The book deals with the problems of philosophy and shows – so I believe – that the formulation of questions about these problems is due to misunderstanding the logic of our language. 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.
We might think here again of Kant’s Critique of Pure Reason: “The exactness of mathematics rests upon definitions, axioms and demonstrations. I shall content myself with showing that none of these, in the sense in which they are understood by the mathematician, can be achieved or imitated by the philosopher. I shall show that in philosophy the geometrician can by his method build only so many houses of cards [Kartengebäude], just as in mathematics the employment of a philosophical method results only in mere talk. Indeed it is precisely in knowing its limits that philosophy consists…” (A 726-727/B 754-755) It is to mere talk and houses of cards that Wittgenstein means to put an end, by showing philosophy its limits. If he can do this, then he will have done (and done with, once and for all) philosophy as Kant defines it here. There is an ethical aspect to this. Again quoting Kant: “it is not in keeping with the nature of philosophy, especially in the field of pure reason, to take pride in dogmatic procedure, and to deck itself out with the title and insignia of mathematics, to whose ranks it does not belong, though it has every ground to hope for a sisterly union with it. Such pretensions are idle claims which can never be satisfied, and indeed must divert philosophy from its true purpose, namely, to expose the illusions of a reason that forgets its limits, and by sufficiently clarifying our concepts to recall it from its presumptuous speculative pursuits to modest but thorough self-knowledge.” (A 735/B 763) The enemy is idle pretense, and the goal modest self-knowledge. Philosophy, know thyself. “Indeed, it is precisely in knowing its limits that philosophy consists.”
Russell’s views are worth comparing with these. Russell sees religion/ethics on the one hand, and science on the other, as leading people to philosophize. Some philosophers are motivated only by one or the other, others by both. But it is from science alone that philosophy ought to take its inspiration. It is the methods of science, not its results, that are most relevant here. Philosophy is the science of the possible, an a priori investigation of quite general truths. Therefore philosophy is logic, conceived in the right way. The essence of such philosophy is analysis, not synthesis.
“The adoption of scientific method in philosophy, if I am not mistaken, compels us to abandon the hope of solving many of the more ambitious and humanly interesting problems of traditional philosophy. Some of these it relegates, though with little expectation of a successful solution, to special sciences, others it shows to be such as our capacities are essentially incapable of solving. … The failure of philosophy hitherto has been due in the main to haste and ambition; patience and modesty, here as in other sciences, will open the road to solid and durable progress.”
Cf. also Schopenhauer Fourfold Root pp. 155-156: “[E]very … analysis that has sprung from mere combinations of concepts is like the note of a bank which for security has again merely deposited other promissory notes. All purely rational talk is thus an elucidation of what follows from given concepts, and so does not really bring anything new to light. It could therefore be left to everyone to do for himself, instead of being put every day into large volumes.”