Sentence (S1) seems to entail sentence (S2), but, the charge is, the paraphrases offered by Walton do not respect this.
A collection of premise sentences logically entails a conclusion sentence just when the negation of the conclusion is logically inconsistent with those premises.
(Or, more colloquially, 'Few professors are such that they both came to the party and had a good time.') This is clearly incorrect, since the sentences of (8) entail that few professors attended the party (i.e., the first sentence entails this), whereas (8a) could be true if many professors attended.[6] But they are not.
A theory may have implicit ontological commitments by entailing existential sentences or propositions according to some entailment relation more generous than logical entailment (see §1.5 and §2).
If so, then the above test entails that the sentence is not context-sensitive.
Standard linguistic theory entails that many sentences that have never been tokened (internally or externally) are well-formed English sentences.
In order to motivate claim (a), platonists would have to refute the paraphrase-nominalist claim that sentences like (P1) and (R1) are equivalent to sentences like 'Mars is red' and 'San Francisco is north of Los Angeles' and that none of these sentences entails the existence of properties or relations.
This entails that unverifiable sentences are literally meaningless, so that no metaphysical claim according to which unobservable nonphysical items exist can be true.
This is problematic, as it entails that the sentences 'George Bush was sitting' and 'Socrates was sitting' express propositions with radically different forms, despite their evident surface grammatical similarity.
The analytic reductionist who wishes to wield the contextual definitions against the existence claim at the heart of platonic realism takes them to show that the apparent reference to abstract objects on the left-hand sides of the definitions is merely apparent: in fact, the truth of the relevant sentences entails only the existence of a range of concrete inscriptions.
