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Kearns (2011: 58-61) views the common noun dog to be of type <e, t>. This makes sense based upon the predicate use of such a noun, e.g. Those animals are dogs. What happens, though, when the noun is NOT used predicatively, but rather its used as an argument of the predicate, e.g. Dogs bark? The problem is perhaps more visible with a singular mass noun, e.g. ice cream:

(1) That is ice cream.

(2) Ice cream is good.

Viewing ice cream in (1) as being of type <e, t> seems appropriate because it functions predicatively there, this predicate taking an argument (i.e. That); the sentence can then be judged to be true or false based upon whether ‘that’ is or is not indeed ice cream in the discourse context. This sort of analysis is not possible for ice cream in (2), though, because ice cream there is the subject argument of the predicate is good. Given that the predicative adjective good is of type <e, t>, there is no way that the noun ice cream, if it is also of type <e, t>, could combine with is good. In other words, an expression of type <e, t> cannot combine with another expression of type <e, t>.

To overcome this difficulty, it seems that type theory of this sort should distinguish between the predicate vs. argument use of common nouns, viewing them as distinct types. A predicate noun can be viewed as type <e, t>, but an argument noun should be viewed as just type e. To the best of my knowledge, standard type theory does not do this, though. Interestingly, Kearns (2011: 58-61) views the common noun dog, when it functions as an argument, as an expression of type <e, t> as stated above, but she views the common noun ice cream, also functioning as an argument, as an expression of type e. There is hence an inconsistency in Kearns’ account that is silently assumed and that hence masks a problem concerning how common nouns are analyzed.

So my question is what I might be missing concerning basic type theory in the context of formal semantics. What have I overlooked?

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    The problem is not so much which role a noun has in the sentence, but rather that "ice cream" is a mass noun rather than a count noun, and I agree that the usage of a mass noun as an example for an argument of type e in the Kearns book is didactically not optimal. Generally only count nouns are considered to be of type <e,t>, whereas mass nouns are more tricky.
    – lemontree
    Aug 8 at 22:54
  • There are different ways of handling mass nouns; one possibility is to introduce a new ontology with a part-of-relation, sums of parts and such, but one can also try to do with ordinary sets (i.e. objets of type <e,t>), or a combination of both approaches. See plato.stanford.edu/entries/logic-massexpress/#MixSetTheMerApp for some ideas about how the denotations should play together (though without types), discussing amongst others the two kinds of example sentences you cite.
    – lemontree
    Aug 8 at 23:03
  • @lemontree, Is the problem due to the absence of a determiner with a mass noun? If yes, then the same problem occurs with determinerless plural count nouns. Is that correct?
    – Tim Osborne
    Aug 9 at 1:27
  • @lemontree, Did you see my further question just above?
    – Tim Osborne
    Aug 11 at 12:42
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For general use as an argument: You need EITHER a silent determiner (or another head) that converts <e,t> to either <<e,t>,t> or e OR a theory of coercion that performs its function for you. Needless to say, I prefer the former.

However, "in other words, an expression of type <e, t> cannot combine with another expression of type <e, t>" is not true. Most models include so-called Predicate Modification: combining λx.f(x) and λy.g(y) leads to λz.(f(z)&g(z)), and that's what derives, e.g., "good dog". The result is <e,t>.

(Dmitrii Zelenskii)

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  • Thanks Dmitrii. I understand your fist comment (first paragraph), but not the second (second paragraph). My reaction to your first paragraph is predictable. The willingness of many formal syntacticians and semanticists to posit null elements to rectify problems with the apparatus is, in my view, quite dubious. I find your position especially problematic from the perspective a language like Russian, in which determiner-less noun phrases are much more common than in English. In any case, thanks for coming here to answer my question.
    – Tim Osborne
    Sep 16 at 4:12
  • Sorry but I really cannot do much to explain Predicate Modification further as I even gave its formula; maybe Heim & Kratzer's book can explain it better, just search for these two words.
    – Viridianus
    Sep 25 at 9:54

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