Fine - guide to ground.pdf - Ted Sider

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this result by means of a different manner of predication; and there is therefore no difficulty in
distinguishing between the propositions or in allowing the grounding relations between them may to
20 obtain.
§10 The Semantics of Ground
There is a standard ‘possible worlds’ semantics for logical consequence or entailment. Under
this semantics, each sentence A of the language under consideration is associated with the ‘truth-set’
|A| of possible worlds in which it is true, and it is then supposed that:
C is a consequence of A 1, A 2,
… iff a world w verifies C (i.e. is a member of the truth-set |A|)
whenever it verifies each of A 1, A 2, … (i.e. whenever it belongs to each of the truth-sets |A 1|, |A 2|,
…).
This semantics is not suited to the notion of ground since it conforms to Weakening. If C is a
consequence of A 1, A 2, … then it is a consequence of A 1, A 2, … along with any other sentences B 1,
B 2,
…. But is there any alternative account of the semantics of sentences and of the connection of
ground that might be made to work?
It turns out that one can provide a very natural semantics of this sort in terms of the idea of
truth-making. I have had some harsh things to say about truth-maker theory. But even though it
might not amount to much as an approach to ontology, it provides an ideal framework within which
Rosen [2010], p. 125, is of the view that the proposition that a is grue (where to be grue is to be
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red or green) and the proposition that a red or green will differ in that (i) the former but not the
latter will contain grue and (ii) the latter but not the former will contain green. Thus where I see
a difference in the manner of composition (or predication), he sees a difference in the
constituents. The first of his two claims is much more plausible than the second, but only the
first is required to distinguish between the two propositions. I could perhaps agree with him on
the first claim (even if not on the second) under a construal of composition in which composition
through abstraction is not allowed. However, I believe that the downward form of composition
should not simply be ignored but should be recognized as a genuine form of composition in its
own right. For more on the underlying conception of composition, see Fine [2011b].