Are such proposals normative claims about how we ought to think/talk, or empirical hypotheses about aspects of psychological/linguistic reality?
Proposed answers to these questions are usually interwoven with claims about why various inferences seem compelling.
So it would be nice to know which inferences really are secure, and in virtue of what these inferences are special.
The most common suggestion has been that certain inferences are secure by virtue of their logical form.
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.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.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.The Stoics discussed several patterns of this kind, using ordinal numbers (instead of letters) to capture abstract forms like the ones shown below.If the first then the second, and the first; so the second.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. The conclusion follows from the premises, without any further assumptions that might turn out to be false.Any risk of error lies entirely with the premises, as opposed to the reasoning.