Contact Info: Paul Pietroski Department of Linguistics University of Maryland Marie Mount Hall College Park, MD 20742 USA Email: [email protected] Phone: +1 301-395-1747..

In my view, meanings are instructions to construct monadic concepts that can be conjoined with others, given a few thematic relations and an operation of existential closure. For example, ‘red ball’ is understood as—and has the semantic property of being—an instruction to fetch and conjoin two concepts that are linked, respectively, to ‘red’ and ‘ball’. Other expressions are more complex. But to a first approximation, ‘I stabbed it violently with this’ is an instruction to construct and existentially close a six-conjunct (...) concept of the form indicated below; AGENT(E, S) & STAB(E) & BEFORE(E, T) & PATIENT(E, 1) & VIOLENT(E) & INSTRUMENT(E, 2) where ‘S’, ‘T’, ‘1’ and ‘2’ stand for concepts of the relevant speaker, time, and things demonstrated. The verb and adverb correspond directly to conjoinable concepts of events. The pronouns correspond to such concepts via certain relational notions, reflected with the tense, preposition, and grammatical relations that ‘stab’ bears to its subject and object. I have argued elsewhere that this neo-Davidsonian conception of semantics is descriptively adequate, and yet. (shrink)

It is, I suppose, a truism that an adequate theory of meaning for a natural language L will associate each sentence of L with its meaning. But the converse does not hold. A theory that associates each sentence with its meaning is not, by virtue of that fact, an adequate theory of meaning. For it is also a truism that a semantic theory should explain the (interesting and explicable) semantic facts. And one cannot decree that the relevant facts are all (...) reportable with instances of schemata like ‘S means that p’ or ‘S, by virtue of its meaning, is true iff p’. Investigation suggests that there is much more for semanticists to explain: natural languages exhibit synonymies, ambiguities, and entailments; for any string of words, there are endlessly many meanings it cannot have; there are semantic generalizations, including crosslinguistic generalizations, that go uncaptured and unexplained by merely associating sentences with their meanings; etc. Initially, one might think these facts are “peripheral” and can thus be ignored if the aim is to explain why sentences mean what they do. But the study of natural language suggests otherwise. (One can’t tell, in advance of investigation, which facts are peripheral to a given domain. It was initially tempting to think that one could ignore falling bodies, and the tides, if the aim was to explain why planets move as they do.). (shrink)

Frege proved an important result, concerning the relation of arithmetic to second-order logic, that bears on several issues in linguistics. Frege’s Theorem illustrates the logic of relations like PRECEDES(x, y) and TALLER(x, y), while raising doubts about the idea that we understand sentences like ‘Carl is taller than Al’ in terms of abstracta like heights and numbers. Abstract paraphrase can be useful—as when we say that Carl’s height exceeds Al’s—without reflecting semantic structure. Related points apply to causal relations, and even (...) grammatical relations like DOMINATES(x, y). Perhaps surprisingly, Frege provides the resources needed to recursively characterize labelled expressions without characterizing them as sets. His theorem may also bear on questions about the meaning and acquisition of number words. (shrink)