Concluding Notes

This chapter revisits from a synoptic perspective two of the main themes of the book. First, the critique of descriptivism based on indeterminacy cases and the proposal of mere roughly sufficient conditions for the reference fixing of demonstratives, proper names, and ordinary natural kind nouns. And second, the proposal that Arabic numerals, ordinary natural kind nouns, and adjectives for sensible qualities have, despite popular eliminativist arguments to the contrary, referents of a relatively ordinary nature appropriately determined in subtle ways by their associated reference-fixing conventions. The two themes of the book revisited in these concluding notes are related to an important part of the spirit of Kripke’s work on reference.

Words for Sensible Qualities and the Problem of Perceptual Variation

This chapter proposes a picture of reference fixing for color adjectives and adjectives for other sensible qualities, according to which the relevant reference-fixing conventions allow those adjectives to be used with different intended standards in different contexts. It is argued that this explains the fact (used by secondary-quality theorists and eliminativists in “perceptual variation arguments”) that different equally normal people classify the same object by means of prima facie incompatible color adjectives, and that the explanation is perfectly compatible with the properties referred to by uses of these adjectives being primary qualities or objective properties. It is also argued that the picture satisfies a number of desiderata not satisfied by other objectivist theories in the literature.

Arabic Numerals and the Problem of Mathematical Sophistication

This chapter begins with a critique of views on which the reference of a complex Arabic numeral is fixed by a sophisticated mathematical description. The chapter proposes instead that that reference is fixed by a convention that assigns to the numeral “1” the number one and that assigns to the numeral for n+1 the number greater by one than the number assigned to the numeral for n. This view, which presupposes that the sequence of Arabic numerals is learned independently of any principle of referential interpretation, evades the objections to sophisticated descriptivist theories. Toward the end of the chapter, a view of the referents of the numerals is defended according to which these are the finite cardinality properties. This view is argued to be the only one compatible with a number of principles constituting the intuitive conception of number and presupposed in the referential intentions of users of the numerals.

Nouns for Natural Kinds and the Problem of Arbitrariness

This chapter explains the “Kripke-Putnam orthodoxy” about the reference fixing of ordinary natural kind nouns, and some objections to it, especially “arbitrariness problems”: for example, a Kripke-Putnam baptism for “water” doesn’t discriminate between, say, H2O and P2O (H2O where the isotope of hydrogen involved is protium oxide, as in regular paradigms of water). The chapter presents a picture of reference fixing for natural kind nouns that refines the Kripke-Putnam picture and that appeals to sets of roughly sufficient conditions for reference and reference failure. It is argued that on this picture the referents of ordinary natural kind nouns turn out to be “ordinary kinds,” kinds which are vague along dimensions along which scientific kinds are precise: the reference of “water” is “the ordinary kind water” rather than H2O or other scientifically identified kinds. It is argued that this suffices to dispose of the arbitrariness worry on a broadly Kripkean view.

Proper Names and Referential Indeterminacy

This chapter begins with a critique of “causal descriptivist” theories and other theories of necessary and sufficient conditions for the reference of proper names. The main criticism appeals to examples of referential indeterminacy for names and argues that no foreseeable way of complicating a “causal” reference-fixing description or other kinds of necessary and sufficient conditions for reference will be extensionally correct for cases of indeterminacy. This leads to the postulation of a picture of reference fixing for name uses according to which this is governed by a set of roughly sufficient conditions for name reference and reference failure. A number of these conventions are stated, and it is argued that they yield extensionally correct predictions for several examples of name reference and reference failure appealed to earlier in the chapter, and no predictions in the cases of apparent indeterminacy.

Demonstratives and Conflicting Intentions

This chapter begins with a critique of “overriding intentions” theories of the reference-fixing conventions for demonstratives, designed to account for cases of conflicting referential intentions behind successful uses of demonstratives. These criticisms and the existence of examples of conflicting intentions where the reference of the demonstrative seems indeterminate are argued to suggest that there may be no general necessary and sufficient conditions for some thing to be the reference of a use of a demonstrative. This motivates the proposal that the conventions governing reference fixing for demonstratives form just a set of roughly sufficient conditions for reference and reference failure of uses of demonstratives. Some of these conditions are listed, and it is argued that they yield an extensionally correct account of the examples of determinate reference and reference failure used in the preceding discussion, and that they do not yield any prediction in the examples that involve indeterminacy.

Reference

This introductory chapter adopts and develops the consequences of two basic ideas about reference: that the reference of an expression use is the thing that constitutes the expression use’s contribution to the truth condition of the sentence in which it appears; and that the reference of an ordinary expression must typically be some thing that some ordinary speaker has at some point intended to refer to with the expression. It is postulated that communication can often be explained by the existence of shared conventions for fixing reference in this sense, viewed as rules that speakers have gotten used to abide by. The chapter sets forth the book’s projects of stating the conventions that govern reference fixing for several expressions, and of dissolving a number of puzzles that have led some to think that those conventions cannot really manage to fix appropriate referents. A preview of the remaining chapters follows.