Four Critics of Mill I: Whewell and the Induction Controversy

Part one of a four part series

William Whewell (1794-1866)

According to the Stanford Encyclopaedia of Philosophy, John Stuart Mill was 'the most influential English language philosopher of the nineteenth century'. Intuitively, this claim feels right. Mill wrote about everything, and everything he wrote - at least for a time - enjoyed considerable popularity. His works on economics became standard textbooks (though they were quickly superseded), as did his A System of Logic (also superseded). He scored a more enduring success with his political manifesto, On Liberty (1859), which was an instant classic and is still read approvingly today. In many ways, we live in a world created after the image of Mill's program for philosophical and social reform. If as one modern interpreter has opined, his tract on The Subjection of Women (1869) reads like a series of truisms, that is because Mill's view ultimately won a total victory. To a greater or lesser degree, we are all Millians today.

Another index of a philosopher's influence is the level of criticism he or she drew in their lifetime and after. By this measure Mill was without question the most influential thinker of his day. In this series of blog posts I want to examine four critics of Mill's project, starting with the great polymath William Whewell, who in their debates over the theory of induction developed a potent critique of Mill's philosophy of science and of the empiricists tradition more broadly.

Unlike Mill, Whewell has been almost completely forgotten by the public, and is only read today by historians of the philosophy of science. And yet, it would require a further blog post to even begin to enumerate all of Whewell's contributions as a scientist and scholar. He held professorships in mathematics, mineralogy and moral philosophy at Cambridge, over which period he produced works in mathematical physics (on mechanics and dynamics), political economy, theology and the architecture of German churches. He translated Plato and Grotius. In his spare time, he created the new nomenclature for the phenomena of electromagnetism that was adopted by Michael Faraday (electrodes, ions, anodes and cathodes all came from Whewell), as well as the labels for the different geological epochs that Charles Lyell used in all eleven editions of his Principles of Geology (1830-33).

The Whewell-Mill debates followed on from the publication of Mill's A System of Logic (1843), which put forward his empiricist theory of the inductive sciences and did so in explicit opposition to Whewell's own positions as outlined in his massive four volume History of the Inductive Sciences (1837). After A System of Logic went through a second edition Whewell produced a rebuttal in his essay ‘On Induction, with especial reference to Mr J Stuart Mill's system of Logic’ (1849), and a series of trenchant exchanges followed. Below I will try to give a blog-sized account of the issues at the heart of their dispute.

One thing to get clear first is that Mill considered induction to be the core of logic. This is clearly stated in the opening paragraph of Book III of A System of Logic, where induction is described as 'the main question of the science of logic—the question which includes all others'.

As for the actual logic of induction, Mill's arguments can be reduced, without too much loss, to a caricature of five theses:

1. Placed in contact with the external world, the mind encounters individuals or particulars. Facts are data pertaining to individuals or particulars and our normal experience furnishes us with an undifferentiated mass of such facts.

2. In some classes of facts we can observe apparent regularities - induction is the process of generalising from particular facts to something that is true of all facts of this class.

3. The logical mechanism for extracting a valid induction from individual facts is provided by Mill in his four canons of experimental enquiry. The canons share the same essential idea that inductive science proceeds by adding (or 'enumerating') and comparing instances of the phenomena in order to establish regular patterns of cause and effect.

4. By careful delineation of such causal patterns, we can rise from the particulars to a generalisation that has the character of experimental law

5. These laws, Mill insists, have all the validity of a 'proof' and are as such definitive - indeed they are the only proofs available to the empiricist and, taken in their totality, make up the deposit of human knowledge.

Whewell's critique looked to knockdown the whole structure of Mill's account of scientific enquiry, and thereby also expose the poverty of his radical empiricism. Mill somewhere describes Whewell as an idealist - a sort of neo-Kantian in Victorian dress - but this is I think a misnomer. If anything Whewell was the originator of a completely separate tradition in the philosophy of science that focused on the central role that hypotheses and symbolic representation play in scientific knowledge. This position is sometimes referred to as holism and is associated with figures as diverse as C S Peirce and Pierre Duhem, Henri Poincare and Willard Van Orman Quine.

I will focus on three lines of attack that are characteristic of Whewell's position.

Whewell's first attack is directed at what in my caricature of Mill is the first thesis - that the materials from which an induction is extracted are facts, and that facts are immediately apprehended by our mind and its sensory equipment. Here is Whewell:

In truth, as I have repeatedly had occasion to remark, all attempts to frame an argument by the exclusive or emphatic appropriation of the term Fact to particular cases, are necessarily illusory and inconclusive. There is no definite and stable distinction between Facts and Theories; Facts and Laws; Facts and Inductions. Inductions, Laws, Theories, which are true are Facts. Facts involve Inductions.

W Whewell, On the Philosophy of Discovery, John W Parker & Son (1860), p. 250

Take temperature, for example. We experience temperature as the feeling of hotness or coldness in different bodies. We know from experience that we can compare two bodies and have a solid sense of which is warmer or cooler, a sense which becomes less and less solid as the two bodies approach equilibrium. In order to measure their relative warmth we need to turn this feeling into a concept that is additive. In other words, to begin to make inductions about the phenomena of temperature we construct an algebraic magnitude which is only related to the 'immediate experience' in the way a symbol is related to the thing it symbolises. The theory and the fact are in this way completely and inextricably enmeshed - or as Whewell puts it 'facts involve inductions'.

