Tuesday, 19 August 2014

De Re & De Dicto Modalities & Counterparts

A vital distinction in modal logic is the one between de dicto modalities and de re modalities.

The former apply to dicta – that is, statements, sentences, propositions, and the like. That is, it is sentences, statements and propositions that are necessarily true or possibly true.

De re modalities apply directly to objects in the world. Even if we use statements, sentences or propositions to talk about objects in the world, when we say that things are necessarily or possibly true of these objects ,we're talking about the objects themselves, not about the statements we've made about them. When we say that ‘horses are animals’ is necessary, the modality involved is de dicto. The sentence ‘Horses are animals’ is necessarily true. Thus it is, perhaps, a conceptual truth: the concept [horse] and the concept [animal].

When we say that

"Socrates is necessarily a person but only contingently a husband."

we'e talking about Socrates himself, not the statement about Socrates. One can see that the modal terms ‘necessarily’ and ‘contingently’ both occur within the actual sentence itself – necessity isn't applied to the sentence. The alternative version would be:

"‘Socrates is a person’ is necessarily true."


‘Socrates is necessarily a person.’

I said earlier that it is necessarily true that a world without animals is a world without horses. Now I can say that it is necessarily true that a world without persons would be a world without Socrates. However, it's not necessarily true that Socrates at a world must be a bachelor. That Socrates is a bachelor at our world is only a contingent truth. He, or his ‘counterpart’, may be married at least one other possible world. (If worlds are infinite, he must be married at an infinite amount of worlds and a bachelor also at an infinite amount of worlds.)

Could Socrates, our Socrates, really exist at any other possible worlds, let alone an infinite amount of them? Not according to David Lewis. According to Lewis, "individuals can each inhabit only a single world" (133). Socrates, then, only exists at one world – ours! However, I used the term ‘counterpart’ earlier. Lewis believes that our Socrates can, or could have had, counterparts at other possible worlds. More precisely, "to say that Socrates is possibly rich is to say that there is a possible world in which Socrates’ counterpart is rich" (133). This counterpart can be almost exactly like our Socrates. However, I think that there are arguments to the effect that he can't be identical to our Socrates. Lewis only accepts numerical identity. This means that if Counterpart Socrates were identical, he would be our Socrates. That would mean that our Socrates would exist at other worlds. Thus he would be a ‘trans-world individual’.

Lewis believes that these other worlds exist. It follows, then, that our Socrates couldn’t exist at any other world other than our own. An identical Socrates at other possible worlds would be a ‘scattered object’ – bits of him would exist, as it were, at other worlds; just as universals are multiply scattered in different locations and at different times.

Would it help the trans-world theorist to argue that Socrates is the sum of his ‘temporal parts’? If he can have spatial parts, perhaps he could also have temporal parts. Are these theses the same? We can say that Socrates at another world is one of Socrates’ temporal parts. Socrates at our world was another of his temporal parts. Socrates at our world in the future would be another temporal part of Socrates. And Socrates in the future of another world would be a temporal part of Socrates.

However, possible worlds aren't only causally disconnected, they're also temporally disconnected. Indeed, if we have causal discontinuity, then we would also have temporal discontinuity. Thus it makes no sense to talk either of temporal or spatial parts of Socrates at other worlds.

However, perhaps we can talk about the temporal and spatial parts of Socrates in our world. That would only be when he actually existed. That is, Socrates at the age of four would have been a temporal part of Socrates. Similarly with Socrates at the age of thirty. The sum of all his ages, before he died, would be the complete Socrates. Thus we would only know of the complete Socrates after his death. Four years before he died he would have been, as it were, incomplete! A minute before he died he would have been incomplete! The spatial discontinuity of Socrates is harder to accept because that spatial discontinuity could occur at the same time. Evidently temporal discontinuity can't occur at one and the same time. Of course we can have spatial discontinuity over time in that when he was four he lived in Athens, but when he was twenty he lived in, say, Islington.

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