Individuating Fregean sense

Abstract

While it is highly controversial whether Frege's criterion of sameness and difference for sense is true, it is relatively uncontroversial that that principle is inconsistent with Millian–Russellian views of content. I argue that this should not be uncontroversial. The reason is that it is surprisingly difficult to come up with an interpretation of Frege's criterion which implies anything substantial about the sameness or difference of content of anything.

Keywords::

• Frege
• sense
• meaning

Acknowledgements

The author thanks for helpful comments on previous versions of this paper to Patricia Blanchette, Ben Caplan, David Hunter, Casey O'Callaghan, and Gurpreet Rattan.

Notes

^1. One might think – especially since the problems to be discussed below arise from just this aspect of Frege's criterion – that we should give criteria for sameness and difference of Fregean sense directly in terms of properties of senses, rather than in terms of properties of bearers of senses. But it would be hard to do this without giving an account of what sorts of entities senses are – and if we could do this, we would hardly need an account of sameness and difference of sense of the sort which Frege's criterion aims to provide. I return to Fregean views which do not rely on Frege's criterion in the final section below.

^2. See, respectively, Salmon (1986) and Fine (2007).

^3. Frege (1979, 197).

^4. But see Van Heijenoort (1977) for some scepticism as to whether Frege had an unequivocal view on this topic.

^5. For some possible solutions to this sort of problem, see Schellenberg (2012).

^6. One might wonder why the modal operator from the previous formulations has disappeared from this one. The reason, as will become clear from what follows, is that sentence tokens have their contents only contingently, so that what we really want to be doing is comparing sentence tokens at worlds and times with each other. See note 7.

^7. The fact that sentence tokens do not have their contents essentially is also the explanation for one feature of Sameness & Difference which might seem puzzling, and that is the fact that the modal locution used in typical statements of Frege's criterion (‘…an ideal subject could do such-and-such’) is absent from it. Given that sentence tokens can have different contents in different worlds, we cannot simply look at all of the possible judgements of ideal subjects about some pair of sentence tokens, on pain of leading to the result that every sentence token differs in sense from itself.For that reason, when we are talking about subjects’ attitudes towards sentence tokens, we should take this as shorthand for attitudes towards sentence tokens in a world and at a time. We can then understand the quantification over sentences tokens in Sameness & Difference to be quantification over triples of sentence tokens, worlds and times such that the relevant sentence token exists in that world at that time.Nor, it is worth noting, would it matter much if we had a view of the metaphysics of expression tokens on which they had their contents essentially. For then our stipulation that we consider the same expression token in different worlds would build in the assumption of sameness of sense, and we could re-raise the dilemma in the text about the conditions under which a given inscription, or sound wave, had the same content as the expression token to be evaluated.

^8. Heck and May (2011, 142–143) point out that the view that Frege's criterion is somehow constitutive of sameness and difference of sense is inconsistent with Frege's aim of explaining sameness and difference of sense at the level of sentences in terms of sameness and difference of sense for subsentential expressions.

^9. Some Fregeans have been content to rely on a condition for difference of Fregean sense without worrying about a condition for sameness of sense; a prominent example is Evans (1982).

^10. As above, more strictly: pairs of triples of a sentence token, time and world.

^11. As above, one could object that we might only consider B's possible uses of that very sentence token. But this delays rather than solves the problem. Given that sentence tokens do not have their senses essentially, we will have to provide some restrictions on the relevant class of possible tokenings, which will amount to giving a relation between sentence tokens which will face the dilemma just sketched.

^12. One suggestion for avoiding this problem would be to define conditions for sameness of sense, not sentence by sentence, but via requirements for sameness of sense of various types of subsentential expressions. We could then ascend to the sentence level via some appropriate compositionality principle. I do not quite see how this approach would work, since I am not sure how to formulate the conditions for sameness of sense of, for example, two predicates. But it is an approach which is not ruled out by any of the arguments above.

^13. Parallel worries arise for the attempt to treat Frege's criterion as part of a ‘local holism’ involving claims also terms like ‘understanding’ and ‘rational’. The worry is that the ordinary interpretations of these terms are too weak to define Fregean sense, leading to problems like those discussed in connection with Reportability. But if we stipulatively define more demanding interpretations of these terms, we run into the same problems as with the deflationary interpretation of ideal conditions.Parallel circularity problems also arise for views of ideal subjects as ones who know all the a priori truths. According to the Millian, after all, ‘Hesperus is Phosphorus’ is a priori (or close enough). One might do better if one could buttress the view of ideal subjects as knowing all the a priori truths with a theory of a prioricity which delivered the result that ‘Hesperus is Phosphorus’ is not knowable a priori, like that given by epistemic two-dimensionalism. For doubts about the epistemic two-dimensionalist's treatment of the a priori, see Schroeter (2005) and Speaks (2010).

^14. One might think that this shows that the Fregean should simply get rid of reference to what a subject who was rational, reflective, etc. would do, and focus on properties of actual subjects. One person who develops an account of Frege's criterion along these lines is Schellenberg (2012). Her account is framed, not in terms of what an ideal subject would do, but in terms of what our rational commitments with respect to a pair of sentences are. Very roughly, and ignoring some important subtleties, the idea is that sentences differ in sense for a subject if that subject is not rationally committed to taking them to have the same truth-value.This does avoid the problems to do with ideal subjects, but it seems to me that those problems re-emerge in another form. Consider a pair of subjects, who are, respectively, unsure whether the following pairs of sentences have the same truth-value:

(1a) Hesperus is Phosphorus.(1b) Hesperus is Hesperus.(2a) Secretariat is a horse.(2b) Secretariat is a steed.

In what sense must the second subject violating her rational commitments in a way in which the first subject is not? Neither might be, in any ordinary sense, irrational. It seems to me that to explain the sense in which the second subject must be irrational, even though the first is not, we will have to use (as above) the premise that ‘steed’ and ‘horse’ have the same sense, whereas ‘Hesperus’ and ‘Phosphorus’ do not. But then we would again be feeding into the account what we wanted to get out of it.

^15. Though, perhaps not coincidentally, neo-Fregeans like Chalmers are sometimes sceptical of the idea that we can make clear sense out of the Fregean's distinction between informative and non-informative sentences, and try instead to supply a kind of successor to Fregean senses which can play many, even if not all, of the theoretical roles that senses were supposed to play.