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.
Though unsurprisingly, conceptions of form have evolved along with conceptions of logic and language.
One ancient idea is that impeccable inferences exhibit patterns that can be characterized schematically by abstracting away from the specific contents of particular premises and conclusions, thereby revealing a general form common to many other impeccable inferences.
The motivations for developing this idea were both practical and theoretical.
Experience teaches us that an inference can initially seem more secure than it is; and if we knew which of inference are risk-free, that might help us avoid errors.
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.
As we'll see, claims about inference are also intimately connected with claims about the nature of thought and its relation to language.
Many philosophers have been especially interested in the possibility that grammar the underlying structure of thought, perhaps in ways that invite mistaken views about how ordinary language is related to cognition and the world we talk about.