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Workshop on Scalar Meaning

Comparatives without Degrees
Friederike Moltmann, Institut d'Histoire et de Philosophie des Sciences et des Techniques

May 20, 2006
University of Chicago

It has become common to analyse comparatives by using degrees, abstract representational objects that form a total ordering, as on the analysis of (1a) in (1b):

(1) a. John is taller than Mary
b. max d(tall(John, d) > tall(Mary, d))

While this analysis (or modifications thereof) seems to get crucial facts about comparatives and degree modification right, there remains a significant unease about such a generous use of abstract degree objects. Clearly, in certain cases as in (2) overt degree modifier seem to make using degrees unavoidable:

(2) John is two centimeters taller than Mary.

However, with adjectives not simply specifying extension or number, such as white, beautiful, wise, or happy, as in (3), the presence of degrees is rather problematic.

(3) John is happier than Mary.

With such adjectives, degrees are (almost) never made explicit and a speaker using them in a sentence will hardly be able to tell what the implicit degree argument is that is to be involved in the logical form of the sentence he utters.

I will pursue a new approach to the semantics of comparatives without making central use of degrees, by using the notion of a 'particularized property' or what philosophers nowadays call a trope, the kind of object nominalizations of adjectives with a determiner, obviously, refer to -- that is, John's wisdom refers to the trope that is the concrete manifestation of wisdom in John. Tropes, unlike degrees, are concrete entities, possible objects of perception and causation and obviously objects of reference. Unlike states of affairs or situations, tropes thus are naturally ordered with respect to the 'degree' to which they manifest the property in question (but here we do not need 'degrees', as the ordering can be immediately read off the tropes themselves). I will pursue the idea that comparatives describe a relation between tropes rather than degrees, and involve a form of 'implicit nominalization'. If f is the function that maps a property, an object, and a world to the manifestation of that property in the object in that world, then, (3) will be analysed as in (4a) making it roughly equivalent to (4b):

(4) a. f(John, [happy], w) > f(Mary, [happy], w)
b. John's happiness is greater than Mary's.