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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.We can express this point by saying that these inferences are instances of the following form: B if A, and A; so B.
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.
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.
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.
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.
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.