By Valerie Adams
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Extra resources for An Introduction to Modern English Word Formation
Dp, ft1t2 . . tn, E1, E2, . . , Eq should be determined on the basis of the semantic connection on D1, D2 . . Dp, f, t1, t2, . . tn, E1, E2, . . , Eq (with ft1t2 . . tn giving way, as before, to f, t1, t2, . . , tn); and d1, d2, . . dp, b, e1, e2, . . , eq will belong to the semantic connection on D1, D2 . . Dp, ft1t2 . . tn, E1, E2, . . e. ft1t2 . . tn will be capable of taking the value b when D1, D2 . . Dp, E1, E2, . . , Eq take the values d1, d2, . . dp, e1, e2, . . , eq, just in case, for some individuals a1, a2, .
Em, as long as this is construed collectively so as to include the meaning relationships among the different components and not just their individual meanings; and compositionality, so understood, will still enable us to trace the meanings of expressions back to the lexicon, as long as the lexicon is also taken to have a relational semantics. From the present point of view, our previous formulation of compositionality should be seen to be the product of this more general formulation and the intrinsicalist doctrine that the collective meaning of the component expressions is exhausted by their individual meanings.
For take any differentiation Fa′, Ga″ of the premises, then the inference from the differentiated premises Fa′, Ga″ to the correspondingly differentiated conclusion Fa′ & Ga″ will be classically valid. Corresponding to this distinction between classical and manifest consequence is a distinction between two kinds of domain. Just as a theory may be taken to be a class of sentences closed under consequence, so we may take a domain to be a class of propositions that is closed under consequence.