Philosophical Investigations, reading it together. §124
§124 comes in something like two parts, with the first part acting as somewhat of a recapitulation of a lot of what has been said so far, and the second part linking what has been said with mathematics.
So: The first part underscores, again, the distinction between facts and understanding that has been operative all throughout these sections, along with affirming that philosophy only ever works at the level of the understanding - that is to say, at the level of idealisations about what language should be, or ought to be. Given then, that Witty has argued all along that all such idealisations should be expelled, and that philosophy only ought to describe language, it follows that philosophy ‘leaves everything as it is’. It does not 'contribute’ in any way to language as it is actually used. Language is, or would be, indifferent to anything philosophy has to say about it.
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Just before going on, it’s perhaps worth pausing to do a quick comparison to some of Witty’s views on philosophy in the Tractatus. For, despite the heavy critique of the Tractatus here (re: idealisation and so on), Witty’s understanding of philosophy remains strikingly similar. For, recall that in the Tractuatus that "Philosophy is not one of the natural sciences” (TLP 4.111: i.e. does not deal with facts, or the empirical); and that famously, one who has ‘climbed the ladder’ of the TLP ought to throw it away; In the PI, philosophy has a similar role, but unlike the TLP, it cannot be done away with so definitively: philosophy in the PI is always something of a standing threat (§109: "a struggle against the bewitchment of our understanding by the resources of our language”), against which one must remain, in some sense, ever vigilant.
Where philosophy in the TLP ought to self-immolate once and for all, in the PI, philosophy is both cure and disease, and one always needs philosophy in order to ‘cure’ oneself of philosophy, indefinitely. If the illusions in the TLP were Cartesian, in the sense that, like the illusions of Descartes’ evil demon, they could be overcome once and for all, the illusions of the PI are Kantian, in the sense that they are always looming. Philosophy in the PI is a pharmakon, to use one of Derrida's terms if anyone is familiar with it.
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The second half of §124 extends Witty’s point about philosophy and language to mathematics. Just as philosophy does not ‘interfere’ with the actual use of language, so too does philosophy not ‘interfere’ with the workings of mathematics. Witty doesn’t really explain himself much here - the bulk of the good stuff is to be found in the Remarks, Lectures, and Philosophical Grammar - but there is one important point that I think is worth noting. If the reason that philosophy leaves everything in language ‘as is’ because it only deals with the understanding and not facts, this cannot be the same reason it leaves everything in mathematics ‘as is’: this is because mathematics, for Wittgenstein, is also not empirical: that is, math also does not deal with facts, or at least, facts in the empirical mode.
This isn’t something that Witty insists upon here in the PI - at least, not that I can recall - but he makes the point almost everywhere that he explicitly deals with math. All of this is simply to say that despite the fact that Witty says that philosophy does not ‘interfere’ with either language or math, this lack of interference does not happen for the same reason in both cases. Something is slightly different about math. This gets brought out somewhat in the next passage, but all I want to do here is mark or take note of this not-so-obvious asymmetry between language and math.