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Even (6) falls short of the demonstrative character exhibited by (1–3).While laws of nature may preclude immortality, the conclusion of (6) goes beyond its premise, even if it is foolish to resist the inference.With regard to (1) and (7), it seems especially clear that the conclusion is part of the first premise, and that the second premise is another part of the first.
By contrast, examples like (4–6) illustrate reasoning that involves at least some risk of going wrong—from correct premises to a mistaken conclusion. John might dance whenever Mary sings, but also sometimes when Mary doesn't sing.
Similarly, with regard to (5), Tweety might turn out to be a bird that cannot fly.
Not both the first and the second, but the first; so not the second. And let us introduce ‘proposition’ as a term of art for whatever the variables above, indicated in bold, range over. They can be endorsed or rejected, and they exhibit containment relations of some kind.
So presumably, propositions are abstract things that can be evaluated for truth or falsity.
Do sentences exhibit grammatical structures that are not obvious?
And if the logical structure of a thought can diverge from the grammatical structure of a sentence that is used to express the thought, how should we construe proposals about the logical forms of inferences like (1-6)?
For example, similarities across sentences like ‘Odysseus arrived’, ‘Nobody arrived’, and ‘The king arrived’ initially suggest that the corresponding thoughts exhibit a common subject-predicate form.
But even if ‘Odysseus’ indicates an entity that can be the subject of a thought that is true if and only if the entity in question arrived, other considerations suggest that ‘Nobody’ and ‘The king’ do not indicate subjects of thoughts in this sense.
Appeals to logical form arose in the context of attempts to say more about this intuitive distinction between impeccable inferences, which invite metaphors of security, and inferences that involve some risk of slipping from truth to falsity.
The idea is that some inferences, like (1-3), are in a way that confines any risk of error to the premises.