But I'd be really curious to hear more about your take on the corollarial/theorematic distinction !
Since you ask, here are a few thoughts.
In my opinion, the corollarial-theorematic distinction is a case of the more general induction-abduction distinction. Peirce clearly recognized that all great discoveries depend on abduction and theorematic constructions, most of which arise from the unconscious mind. The only problem is that he calls it reasoning and logic.
Peirce: Now, that the matter of no new truth can come from induction or from deduction, we have seen. It can only come from abduction. Somewhere else Peirce says, I show that no considerable advance can be made in thought of any kind without theorematic reasoning.
This was nothing new. Many of Peirces contemporaries, Hertz, Poincaré, Mach, James, who had thought about how great discoveries come about, recognized that logic in the classical sense was not the source of new truths or advances in thought.
To me an obvious question is why Peirce so often talked about abduction as if it were a part of logical and reasoning when he clearly saw that logic and abduction were completely different types of thought.
Peirce: Abduction and induction have, to be sure, this common feature, that both lead to the acceptance of a hypothesis because observed facts are such as would necessarily or probably result as consequences of that hypothesis. But for all that, they are the opposite poles of reason, the one the most ineffective, the other the most effective of arguments. The method of either is the very reverse of the others.[HP italics] If not illogical, it is at least confusing to lump opposites together in one category and call it reasoning.
I think Peirce thought of himself primarily as a logician, at least logic is the field in which he made his most recognized discoveries. It is understandable that he would be defensive toward any criticism of logic, but he still confused logic and abduction. For example, he should have agreed with Poincaré: I find nothing in logistic for the discoverer but shackles. Even though he knew that discovery is not logical, Peirce responded derisively: It seems to me strange that a profound mathematician, even though he be a Frenchman, should harbor such a notion; but his essay is only a fine example of the utmost that a brilliant mind can contribute toward the solution of a problem to which he comes without adequate preparation.
Peirce describes abduction as, a process in which the mind goes over all the facts the case, absorbs them, digests them, sleeps over them, assimilates them, dreams of them, and finally is prompted to deliver them in a form, which, if it adds something to them, does so only because the addition serves to render intelligible what without it, is unintelligible.
I wonder what motivated Peirce to spend so much effort on logic when he knew that the path of inquiry is not logical?
Howard
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