One could put the whole sense of the book perhaps in these words: What can be said at all, can be said clearly; and whereof one cannot speak, thereof one must be silent.But what is it to say something clearly? In Joan Weiner's paper "Theory and Elucidation" there is a nice quotation from Frege:
When a straight line intersects one of two parallel lines, does it always intersect the other? This question, strictly speaking, is one that each person can only answer for himself. I can only say: so long as I understand the words ‘straight line’, ‘parallel’, and ‘intersect’ as I do, I cannot but accept the parallels axiom. If someone else does not accept it, I can only assume that he understands these words differently. Their sense is indissolubly bound up with the axiom of parallels. [Weiner, p. 20]What could be clearer than the axioms of Euclidean geometry? Or that a straight line intersecting one of two parallel lines must also intersect the other? And yet, as Weiner points out, that doesn't mean we can all understand these axioms without elucidation. There is nothing to guarantee that everyone will accept or understand any given such axiom. Recall Frege on "Logic in Mathematics":
Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind. But all this precedes the construction of a system and does not belong within a system. In constructing a system it must be assumed that the words have precise Bedeutungen and that we know what they are.Without checking the context of this quotation, I would say that it suggests a three-part distinction: what precedes the construction of a system, the construction of a system, and what is done within a system. As distinct as these three are, they might not always be completely distinct. Wittgenstein's remarks about the riverbed in On Certainty suggest this, but it is quite evident in Frege's work too (as, again, Weiner makes clear). In his work to construct a system he ends up dropping hints and counting on others' guessing what he has in mind. The precise sciences are born of the 'poetic' humanities, most obviously philosophy (most obviously, that is, if we accept the common story that philosophy is the mother discipline from which other disciplines are off-shoots). If we think in terms of a system, game, or calculus, then I'm inclined to say that the expressive arts, works of color and shade, the land of hints and guesses, belong to something like a foundational level or outer sphere, on top of or within which is the level or sphere of construction of the system or rules of the game, and then inside or above that is the working of the system or playing of the game itself. So the expressive arts or poetry or whatever we want to call it provides, or perhaps merely shapes, something like the context needed for the construction of games, systems, etc. This construction in turn is necessary for the use of the system, the playing of the game, etc. And hence mathematicians, logicians, scientists, need poetry.
And there's more. Problems can arise within the game that call for interpretation of the rules, or the introduction of new rules. And in constructing a system or game we can find that we have to resort to the undefined, to communication by non-scientific means. So the levels or spheres are not completely distinct. So science is continuous with poetry, not merely dependent on it but involved in a somewhat fluid relationship with it.
But: a) I need to check the context of the quotation from Frege, b) I need to think about whether he is really right, c) I especially need to be careful to distinguish the expressive arts' belonging to a sphere of communication or human relations on which technical work depends and the more dramatic claim that technical work depends on the expressive arts themselves (if Frege has to do the work of a poet it does not follow that without Goethe there could be no Frege, or anything like that), d) what about Wittgenstein on saying things clearly? I might get to that in my next post.