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And from there perhaps we can explain logical implication by deploying the fact that the premises of valid arguments are inconsistent with the negation of the conclusions of those arguments.
One motivation for such views is the present one: Hybrid theorists hope to explain logical relations by using the descriptive component of meaning to do much of the work.
One motivation for such views is rooted in a strategy for solving the embedding problem: Hybrid theorists hope to explain logical relations among moral judgements by using the descriptive component of meaning to do much of the work.
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"Realists" typically prefer explaining logical consequence in terms of truth in models, and "Anti-realists" typically prefer explaining logical consequence in terms of proof.
On the other hand, explaining logical consequence in a proof-centred way seems to require none of this.
Explaining logical consequence in terms of truth in models is rather close to explaining logical consequence in terms of truth, and the analysis of truth-in-a-model is sometimes taken to be an explication of truth in terms of correspondence, a typically Realist notion.
A recent objection to non-cognitivism pays close attention to the distinction between explaining logical relations on the one hand, and explaining the use of moral judgments in reasoning on the other.
On its stronger reading, Austin's suggestion would have to contend with an aspect of what is known as the Frege-Geach problem: the challenge of explaining logical connections amongst speech acts with different forces where those connections appear to depend upon their sharing (elements of) a locutionary core (see Geach 1965).
One would think that, to be able to achieve this, Heyting must have had quite precise ideas on how to explain the logical connectives intuitionistically.
Unfortunately, discussion of theories of this sort, which attempt to explain the logical form, or syntax, of natural language sentences, is well beyond the scope of this entry.
Hybrid theorists of this sort then propose to use the descriptive contents contributed by moral terms and moral sentences to explain the logical relations between these.
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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