The Temperature Paradox as Evidence for a Presuppositional Analysis of Definite Descriptions

Montague's (1973) analysis of the temperature paradox is well known. Sentences (1), (2),and (3) are assigned logical translations equivalent to (4), (5),and (6), respectively.

(1) The temperature rises.

(2) The temperature is ninety.

(3) Ninety rises.

(4) Ɗx[∀y[temperature´(y) ↔ x = y] ∧ rise´(x)]

(5) Ɗx[∀y[temperature´(y) ↔ x = y] ∧ ∨x = n]

(6) rise´(∨n)

Here, x and y are variables of type 〈s, e〉, ranging over "individual concepts" (functions from indices to individuals); temperature´ and rise´ are predicates of type 《s, e〉, t〉, taking individual concepts as arguments; n is a constant of type e, denoting an individual (presumably the number 90); ∨x is an expression of type e, denoting the individual yielded by x for the index of evaluation; and ∧n is an expression of type 〈s, e〉, denoting the constant function that yields at every index the individual denoted by n.¹ In this way, sentence (1) is analyzed as asserting that the unique temperature function rises; (2) is analyzed as asserting that the value of this function for the index of evaluation is 90; and (3) is analyzed as asserting that the function that picks out 90 at all indices rises. Because the temperature function might yield 90 at the index of evaluation, without being identical to the function that yields 90 at all indices, sentences (1) and (2) may be true even while (3) is false, resolving the paradox.

This analysis has been criticized on a number of grounds. In some cases, however, it is possible to reconstruct the temperature paradox using examples to which these criticisms do not apply.

For example, Jackendoff (1979) argues that sentence (2) should not be analyzed as equative, and that the paradox disappears if we treat it instead as locative, on analogy to sentences like (7).

(7) The temperature is at ninety.

But as Thomason (1979) hints and Löbner (1981) points out explicitly, it is possible to reconstruct the paradox using examples that seem more clearly equative rather than locative, such as (8), (9), and (10).

(8) The temperature in Chicago is rising.

(9) The temperature in Chicago is the very same as the temperature in St. Louis.

(10) The temperature in St. Louis is rising.

So even if we accept Jackendoff's criticism for examples like (1) through (3), something like Montague's analysis might still be appropriate for examples like (8) through (10).

A different line of criticism comes from Bennett (1975), who expresses reservations about treating numbers as individuals, and also objects that Montague's analysis does not appeal at all to the notion of measurement, which seems intuitively involved in the temperature sentences. He suggests that temperatures might be better represented as functions from indices to "entities such as twenty degrees Fahrenheit" (p. 32). This objection is supported by the fact that sentences like (2) may be paraphrased as in (11).

(11) The temperature is ninety degrees Fahrenheit.

Similar concerns provide part of the motivation for the analysis suggested by Thomason (1979).

But nothing in Montague's original analysis actually requires us to regard temperatures as functions from indices to numbers; all that is formally required is that they be functions from indices to individuals of some kind or other. The presumption that these individuals must be numbers comes only from the assumption that the name ninety must denote a number. There is actually nothing to prevent us from regarding ninety in (2) and (3) as elliptical for ninety degrees Fahrenheit, and understanding the temperature function in Montague's analysis as picking out a "degree" at each index rather than a number; nothing in the formalism need change.²

Moreover, sentence (2) may also be paraphrased as in (12), and in this case it seems quite reasonable to treat the subject noun phrase as denoting a number.

(12) The temperature in degrees Fahrenheit is ninety.

We could reconstruct the entire paradox using this example instead of (2).³

So none of these objections seem to me to seriously undermine Montague's basic strategy in resolving the paradox.

A more...