"I believe that [W.E.] Johnson, like McTaggart and Aristotle, deserves commentators." A.N. Prior (1949) MIND.
"Mesmerized by Homo economicus, who acts solely on egoism, economists shy away from altruism almost comically. Caught in a shameful act of heroism, they aver: "Shucks, it was only enlightened self interest." Sometimes it is. At other times it may be only rationalization (spurious for card-carrying atheists): "If I rescue somebody's son, someone will rescue mine.
I will not waste ink on face-saving tautologies. When the governess of infants caught in a burning building reenters it unobserved in a hopeless mission of rescue, casuists may argue; "She did it only to get the good feeling of doing it. Because other-wise she wouldn't have done it." Such argumentation (in Wolfgang Pauli's scathing phrase) is not even wrong. It is just boring, irrelevant, and in the technical sense of old-fashioned logical positivism "meaning-less." You do not understand the logic and history of consumer demand theory — Pareto, W. E. Johnson, Slutsky, Allen-Hicks, Hotelling, Samuelson, Houthakker,... — if you think that is its content."--P. Samuelson (1993), The American Economic Review.
There is a school of thought that locates the origins of analytical philosophy in the Cambridge of the philosopher-economist, Sidgwick and his students. After all, in Sidgwick's writings we find all the analytical virtues, and it is, thus, no surprise that Rawls and Parfit treat him as our vital interlocuter. Those (that is, the circle around Sidwick) recognized in Boole's work -- to quote W.E. Johnson -- "the first great revolution in the study of formal logic...comparable in importance with that of the algebraical symbolists in the sixteenth century." (2.6, p. 136) While it is not the story I tend to tell (say, here and here), I like this approach because it reminds us of the non-trivial overlap between logicians and economists so distinctive of Cambridge between 1870-1940, and thus, puts Keynes (father and son) and Ramsey back into the origin of analytical philosophy.
Now, the logician-economist, W.E. Johnson (1858 – 1931), is a test-case for this school of thought. (Recall the significance of Johnson to of our very own Mohan [and here].) For, while Johnson does not belong to the British Idealists, he does not figure in the stories we tell about our origins at all (selective evidence: Landini's Russell nor Candlish's The Russel/Bradley Dispute do not even mention Johnson). Even Wikipidia claims that his "Logic was dated at the time of its publication, and Johnson can be seen as a member of the British logic "old guard" pushed aside" by Russell and Whitehead. Wikipedia fits our narrative of progress; yet what to make of Prior's judgment?
W.E. Johnson wrote the world's most advanced piece of mathematical economics in 1913. (This is not to deny the ongoing controversy over his debt to Pareto.) The technical contribution of "The Pure Theory of Utility Curves," is aptly summarized by Paul Samuelson (in 1938) as "two dimensional analysis of indifference curves." (We might add that in the wake of Pareto, Johnson also moves the subject to ordinal analysis.)
Moreover, following IJ Good, Sandy Zabel has been documenting the original insights of Johnson's account of probability (in part presented in the Appendix to the Logic and in part in the appendix to this posthumous piece). Johnson's work in probability theory, which anticipates, as Zabel notes, non-trivial work by Carnap and Di Finetti, is a clear instance of a Kuhn-Loss.
So, there is no doubt that Johnson had impressive technical skills. In fact, in his Logic, he greatly admires the achievement of Russell and Whitehead's PM (e.g., 2.7. p. 138). His opposition is directed at Russell's account of functions, which, in his entry on Keynes (the father) and Johnson in the 1967 Routledge Encyclopedia of Philosophy, A.N. Prior singles out as noteworthy (volume 4, pp. 550-1--I am grateful to David Levy for sending me these pages and his general encouragement to look at the logician-economists). Some other time I hope to return to Johnson's criticisms of Russell (if I can't find scholarly treatment). In a separate post (before long), I discuss Johnson's account of analysis in his two-part essay (1918) "Analysis of Thinking," which is crucial to answering the question to what degree Prior's approach to analysis can be fit into the history of analytical philosophy.
But here I want to conclude with a speculative thought. It is hard to see, at first, how Johnson's work in economics and philosophy (m athematics, etc.) hang together in any interesting way. These just seem like contributions to particular problems. (And, if so, this might tempt some to see this as decisive evidence for the thought that Johnson was the very first genuine, analytical philosopher in our, problem-solving sense.) In reading Prior's important two-part article "Determinables, Determinates and Determinants," I got some helpful hints. Prior captures one important insight of Johnson as follows:
The importance of this discussion is that it exhibits structural propositions as expressions of which we can say that although their own significance is doubtful, upon their truth the significance of other propositions depends. Now it is not only in the logic which tries to take account of the relation between determinates and determinables that we encounter propositions which are related to other propositions in this peculiar way, their truth being a presupposition of the significance of these other propositions, while their own significance is hard to see (though of course if truth implies significance, they must have significance of some sort). In this respect, Johnson's " structural propositions " bear a striking resemblance to Wittgenstein's " tautologies ", that is, to the " laws of thought " of the older logicians, and to others like them or derived from them. (Prior, (1949), Mind, p. 20)
Now this is neat stuff, but it's not what I am ultimately after in this post. For Prior focuses ultimately on the proposition-side of the "relation of accordance with a certain fact attributed to the true proposition" (1.7, 16-17). What about (ahum) the facts? David Sanford concludes his gripping (!) encyclopedia article, "Determinates vs. Determinables" as follows:
Johnson said that it is a “universally adopted postulate that the characters of things which we can only characterise more or less indeterminately, are, in actual fact, absolutely determinate.” In saying it is a postulate, Johnson does not mean we merely assume it in order to deduce its consequences. He means rather that it is both obviously true and cannot be inferred from truths that are even more obvious. But the so-called postulate is not obviously true.
As regular readers know, I am also inclined to think that the "so-called postulate" ought to be treated warily. But does Sanford accurately capture Johnson's position?
In his Logic Johnson writes that, "a postulate stands for a proposition which cannot be brought to the test of experience, but the truth of which is demanded by the thinker." (Vol. 1, p. 6 n.2) This need not imply that Johnson thought a postulate to be "obviously true." After all, in context, Johnson is describing "different attitudes" toward a proposition a thinker can take, and the "prominent logical terms" are "hypothesis, postulate, axiom." So, in line with Prior's point above, it looks to me that Johnson allows something like a contingent/revisable a priori. But this is connected to a further stance; to be precise, I hypothesize that for Johnson a postulate must be treated as subjectively, necessary true. But one can, thus, recognize upon reflection, that one's postulate 'need' not be so objectively (or in Johnson's terms, constitutively).
Given that the younger, more famous Keynes was a close student of Johnson (who was a close friend of Keynes' less famous father), we might be left wondering if the very idea of the possibility of metaphysical and epistemic indeterminacy, which Keynes embraced, wasn't first suggested to him by the forgotten Johnson. Johnson's and Keynes's views on indeterminacy were not very popular after the technocratic turn in economics and philosophy (post WWII). But luckily there has been a recent revival of interest in metaphysical indeterminacy in Leeds and Toronto, so perhaps it's time to reconsider our our roots in the logician-economists that according to at least one attractive story co-founded analytical philosophy.
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