Denoting and Disquoting

ABSTRACT

Fregeans hold that predicates denote things, albeit things different in kind from what singular terms denote. This leads to a familiar problem: it seems impossible to say what any given predicate denotes. One strategy for avoiding this problem reduces the Fregean position to form of nominalism. I develop an alternative strategy that lets the Fregean hold on to the view that predicate denote things by reconceiving the nature of singular denotation and of Fregean objects.

KEYWORDS:

• denotation
• concept horse paradox
• singular terms
• predication

Notes

¹ Compare the following familiar clause for disjunction:

• or is true iff is true or is true.

This specifies what is required for the truth of any compound sentence formed using ‘or’, but doesn't treat ‘or’ as denoting anything. Contrast it with the following clause:

• Den( or ) = Truth iff Den(‘or’) applied to Den() and Den() yields Truth,

which treats ‘or’ as denoting a function on pairs of truth values (and sentences as denoting truth values).

² I've here used cognates of ‘denote’ for the German ‘bedeuten’, following the usage in Furth's translation of Basic Laws. I will also generally use the term ‘property’ in place of Frege's term ‘concept’. Frege himself uses the term ‘property’ in a different but related sense [1892b: 189]: ‘I call the concepts under which an object falls its properties.’ So, Frege is willing to identify concepts with properties; it's just that he conceives of properties always as properties of an object. I will here use ‘property’ in the way that Frege uses ‘concept’—as a label for the kinds of things that predicates denote.

³ See Proops [2013] for an overview of the various interrelated problems that this generates.

⁴ Compare Ajdukiewicz [1935]. Frege himself might have set things up differently, since he regarded sentences as singular terms or names (of truth values). Again, my aims are not historical.

⁵ One natural starting point would be Dummett's [1973] proposal, inspired by remarks in Frege [1892a], that we state the denotation of predicates by means of constructions of the following sort: wise is what ‘wise’ denotes, by analogy to how we might say that wise is what Socrates was. For critical discussion of this and other proposals in the vicinity, see my [2016]. Objections of a somewhat different sort to Dummett's proposal are raised by Dudman [1976], Wiggins [1984], Wright [1998], MacBride [2006], Textor [2010], and Hale and Wright [2012], among others.

⁶ Compare also Krämer [2014] and Jones [2016] for similar proposals about predicate ‘denotation’.

⁷ Frege [1902: 136-7] appears to endorse the nominalist conclusion in a letter to Russell:

We cannot properly say of a concept name [predicate] that it denotes something; but we can say that it is not denotationless. It is clear that function signs or concept names are indispensable. But if we admit this, we must also admit that there are some that are not denotationless, even though, strictly speaking, the expression ‘the denotation of a function name’ must not be used.

Predicates, in other words, are not meaningless (bedeutungslos, or ‘denotationless’) since they occur as parts of meaningful sentences. But their meaningfulness does not lie in their denoting anything.

⁸ I have previously [2016] noted the role that disquotation plays in generating the paradox, and the possibility of avoiding it by rejecting disquotation. In that work, I pursued an alternative, non-Fregean, approach to predicate denotation.

⁹ Although I'm not convinced by Trueman's argument, it does demonstrate an intriguing point: namely, that the co-referentiality of two terms can entail something about what one of the terms refers to, provided that one of the terms itself involves the notion of reference (and granted some auxiliary assumptions about the semantics of identity statements and the disquotational character of the truth predicate). Still, the fact that two expressions are co-referential does not in general entail anything about what either of them refers to.

¹⁰ Compare Kaplan [1989] and Pryor [2007], who articulate proposals involving singletons and ordered pairs, respectively. Another non-disquotational view in the vicinity is Montague's [1973] proposal that singular terms denote second-order properties. For example, ‘Alice’ denotes (not Alice but) the property that holds of all properties under which Alice falls. However, this proposal is open to the charge that it is not an anti-disquotational account of singular denotation, but rather a proposal to eliminate the category of singular terms by assimilating them to quantifiers phrases.

¹¹ See Heim and Kratzer [1998: sec. 2.5], who recommend reading lambda-expressions as terms. This contrasts with a view sometimes found in the literature according to which lambda expressions like ‘ is wise]’ are predicates.

¹² On the anti-disquotationalist view, the quote name ‘“wise”’ doesn't denote the predicate ‘wise’ but, rather, denotes (‘wise’), a Fregean object that unpacks into the predicate ‘wise’.

¹³ The problem that Liebesman [2015] raises is reminiscent of a problem about ‘denoting concepts’ that Russell [1905] discusses in his Gray's Elegy Argument, having to do with how to construct propositions that are about denoting concepts themselves, rather than about the things that they denote. (Thanks to an anonymous referee for noting this.) Here, too, the natural suggestion is that such propositions must contain ‘second-level’ denoting concepts, i.e. ones that denote denoting concepts. Russell rejects this proposal, although his reasons are not entirely clear. For attempts at reconstructing Russell's argument, see Hylton [1990], Noonan [1996], and Salmon [2005], among others.

¹⁴ Thanks to an anonymous referee for pressing this point.

¹⁵ Or (to take a more mundane example) I've been investigating the denotation of ‘wise’, but I could also investigate a crime scene, so the investigation relation can relate me to both semantic and non-semantic entities. An example of functions that occupy the non-semantic realm (in the sense of not being denotations) and that don't obey type restrictions are our pair of and its inverse : the latter, for example, has among its values semantic entities of different types, as well as non-semantic entities like Alice.

¹⁶ Thanks to Devin Frank, André Gallois, Richard Lawrence, Kris McDaniel, two anonymous referees, participants in my spring 2016 seminar at Syracuse, and audience members at a symposium at the 2017 Central APA for discussion of this material.