Two aspects of propositional unity

Abstract

The paper builds upon familiar arguments against identifying the proposition that Brutus stabbed Caesar with a given sequence containing Brutus, Caesar, and the stabs relation. It identifies a further problem, one that affects not only traditional Russellian accounts of propositions, but also the recent act-theoretic approach championed by Scott Soames and Peter Hanks. The problem is that there is no clear content to the idea that the pair  < Brutus, Caesar> instantiates the stabs relation. It is argued that this further problem presents a decisive objection to the act-theoretic approach to propositions.

Keywords::

• Benacerraf problem
• cognitive act
• predication
• Bertrand Russell
• Scott Soames
• unity of the proposition

Notes

^1. Contemporary Fregeans hold a similar view, and differ from Russellians only in the nature of the constituents. I will limit discussion here to the Russellian approach, but the conclusions apply with the same force to contemporary Fregean approaches. (I will, however, omit discussion of the traditional Fregean approach to the unity problem.)

^2. Of course, most Russellians do not address the question raised here. But it would seem that, between (i) assuming arbitrarily that, say, < < Brutus, Caesar>, stabs> and not, for example < stabs, < Brutus, Caesar>> counts as the proposition that Brutus stabbed Caesar and (ii) acknowledging that propositional structure is resistant to analysis, she would choose (ii).

^3. Brandom (1994, 6–7) expresses a more general worry, concerning how representations represent. But since his particular concern is with ‘intentionality in the sense of the propositional contentfulness of attitudes’ (7; emphasis added) it seems not too far removed from the representation problem.

^4. See also Jubien (2001) and King (2007).

^5. I owe this point to Robert Stalnaker, made during the question period after Peter Hanks' paper, ‘Propositional Content, Semantic Content, and Types of Speech Acts,’ Columbia University, 28 September 2013.

^6. If Williamson (1985) is correct, then a relation like stabs is identical to its converse. In that case, not only is there no unique proposition corresponding to, say, (2), there is no unique interpretation of (2) even relative to (C-1).

^7. One might have argued as follows: ‘If something is to count as the proposition that Brutus stabbed Caesar it must be intrinsically representational: that is, have its truth conditions essentially and absolutely, without relativization to a language or set of conventions. Since neither (2) nor (3) has its truth conditions independently of (C-1) or (C-2), it immediately follows that neither (2) nor (3) can be identified with this proposition.’

The general thrust of the argument is that since, say, (2) is not intrinsically representational, it cannot count as the proposition that Brutus stabbed Caesar. As I have already stated above, in my view the central problem concerns unity, and not representation. Accordingly, the reason that (2) is not a proposition is precisely that it lacks unity – it is a mere list of propositional building blocks (a phrase I've appropriated from Stephen Schiffer) rather than a content-bearing item. Moreover, as a mere list it is in competition with other lists that would seem to be equally good candidates for the relevant proposition. Thus, while the quoted argument is indeed a more expedient route to our conclusion, it obscures the real problem – namely Russell's problem of unity.

^8. But see Candlish (1996, 111–112) and Sainsbury (1996, 141–142).

^9. To get a feel for what I have in mind, imagine an indexical relation, R, such that aRb if either a is taller than b and it is an even-numbered day or b is taller than a and it is an odd-numbered day. R here unifies a and b but does so differently depending on the day. I am imagining a similar relation, but where the mode of unification is entirely random – not a ‘function’ of anything.

^10. It may well be that there can be no process that unifies a and b without doing so in a structurally determined manner – i.e. such that the resulting unity is a function of a, b and their order of occurrence. This is just to say that the two problems are at root one. If so, then one cannot address the problem of generic unity without addressing the problem of structurally determined unity. This would suggest that, to the extent that the efforts of Soames and Hanks to solve the problem of unity fail to solve the sub-problem, they really do not solve the problem at all: the ‘sub-problem’ just is the problem of unity in another manifestation. See Candlish op. cit. and Sainsbury op. cit.

^11. In contrast, we are assuming for argument's sake that there is intuitive sense to be made of the definiendum. But there may be a problem here as well; see Section 5, below, for discussion.

^12. I defer, for the moment, discussion of the ‘qua’ idiom.

^13. In Section 5 I try to make sense of what this might mean; for the moment I take the attribution of argument structure as a primitive.

^14. I can rest with a weaker point here: Unless the proponent of (7) shows that the added requirement does not simply amount to the condition that the occupant of stabs_STABBER stabs the occupant of stabs_VICTIM, we are not assured of a non-circular analysis. It is difficult to see how this could be done.

^15. Soames appears generally insensitive to the worry about predetermined unity, but he clearly has in mind that an agent predicates a relation of a sequence, and not an undifferentiated multiplicity.

^16. I assume this for the sake of argument. As I show (Section 6), the monadic case is also problematic.

^17. This is clear from an equivalent formulation:

15* ‘x stabs y’ is true of < a, b> just in case < a, b> is in { < z, w>|‘x stabs y’ is true of < z, w>}.

^18. But it is crucial to see that merely being told that S is true just in case < a, b> is in I(stabs) doesn't tell us whenS is true. A convention is typically adopted according to which the ordering in < a, b> mirrors the ordering in ‘aRb’ – that is, that < a, b> is in I(R) just in case ‘aRb’ is true. Once we know this, we can know precisely when ‘aRb’ is true. The problem is that, without the convention, the statement of the truth condition is incomplete – we don't know yet when the sentence is true – and given the convention, the statement of the truth condition is superfluous – we already know when it is true. Again, since the model theorist is providing a definition of truth, not revealing a mysterious property of sentences in the language, this is not a problem. Still, it is important to appreciate what she is not doing.

^19. This and the following paragraph use techniques developed in Kaplan (1968).

^20. Collins (2011, 33–34) argues (convincingly, to my mind) that we cannot genuinely explain unity if we begin, as here, with a unified whole. In particular, if we begin with a unity we cannot explain why there are certain unities or wholes and not others. I cannot do justice to Collins' arguments here. For further discussion, see Chapter 3 of Collins (2011).

^21. Thanks to Ray Buchanan, David Hunter, Oliver Marshall, Frank Pupa, Gurpreet Rattan, Adriana Renero and Rosemary Twomey for helpful comments on a previous draft, and to Frank, Ray and Gurpreet for extended and fruitful discussions on the topic.

Additional information

Notes on contributors

Gary Ostertag

Gary Ostertag is the Director of the Saul Kripke Center at The Graduate Center of the City University of New York, where he is Adjunct Associate Professor of Philosophy. He is also on the faculty of Nassau Community College. He is the editor of Definite Descriptions: A Reader (MIT Press, 1998) and Meanings and Other Things: Essays on Stephen Schiffer (Oxford University Press, Forthcoming) and has published in the philosophy of language, the history of analytic philosophy and musical ontology.