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An influential contrasting non-cognitivist approach to explaining the logic of normative sentences and attitudes starts from the other end, postulating norms governing combinations of attitude that do not (much) depend on prior relations of implication or consistency among their contents.
On the other hand, some normative sentences do seem to follow from others, so deontic logic must be possible.
(1) One is compositionality; the meaning of a complex sentence embedding a moral claim should be a function of the meaning of its parts so as to explain the ease with which speakers can understand novel normative sentences.
Extensions of this minimalist strategy have attempted to deploy minimal conceptions of other notions such as truth-aptness, proposition (Horwich 1990, 18 22) and more besides to extend the account to normative sentences seeming to employ these notions.
What we need to note is just that the suggestion helps explain the meaning of normative sentences in one embedded context, namely the one in which it is embedded along in an 'is true' construction.
The idea behind a logic of attitudes is to change the normal order of explanation to explain why normative sentences and attitudes bear the logical relations that they do to other sentences and attitudes.
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The activity of using a normative sentence as in the first example is sometimes referred to as "norming"—it creates a norm by granting permission by the very use.
The idea is that a normative sentence such as "You may park here for one hour" may be used by an authority to provide permission on the spot or it may be used by a passerby to report on an already existing norm (e.g., a standing municipal regulation).
And it must also extend the approach back to simple non-normative sentences as well.
As a non-normative declarative sentence, 'I approve of X' is passively disposed, Stevenson thinks, to be used by a speaker or writer who believes the world is as described in this case, by a speaker or writer who believes that she approves of that which is demonstrated by 'this' and is actively disposed to evoke a similar belief or cognitive state in an audience upon its being heard or read.
But they might still be able to do justice to the fact that normative judgments and sentences stand in logical relations to one another if they can explain how the judgments themselves stand in certain logical relations to to one another and then go on to explain that the sentences are inconsistent just because they express judgements that are inconsistent.
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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