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But in fact, (given sentences of sufficient complexity), there are "intermediate" meanings of 'that' that combine with the sentence in question to form names of entities whose grain is "between" intension/sets of worlds and the "maximally fine grained entity".
This is important to bear in mind, since for Cresswell, strictly speaking, a sentence not in a 'that' clause does not express this fine grained entity.
For example, even if 'All brothers are siblings' and 'All bachelors are male' are true in exactly the same worlds, the fine grained entity associated with the latter will contain the meaning (function from individuals to sets of worlds) of 'male' and the fine grained entity associated with the former will not.
On the other, it combines with a sentence to form the name of the "maximally fine grained entity" that can be named by a 'that' clause containing the sentence.
Again, since our concern here is with more fine grained entities, we ignore this complication and focus on the maximally fine grained entity that can be named by a 'that' clause containing a sentence on Cresswell's view.
For recall that sentences don't express fine grained entities in isolation; it is only when combined with 'that' (on certain of its meanings) that a fine grained entity is associated with a sentence-plus-'that'.
Similar(54)
It should be clear that as on the neo-Russellian approach, sentences that are true in all the same worlds may be associated with different fine grained entities of the sort posited by Cresswell.
So these seem to be the primary bearers of truth and falsity for Cresswell.[25] Thus, it appears that for Cresswell, in contrast to the neo-Russellians, the primary bearers of truth and falsity and the fine grained entities associated with the sentences (or 'that' clauses) that verbs of attitude embed and to which they are (sometimes) sensitive are different.
Recent work in this direction includes projects on minimax theory for multiple testing, code generation from natural language specifications, fine-grained entity typing, and function-specific mixing rates for MCMC.
For example, the semantic value of 'runs' as it occurs in (7) is a constituent of the fine-grained entity expressed by (7) (i.e. (7a)).
However, 'that' has another meaning on which it combines with a sentence to form the name of a much more fine-grained entity (in the sense that sentences true in all the same worlds may be associated with different fine-grained entities).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com