Background
We said that, on a possible interpretation of paragraph 6 of the Second Meditation, Descartes offers there what amounts to an argument for the conclusion that he is not his body.
That argument trades on Leibniz’s Law (also known as the principle of the indiscernibility of identicals) – the principle that a thing and itself have all ‘their’ properties in common. If a is the very same individual as b, then a and b must be exactly alike in all respects. And that is dead obvious: after all, ‘they’ are not two things but one thing; and one thing cannot simultaneously be both this way and that way in the same respect. A thing cannot, for example, be both green all over and red all over, or both cuboid and spherical in shape.
Leibniz’s Law, though completely obvious, is a useful rule that we apply subconsciously every day. For example, if I have forgotten exactly where I parked it, I can pick my bicycle out of the crowd of bicycles not merely by looking for a bike with its features, but also by differentiating it from others: by spotting features of other bikes that I know my own bike does not share. My bike is green; so in scanning the racks I can instantly dismiss all the non-green bikes. My bike hasn’t got mudguards; so I can dismiss all the bikes with mudguards. And so on.
In doing so I can be thought of as subconsciously running arguments of the following kind through my head:
(1) My bike is green
(2) That bike is not green
Thf
(3) That bike is not my bike
My bike has a property – being green – that that bike lacks. So that bike is not my bike.
The argument that Descartes presents (if he is to be interpreted as so doing at all) is of similar form:
(1) I can coherently entertain doubt about whether my body exists.
(2) I cannot coherently entertain doubt about whether I exist.
Thf
(3) I am not my body.
That is: My body has a property that I do not have: It has the property of being able to be doubted by me. I lack the property of being able to be doubted by me. So I and my body must be two different things.
The fallacy
Descartes’s argument – unlike the one about my bike – is clearly fallacious. It is an instance of what is known as the ‘masked man’ fallacy – so called because it can be presented in a standard way as follows: imagine that you have witnessed a bank robbery by a masked man, and that in considering the possible identity of the robber you reason thus:
(1) I don’t know who the masked man is.
(2) I know who my father is.
Thf
(3) The masked man is not my father.
In doing so, you are applying Leibniz’s Law as before: you are reasoning that your father has a property (the property of having his identity known by you) that the masked man lacks; and concluding that your father and the masked man must therefore be different individuals.
But if you reason like that, you are making an obvious mistake: for it could be, for all you know, that it was your father who was robbing the bank. (It would hardly be surprising if he was, given the level of the school fees…)
The explanation of the inapplicability of Leibniz’s Law in these cases is that the principle cannot be applied where the properties on the basis of which a distinction is made are properties that involve reference to a person’s intentional states (doubting and knowing, in the two cases above).
You get a similarly fallacious result if you try to apply Leibniz’s Law on the basis of a difference in modal properties (properties including reference to necessity and possibility), as shown by the following fallacious argument:
(1) Michael Clarke is necessarily Michael Clarke. (True: everyone is necessarily self-identical).
(2) Michael Clarke is not necessarily the captain of the Australian cricket team. (True: the ACB could have appointed someone else)
Thf
(3) Michael Clarke is not the captain of the Australian cricket team. (False: he is)
Alleged difference between Michael Clarke and the captain of Australia: one of them but not the other has the property of being necessarily identical with Michael Clarke. But again, the argument is clearly fallacious: the premisses are true, but the conclusion is false.
OK but which properties? How to identify them?
The interesting question is this: What is the mark of these special properties that mean that you cannot apply Leibniz’s Law?
In most sentences, you can replace one name for a person or thing with any other name or definite description that refers to that same person or thing, and the truth value of the sentence will remain unchanged. We say that the different names or descriptions can be substituted, one for another, ‘salva veritate‘ (Latin: literally, ‘with the truth intact’ – i.e. without affecting the truth or falsity of the sentence).
(a) David Mackie is underpaid.
(b) The Philosophy teacher is underpaid.
(c) The father of Nicolas and Andreas is underpaid.
(d) Phoenix’s owner is underpaid.
Given that (a) is true, then (b), (c) and (d) are all equally true. And if (a) is false, then so are (b), (c) and (d). All the underlined phrases refer to the same individual, and using one name or description rather than another makes no difference to the truth-value of the sentence.
Where names and definite descriptions can be interchanged salva veritate, we say that the context in which the name/description appears is ‘referentially transparent’.
In other contexts, you cannot substitute salva veritate in the same way:
For example:
(e) Jones believes that David Mackie is David Mackie.
This is true. Jones would have to be an utter moron not to believe that: even if Jones had never previously heard of me, he would still believe it, because it’s obvious that such statements of identity that repeat the name of an individual must be true.
But
(f) Jones believes that David Mackie is Phoenix’s owner.
Sentence (f) may be false, even if (e) is true. If Jones doesn’t know that I own a thing called Phoenix, then he won’t believe that I am Phoenix’s owner; and so (f) will be false. So the substitution of ‘Phoenix’s owner’ for ‘David Mackie’ makes (or may make) a difference to the truth value of the sentence. You cannot substitute salva veritate.
Again:
(g) It is impossible that David Mackie should be someone other than David Mackie.
Obviously true: no one can be anyone other than the person that (s)he is.
(h) It is impossible that Phoenix’s owner should be someone other than David Mackie.
Obviously false: I could sell Phoenix.
Sentence (g) is true, but sentence (h) is false. But the only difference is that, once again, we substituted the definite description ‘Phoenix’s owner’ in place of ‘David Mackie’. So in this context too, you cannot substitute salva veritate.
Contexts in which you cannot substitute salva veritate are labelled ‘referentially opaque’. As you can see in the examples above, intentional contexts ‘Jones believes that…’ and modal contexts ‘It is impossible that…’ are the culprits.
Why does this happen?
Well, the point about the referentially opaque contexts is that they are contexts in which whether what is said of some individual is true or false depends on the way in which the individual is referred to – the truth or falsity of the sentence depends on how the individual is named or described.
The properties with which you cannot invoke Leibniz’s Law to demonstrate a non-identity are precisely the properties that create referentially opaque contexts.
Finally
All of the above is just a technical and fussy way of spelling out what is very obvious anyway, at least insofar as the Cartesian argument (if that is what it is) is concerned.
This is because, of course, Descartes is in no position to deny the possibility that his thought may in fact depend on his possession of a body: for all he knows, thinking requires the brain (as we all believe). The fact that he is unable to doubt his own existence, but at the same time apparently able to doubt the existence of his body, reveals only that he is ignorant of the essential link between thinking and having a body. If he knew all the facts, including the fact (if it is a fact) that thinking requires a brain, then he would no longer be able to doubt the existence of his body, given that he cannot doubt his own existence.
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