[Mathematicians do not get into fistfights about whether a problem has been solved; but as "normative scientists" logicians obviously do.]
Wittgenstein drops this cryptic notion in the PI,
F.P. Ramsey once emphasized in conversation with me that logic was a 'normative science'. I do not know exactly what he had in mind, but it was doubtless closely related to what only dawned on me later: namely, that in philosophy we often compare the use of words with games and calculi which have fixed rules, but cannot say that someone who is using language must be playing such a game. (81)which characterizes two things: Ramsey's view of logic and Wittgenstein's view of rules. Ramsey, one would think, thinks of logic as telling men how to think, i.e., as normative; i.e., logic is something to which men's thoughts, action and language must fit. Humans needn't play by logical rules. It's something to which they could aspire, maybe.
Wittgenstein's remarks later in the PI concerning 'able to go on' and rule following better characterize his view on rule. (Of course, I'm conflating rule and logic here taking Ramsey to mean that logic is a higher order-type set of rules.) It seems from sections 201 and 202 that Wittgenstein sees grasping a rule to connect to being certain of a rule, and the obeying of a rule is an actual--an act--and not discursive--thinking. That is, every time someone acts, he is obeying a rule. The thought might hold better in the converse: Every time someone obeys a rule, he is acting. The operative contrast is to thinking one obeys a rule.
This all seems to connect to OC, certainly. To be able to go on is to act without reasons; just as to act under threat of soon impending physical harm is to act with certainty. Logic seems to me to be wholly discursive, a set of symbols that fail to fit (i.e., belong necessarily to) our every day actions. I believe this thought lay behind Wittgenstein saying, "My symbolic expression was really a mythological description of the use of a rule" (221). (Which also relates to his remark on rules being ornamental and architectural.) The symbolic expression--the discursive irruption of logic onto the scene--is merely an inadequate stand in for the actual events. The difference between a box score and a ball game.
But his use of the word "mythological" is quite suggestive, too. This passage relates, and it's quite packed; when he says,
Would it not be possible for us, however, to calculate as we actually do (all agreeing, and so on), and still at every step to have a feeling of being guided by rules as by a spell, feeling astonishment at the fact that we agreed? (We might give thanks to the Deity for our agreement.)it seems to link up to his use of "mythological" above. It seems as if Wittgenstein were taking a dig at the logical positivists' absolute worship of logic. Why not a Deity guiding us? Why must logic guide our actions? We made logic. Our tendency is to sublime logic. But logic is just another language game. Being guided is a family of situations, and all but the most rudimentary I think Wittgenstein precludes our being guided by logic. But what else guides us? Institutions, culture, traditional practices and training? But wherefore ethics? That's the question I continually ask.