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Notice that conditional probability functions apply only to pairs of sentences, a conclusion sentence and a premise sentence.
One way of construing degrees of entailment in this framework is in terms of the entailment probabilities relating each possible logical form of the premise sentence to each possible logical form of the hypothesis in question.
But for this to be so, what the arguer actually expresses by the premise sentence must provide good reason to accept what she actually expresses by the conclusion sentence.
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A collection of premise sentences logically entails a conclusion sentence just when the negation of the conclusion is logically inconsistent with those premises.
For, the whole idea of inductive logic is to provide a measure of the extent to which contingent premise sentences indicate the likely truth-values of contingent conclusion sentences.
turn out on this revised non-cognitivist view to be straightforwardly valid: for the proposition semantically expressed by the conclusion sentence is entailed by the propositions semantically expressed by the premise sentences.
Since some of these sound argument instances contain as premises sentences attributing truth to the designata of that-clauses, those designata must be bearers of truth-values.
So these logicians attempted to specify inductive support probabilities solely in terms of the syntactic structure of premise and conclusion sentences.
The classical consequence relation ⊢ (conceived of as a relation between two sentences rather than as a relation between a set of sentences, the premises, and a sentence, the conclusion) is non-ampliative in the sense that the conclusion of a classically valid argument does not convey information that goes beyond the information contained in the premise.
Some inductive logicians have tried to follow the deductive paradigm very closely by attempting to specify inductive support probabilities in terms of the syntactic structures of premise and conclusion sentences.
Luo et al. developed their clusters for entire eligibility criteria sentences on the premise, that 'each eligibility criterion sentence is an independent patient characteristic'.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com