The ideal of a pure language in which a pure, pared-down, unambiguous translation of the truths of pure mathematics can be effected deserves a more extended discussion than I have given it here. But I will limit myself to pointing out that this ideal language is very far indeed from the languages of man as conceived by Whorf; for to Whorf the least visible structures of a language, those that seem most natural to its Speakers, are the structures most likely to embody the metaphysical preconceptions of the language Community. On the other hand, the case of gravitational attraction does not at all demonstrate what Whorf asserts about Newtonian cosmology as a System, namely that the key concepts of the cosmology emerge smoothly from or fit smoothly into, the structures of Newton's own language(s). Instead we find in Newton a real struggle, a struggle sometimes — e. g., in the General Scholium to Book III of the Principia — carried out in awareness of the issues involved, to bridge the gap between the non referential symbolism of mathematics and a language too protean to be tied down to single, pure meanings.--J.M. Coetzee (1982) "Newton and the Ideal of a Transparent Scientific Language," Journal of Literary Semantics.
Among recent philosophy the Whorf hypothesis is primarily an object of curiosity as background to Kuhn's Structure (and maybe Quine's Word and Object), although two of my favorite philosophers, Lieven Decock and our very own Helen de Cruz (and a few others), work on it. (Undoubtedly part of the lack of interest is recent, philosophical abhorrence of relativism, but the thesis has not disappeared from linguistics and psychology.)* A charismatic economist, Keith Chen, rediscovers a version of it in economics by focusing on the surprising impact of linguistic structure and financial activity (saving rates)--here's a popular video. (HT Hülya Eraslan; I ignore my methodological qualms today.) In the article quoted in the epigraph above (it's his conclusion), Coetzee is interested in the version -- he attributes it directly to Whorf -- that "we see nature along lines laid down by our native languages." I call this version, the "narrow Whorf thesis" (to distinguish it from broader claims about linguistic/cultural relativism and also Whorf's explanation for the narrow Whorf thesis.)
Now, what does the narrow Whorf thesis have to do with Newton and Coetzee?
Newton in fact emerges as an exemplar of how one can unconsciously project the structure of one's language out on to the stars and then believe that the resulting map is a true picture of the universe, rather than a picture determined by one's own particular linguistic perspective. Newton typifies what Whorf elsewhere calls a "mechanistic way of thinking" which has its basis in certain features of Indo-European syntax as "rigidified and intensified" by the Artistotelian tradition in logic.
So, Newton is exemplar (to Whorf). While Newton may have thought and is often taken to have refuted the Aristotelian world view, he remains fundamentally influenced by the categories inherited from Aristotelian logic. (In recent Newton scholarship, SteffenDucheyne has explored the influence of Aristotelian logic texts on Newton.) We can't underestimate the rhetorical force here; even the highest peaks of scientific achievement are influenced by hidden causes. The very best (natural) philosopher lacks proper self-understanding. (Such a charge against Newton was first promoted on other grounds by Hume.)
As I pointed out before, the narrow Whorf thesis (without commitment to Whorf or any of his claims) gets trotted out as an error theory by people as diverse as Tim Maudlin and Judith Butler (in discussion with our readers I learned that "Thomas Aquinas repeatedly accuses Platonic metaphysics of reading the existence of Forms off of the language of universals.) Surprisingly enough, in a short piece on "Ancient Logics and Metaphysics," Adam Smith ties the narrow Whorf thesis directly to Aristotle. Smith argues that our tendency toward a natural taxonomy is at the root of the Aristotelian metaphysical system. Smith insists that many of the “doctrines” of Aristotle seem “to have arisen, more from the nature of language, than from the nature of things.” (“Ancient Logics,) Here Smith shares here in a mistrust of the epistemic capacity of language more general among early modern thinkers (e.g., Berkeley Principles of Human Knowledge, Introduction, Section 25). Not unlike Spinoza, who attributes Aristotelian teleology to a projection of human desire (and fear) in the Appendix to Ethics 1, Smith offers a psychological account to explain why even earlier philosophers had been led to erroneous conclusions. While Smith is not harshly critical of Aristotle’s system (“with all its imperfections it was excusable, in the beginnings of philosophy, and is not a great deal more remote from the truth, than many others which have since been substituted in its room by some of the greatest pretenders to accuracy and precision.” (“Ancient Logics,” 5) he does not endorse it either; the narrow Whorf thesis is an error theory in Smith's hands, too.
