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.
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