leibniz’ law of indiscernibles, this means that pain cannot be the same thing as c-fibres firing.
This then takes us to Kripke’s argument. Kripke argues that a=b is a logically necessary relation – meaning that a must = b in every possible world. Secondly, he argues that the relation between mental and physical things is not a necessary relation (see Descartes/Leibniz above). Therefore, mental things (a) are not the same as physical things (b).
Since this is a valid argument (the conclusion follows logically from the premises), if we are to dispute its conclusion, we must argue that one or the other of its premises is untrue. One way to do this would be to say that there are possible worlds in which a does not equal b. To do this for the example of pain, you could argue that ‘pain’ is a non-rigid designator. A rigid designator is something that designates (points to) the same thing in every possible worlds (example = me). A non-rigid designator then is something that does not designate the same thing in every possible world (example ‘the person called Sally’). If we argue that pain (the experience of it, not the word) is conceivably something other than pain in another possible world, then we sidestep the first premise.
To sidestep the second premise, we would have to argue that mental things are the same things as physical things, so a pain cannot be anything but a c-fibre firing, and vice versa. But as we saw earlier, pains and c-fibres have different properties, which means that – according to Leibtniz’ law of indiscernibles, – they cannot be the same thing.
Moreover, the properties that differ between physical things and mental things aren’t merely contingent properties – (my eyes are blue, but they could have been brown); they are necessary – (as a human being, I am bipedal). There is something necessary to pain that isn’t necessary to c-fibres – i.e. it’s subjective content; what it feels like. If this is true, then we must conclude that mental things and physical things are ontologically different – taking us back full circle to the argument that Descartes made in the sixteen hundreds.
When we try to think of pain as c-fibres firing in the brain, we lose the thing that makes pain pain (its subjective content), meaning, more broadly, that whenever we ascribe a physical state to a mental state, we don’t merely point to the mental state in the way that I would point to ‘me’: we eclipse it.
*This post is a written run through of a lecture given by Marianne Talbot at the University of Oxford, which you can watch here.