26 August 2007

my morphosemantically creative fridge

one of my recent move-in tasks was stocking my kitchen. as i loaded up my freezer after my initial grocery run, i noticed the temperature control knob. it was, rather prudently i thought, turned to the position marked "Recommended setting." what baffled me were the two ends of the spectrum:

i'm certainly glad that the warmest option is cold, but the coldest option is not coldest, but colder. yet there sits the knob, somewhere between the two. how is that even possible?

disclaimer: i am not a semanticist. nevertheless, i thought as a native speaker i understood something about the degrees of adjectives in English and their corresponding meanings. to be sure, adjectives like cold can indicate a reference point at various places along the absolute scale of temperature. for example:

  1. it gets cold in February. (0-30 degrees F)
  2. it was cold yesterday [in August]. (50-65 degrees F)
  3. red dwarfs are cold stars. (3500 degrees F)
i have some idea where on that scale the cold setting on my freezer should be: probably something like 20 degrees F. here's where things get tricky. slave to scalar implicatures that i am, if you ask me what colder means in this context, it means "anything on the absolute scale of temperature below the point marked 20 degrees F." members of the set include 0 degrees F, 10 degrees K, -10 degrees F, and 19.8 degrees F, just to give a few examples. members not within the set include 50 degrees F, 0 degrees C, 21 degrees F, and 20 degrees F. remember number lines from when you learned inequalities in pre-algebra? this scenario looks like this:

colder is a ray on the number line in this scenario. but by defining the rightmost position that the knob can turn to as colder, suddenly colder must be defined as a point on the number line.

this is productive in some ways. as you can see from the number line, it effectively places a lower bound on the range of temperatures that the freezer can be set to. (the fact that no numerical values are given is another issue, but i think it's safe to use my knowledge of the world to say that 10 degrees K is now outside of this set, whereas 10 degrees F is definitely within the set)

what arises now is the horrible morphological problem that makes my head hurt. we have determined that the possible range of temperatures in my freezer is

{ t : colder < t < cold } , where cold and colder are constants

this is an okay definition except that it flies in the face of morphology. every adjective in English has three degrees: positive, comparative, and superlative. in the morphology they are either represented by bound morphemes (X, X-er, X-est) or by paraphrasis (X, more X, most X). the morphology-semantics interface tells us what these degrees refer to. positive and superlative adjectives denote points, or single-member sets; comparatives denote rays or line segments, sets with multiple members. so for any cold, colder, coldest scheme, the cardinality of the sets should be as follows:

|cold| = 1
|colder| > 1
|coldest| = 1

therefore the problem with our definition of the set t above is the assertion that colder is a constant. this definition entails that |colder| = 1, and therefore clashes with the morphosemantics.

fun thought exercise to leave you with. ask yourself: give a name to what is between cold and colder. try to say it out loud. you'll probably say "cold" and halt, longing for some morpheme to tack onto the end of it that means "between the positive and comparative form of this adjective." what's remarkable about that is the fact that we're willing to admit that this distinction might be possible, so the semantics is not broken here. the morpheme just doesn't exist in the lexicon, so you can't produce it.

oh and a parting shot for real: if whoever made the damn knob just labeled it coldest, you wouldn't even be reading this.


Anonymous said...

I think you want to be working in the nonstandard reals. We have the usual real numbers plus infinitesimals. This would allow us to make sense of a number which is smaller than 'cold' but bigger than any number in the usual interval (-infinity, cold) = colder.

See wikipedia or some blog post for more information.

Ed said...

you're right, the nonstandard reals absolutely allow for this contrast. the only problem is that at least the way i interpret scalar implicatures, my brain only operates using the standard real system, as i described in the post.