Frege pipes up

Abstract

During his recent discussion of whether theories of demonstratives can handle Frege’s Puzzle, Martone considers the following case:

The Pipe Case: Two plumbers come to my house to fix a leak in a kitchen pipe. With a chisel, the first plumber opens two holes in the wall, exposing two pipe segments. He wonders whether they are the same pipe. To inform him that they are, I say ‘that pipe is that pipe’. Unbeknown to us, his chiselling made the plaster on the other side of the wall fall off, exposing the whole pipe from that side. The other plumber was on that side of the wall, and was able to perceive and understand my utterance through a large window. He could see clearly that the two segments I pointed to belonged to the same pipe, so my utterance of ‘that pipe is that pipe’ was uninformative to him. (2023: 63)

He reaches quite a pessimistic conclusion: first, he claims that it is clear that any theory of demonstratives that aims at accommodating cognitive significance so as to solve Frege’s Puzzle should explain the Pipe Case. Second, he maintains that any explanation of the Pipe Case would need to rely on an implausible individualistic theory of demonstratives, according to which, for each individual hearer in the context, the semantic value of a demonstrative utterance depends on some facts about the hearer, such as facts about their perceptions, so that the semantic value can vary from hearer to hearer (2023: 66–67). He then concludes that any attempt to exploit the ingredients of the semantic machinery of demonstratives to solve Frege’s Puzzle seems hopeless.

It is surely the case that any theory that aims at accommodating all that is cognitively significant should explain the Pipe Case, but is it clearly the case that any theory of demonstratives that aims at accommodating cognitive significance so as to solve Frege’s Puzzle should explain the Pipe Case?

Let us check (once again!) Frege’s ‘Sense and Reference’:

a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extension of our knowledge and cannot always be established a priori. (1948 [1892]: 25, my emphasis)

What are the relevant a = a and a = b in the case of demonstratives? We need two utterances such that, in the first, the same means to refer to the relevant object occurs twice, exactly as with ‘Hesperus is Hesperus’, where the same means to refer to Venus is employed twice, while, in the second, two different means occur, exactly as with ‘Hesperus is Phosphorus’, where different means to refer to Venus are employed. Let us then use ‘that_d’ to indicate a particular utterance of ‘that’ together with the demonstration d it is linked to. Let us set aside particularly unusual cases such as those in which multiple demonstrations occur simultaneously, or in which the directing intention departs, for whatever reason, from the demonstration. To avoid the orthogonal problem of establishing what kind of thing is demonstrated (a colour? a pipe? an undetached part of a pipe?), together with Martone, let us employ complex demonstratives. Frege’s Puzzle seems generated by the following utterances:

• (1) That_d′ pipe is that_d′ pipe.

• (2) That_d′ pipe is that_d″ pipe.¹

The cognitive difference any solution to Frege’s Puzzle needs to accommodate is the one between (1) and (2), and the puzzling question that needs to be answered is how it is possible for two utterances apparently identical in structure and reference to be such that only one of the two often provides subjects with something new.² Frege’s Puzzle is not a puzzle about how the same utterance often but not always provides subjects with something new, and it is unclear why a theory aimed at solving Frege’s Puzzle should explain that. It is surely true that (2) does not provide everybody with something new, the second of Martone’s plumbers arguably being a case in point. But if this is a puzzle, it is not Frege’s Puzzle, exactly in the same way that we do not have Frege’s Puzzle in the fact that what is expressed by ‘The author of this piece is’ followed by my surname would provide the reviewer for this reply, reviewing anonymously, with something new, but would not provide me with something new. Why would a theory of demonstratives need to explain this?

Any theory that aims at accommodating all that is cognitively significant will indeed need to explain Martone’s case, and the explanation will, plausibly, be individualistic, as it will take into account the difference in the perceptions of the two plumbers. But a theory of demonstratives that aims at solving Frege’s Puzzle does not need to explain all cognitive differences. For example, it does not need to explain why my utterance of ‘After that claim, Frege piped up’ led only one of my friends to learn of the existence of ‘to pipe up’. As it does not seem to need to explain Martone’s case either, such a case seems unable to shatter our hope of getting a solution to Frege’s Puzzle by exploiting the ingredients of the semantic machinery of demonstratives.

Funding

This work was supported by the AHRC (grant number AH/Y001494/1).

References

Footnotes