Resemblance does not make things as much alike as difference makes them unlike. –Montaigne
Wittgenstein considered using “I will teach you differences” from King Lear as a motto for Philosophical Investigations. It is not entirely clear why Wittgenstein was drawn to it. Commentators have sometimes understood the line as an Anti-Essentialist slogan. Philosophers snub particulars; they crave generality and trust it. Differences do not matter; differences bury the essential. Wittgenstein will teach that differences matter. Generality should be mistrusted. Philosophers must grace particulars, attend to them, stop excavating the essential.
No doubt there is truth in this understanding of the line. But it seems to me to that there is looseness in it: a 7/16 wrench on a 3/8 nut. Taking the motto as an Anti-Essentialist slogan makes the book too metaphysical, metaphysical in a rather too up-front way. Wittgenstein’s challenge to philosophy looks too fraternal. Wittgenstein looks like a placard bearer for a minority position in metaphysics.
When Wittgenstein teaches differences he teaches the significance of logical differences, not metaphysical differences. Part of assessing the significance of logical differences is recognizing that the difference between logical differences and metaphysical differences is itself a logical difference. From the beginning of his work until the end, Wittgenstein cleaved to the idea that “logic must take care of itself”. Teaching differences is teaching logical differences. Learning to read PI is largely a matter seeing that and how Wittgenstein teaches the significance of logical differences–and that means seeing how Wittgenstein understood philosophical problems and proper responsiveness to them.
In an important moment of “Art and Sacrament”, David Jones remarks that understanding a painter correctly involves understanding how the painter can acknowledge his own making and yet insist on its identity with, say, some object or type of object he encounters. Jones’ point is that, for a painter, what is painted is not so much a painting of a mountain as it is mountain–under the form of paint. Similarly, when Wittgenstein takes up a philosophical problem–say, Essentialism, since I have mentioned it–he is not taking up the metaphysical problem of Essentialism; he is taking up Essentialism–under the form of logic. For Wittgenstein that is not a change of topic. He in effect insists on the identity of the traditional metaphysical problem and what he is taking up. But he does radically reorient himself on Essentialism. (The trick of course is reckoning with ‘under the form of logic’.)