Dummett's Backward Road to Frege and to Intuitionism - Tripod

I think this way out makes nonsense of the metaphysical gap-and-binding Frege requires to
unify the thought as an entity. Frege says he cannot explain the unity of a thought without admitting
unsaturated senses (1970d: 54), as Dummett is well aware (1981: 265). And if unsaturated senses are
not really unsaturated, they cannot really unify thoughts. On the face of it, Frege’s texts expressly make
saturation a transcategorial bond applying in the realm of references and the realm of senses alike.
Frege’s arguments and his language are equally serious in both realms. 22 Frege says that if we allow the
same thing to “occur now as object, now as concept[,]....the difficulty...is only shifted” because
thoughts need to “hold together” (1970d: 54; see 55), implying that functions and incomplete senses
face the very same metaphysical difficulty. Indeed, he says, “The words ‘unsaturated’ and ‘predicative’
seem more suited to the sense than the meaning [i.e. reference]; still, there must be something on the
part of the meaning [i.e. reference] that corresponds to this” (Frege 1979e: 119 n.*, my emphasis). This
implies that the unsaturatedness of incomplete senses is primary and that of functions derivative. Thus
if incomplete senses are really complete entities with gaps in a merely nominal sense, then functions
are really complete too, and even more so, since their incompleteness is derivative. 23
Frege states his metaphors of incompleteness and unsaturatedness for incomplete senses and
functions alike. On Dummett’s view, why would Frege even bother with these metaphors in the case of
incomplete senses? There would be nothing real for them to be metaphors of. On Dummett’s view,
perhaps Frege should have said that incomplete senses are not like functions because incomplete senses
are really complete. Perhaps Frege should have offered metaphors of their real completeness. Perhaps
Frege should have said that an ostensibly incomplete sense is not like a cloak, and is really like a body
that fills out a cloak, unlike functions, which are really like cloaks. But Frege says the opposite.
Thus Dummett’s way out vitiates Frege’s thesis that expressions, senses, and references stand in
a modeling relationship such that all mirror each other (Frege 1970e: 123). Surely it is unrewarding to
hold that the mirroring merely implies “There is a so-called incomplete sense,” and not also that it has a
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