Through a careful analysis of Newton's English and Latin, Coetzee argues that Newton's account of force does not "emerge smoothly from or fit smoothly into, the structures of Newton's own language(s)." Even though Coetzee's scholarly sources a bit dated, the crucial features of his argument are a direct engagement with Newton's texts; unsurprisingly, Coetzee is a very careful and subtle reader of Newton. He argues that the details of Newton's linguistic constructions,
precisely suit Newton's purpose in that they commit him to neither the agentive nor the instrumental reading. Indeed they do; but only äs long äs Newton's purpose is understood to be a Strategic or rhetorical rather than a scientific one — that is, to present an incomplete theory as persuasively äs possible. We ought to be clear about the nature of the ambiguity of (3a) [that is, "viribus centripetis Planetae . . . retineri possunt."--ES]: while it Stands uncommitted between two semantic interpretations, it in no way brings out the fact that the agentive reading and the instrumental reading are either-or alternatives. In effect, the passive in (3a) therefore allows Newton a rhetorically successful evasion of a choice between the alternatives of gravity as prime cause and gravity as mediate cause.
I am no Latinist, but Coetzee's argument (which is backed up with quite an impressive command over Newton's texts) and conclusion strikes me as correct about Newton. In fact, Newton tried very hard not to be captured by either pre-existing linguistic commitments and pre-existing philosophical commitments; later generations have generally projected other people's philosophical commitments onto Newton (recall my post yesterday about Thomas Nagel).
Of course, for the sake of argument, Coetzee, does work with a close cousin of the narrow Whorf thesis:
if he had worked in a radically different linguistic medium from Latin and English, Newton might have been better able to do justice to his thought....Such a language is conceivable, though whether the rest of Newton's physics could have been elaborated in it I do not know: probably not. But if one tries for a moment the (literally mind-bending) experiment of locating oneself within such a language, one can see that the entire controversy over occult causes would never have occurred, simply because from inside the language the distinctions that people like Leibniz were making would have been unnatural or even invisible.
Coetzee allows that within a given language some distinctions remain naturally inaccessible. This is a kind of linguistic relativism and for present purposes it is unobjectionable. (We can leave aside to what degree one can translate -- by way of paraphrase -- the Leibnizian distinctions into the conceivable language.)
So, Coetzee is adamant that Newton is a terrible exemplar for the narrow Whorf thesis. Why does Coetzee care so much about Newton?
As the epigraph above reveals, Coetzee signals that Newton's adoption of mathematics facilitated the move away from the dangers associated with the narrow Whorf thesis. But this does not exhaust Coetzee's analysis of Newton's rhetoric surrounding mathematics; drawing on Newtonian passages that I (much later than Coetzee) have also called attention to (including here at NewAPPS), Coetzee writes:
What is revealed in...these instances is an awareness of the risks involved in popularizing his work, in extending its range of readership from a circle of savants to an audience that needs to have mathematical findings interpreted to it in figures, i. e., analogies.
"Mathematical philosophy" (in the seventeenth and twentieth century notions of the term) creates a barrier between expert and ordinary person (recall also this post on Coetzee). Coetzee thinks some such gulf is indespensible to maintaining standards of quality. This is not to deny that the adoption of mathematics can faciliate communication among experts, including folk from very different cultures, so it certainly can also be thought of as expanding who gets to participate in the conversation. So, while mathematics can be topic neutral, the choice for it as the privileged form of communication and articulation is -- as, say, Carnap also well understood -- part of the moral politics of philosophy (recall this post on Quine and Carnap and more indirectly this one).
That is, on my reading of Coetzee, he urges philosophers to be more self-aware and more ambitious--the details are for another time. But given the protean nature of language, he's probably saying a lot of other things to us, too.
*I thank Helen de Cruz, Leon de Bruin, Bryce Huebner, Stephen Clark, Charles Wolfe, and Benny Goldberg.
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