[FOM] Mass and count terms

[Richard G Heck]

>The whole concept of a distinction between mass and count nouns was
>introduced by the linguist Otto Jespersen[...].
>
Jespersen does have some helpful things to say about the distinction 
between mass and count nouns, but the distinction itself goes back at 
least to Aristotle. I believe it was heavily discussed by logicians in 
the middle ages, and I'd be shocked if it isn't mentioned in the Port 
Royal Logic. One could check Kneale and Kneale on this point.

>As Davidson wryly points out, in none of the languages for which Tarksi
>provides a definition of truth is it possible even to formulate the sentence
>    "Snow is white" iff snow is white
>let alone prove it (Prior p. 182).
>
There is now a large literature on mass terms in semantics. None of the 
going theories, unfortunately, seems to be fully adequate to the 
phenomena, but things are not as bad now as they used to be. It is 
possible, in many of these theories, to prove T-sentences for such 
sentences as "snow is white". The difficulty, in the end, is to a 
significant just syntactic. Apriori, it is just not clear what the 
syntax of "snow is white" should be taken to be. Should "snow" be 
construed as a name? or as a predicate? If a name, then of what? If a 
predicate, then of what is it predicated? Such sentences pose another 
challenge, because they are plausibly taken to be generic. The sentence 
"Spiders have eight legs" is true, even though, as any little boy can 
tell you, not all spiders have eight legs. The sentence does not, then, 
express universal quantification, but instead seems to express some sort 
of generic quantification. It means something along the lines of: 
Spiders (generally, typically, or normally) have eight legs. The same is 
true of "Snow is white". Although snow is indeed white, not all snow is 
white. The sentence "Snow is white" means something like: Snow is 
generally, typically, or normally white.

All of the remotely plausible approaches to mass terms make heavy use of 
fairly sophisticated mathematical machinery, for example, the techniques 
of Boolean algebra or the theory of lattices. In general, there is good 
reason to believe that our everyday comprehension of "ordinary language" 
involves the tacit deployment of such machinery, not just in this case 
but in many others as well. To my mind, that makes objections to 
mathematics that are grounded on the supposed purity of natural language 
peculiarly self-defeating.

Richard Heck