The second line of attack builds on the first. Having collected or constructed the set of relevant data, the logical mechanism for induction is, according to Whewell, not merely to compare phenomena but to introduce 'a new conception' that is in a way largely arbitrary and creative - in other words, to bring the data under the organising principle of some 'idea' of the mind, which creates relationships between the facts:

And there is the same essential element in all Inductive discoveries. In all cases, facts, before detached and lawless, are bound together by a new thought. They are reduced to law, by being seen in a new point of view. To catch this new point of view, is an act of the mind, springing from its previous preparation and habits. The facts, in other discoveries, are brought together according to other relations, or, as I have called them, Ideas.

W Whewell, On the Philosophy of Discovery, John W Parker & Son (1860), p. 254

An example that Mill and Whewell debated at length was the discovery of Kepler's law. Kepler's innovation was to re-describe the orbits of planetary bodies as ellipses with the sun situated at one focus. This was a departure from the long and unbroken tradition, uniting Ptolemy and Copernicus, that represented planetary orbits as circular, moving concentrically to either the earth or the sun. Here is Mill:

The object of Kepler was to determine the real path described by each of the planets, or let us say by the planet Mars (since it was of that body that he first established the two of his three laws which did not require a comparison of planets). To do this there was no other mode than that of direct observation: and all which observation could do was to ascertain a great number of the successive places of the planet; or rather, of its apparent places. That the planet occupied successively all these positions, or at all events, positions which produced the same impressions on the eye, and that it passed from one of these to another insensibly, and without any apparent breach of continuity; thus much the senses, with the aid of the proper instruments, could ascertain. What Kepler did more than this, was to find what sort of a curve these different points would make, supposing them to be all joined together. He expressed the whole series of the observed places of Mars by what Dr. Whewell calls the general conception of an ellipse.

J S Mill, A System of Logic, Longmans, Green & Co (1865), p. 327

Mill's disagreement with Whewell concerns the process by which Kepler settled on the geometry of an ellipse. For Whewell this is a classic case of what he calls 'colligation'. Kepler inherited a set of data to which he added his own observations. To make something coherent out of the data they need to be colligated - that is, connected in a system under the 'superinducing' influence of a new idea, in this case, that of an ellipse. Importantly, Kepler chose the ellipse from among a set of possible ideas which could have done the job of colligating just as well. This language is completely incomprehensible to Mill. As he puts it later in the System, 'Kepler did not put what he had conceived into the facts, but saw it in them'. The role of the mind in this discovery is not creative in any way; the idea is obtained by 'abstraction from the very facts … which it afterward called in to connect'. The problem with Mill's argument is that abstraction from the facts could have yielded a number of different geometrical models. For example, the Ptolemaic-Copernican epicycles could be retained and made increasingly accurate by the addition of more cycles to correct errors. Let's suppose Kepler was given occult knowledge of Fourier analysis, two hundred years ahead of schedule, and developed an algorithm for precisely calculating planetary motions on this basis. Would Mill then be committed to saying that we could see this in the facts, in the same way Kepler saw the ellipse? And is deciding between the two models a matter of induction?

Whewell also contested the accuracy of Mill's reconstructed history of Kepler own method. The difficulty for Kepler and for contemporary astronomers was not a matter of facts; it was a question of 'getting hold of the right conception'. Were Mill's theories right, then science would be like a piece of deterministic machinery, into which facts are fed, and out of which new inductive laws are generated with a dependable regularity. Progress would only stop when the facts ran out, which brief acquaintance with the historical record shows is not the case.

This flows nicely into Whewell's third line of attack, which infuses everything he wrote in response to Mill - that his theory of induction would have paralysed the sciences. On this point, Whewell is close to another critic of Mill, Gottlob Frege, who in his Grundlagen der Arithmetik (1884) argues that Mill's epistemology would make mathematical thinking of even the most elementary kind effectively impossible, as it is difficult to see how we can arrive at the system of natural numbers through an unreconstructed empiricism. Frege and Whewell's arguments are complementary; the Millian scientist will not only struggle to do any work of scientific value with his 'canons of induction’, if he's a true believer he'll also have to formulate what little he has achieved without even the most rudimentary mathematical concepts. Attempts have been made, for example by Hjelmslev, to create a purely approximative geometry, variously styled as 'Die natürliche Geometrie' or 'Geometrie der Wirklichkeit', which he opposed to Euclidean-Platonic-Hilbertian geometry. The prospects for such an empirical mathematics were, I think, neatly summarised by Hermann Weyl:

'Hjelmslev, incidentally, is far too concerned with figures drawn on a blackboard and is apt to forget that geometry must also serve as an ideal basis for astronomy and atomic physics […] the sensualism of Hume and Hjemslev - which on principle would recognise as real only the immediately given, without being able to carry this through - is deadly for science'

H Weyl, The Philosophy of Mathematics and Natural Sciences, Princeton University Press (2009), p. 144

These are the main elements of Whewell’s critique, but just as much caricatured as my version of Mill's own theory. For what it's worth, I am inclined to agree with C S Peirce's assessment of the debate, though I may just be revealing my own biases:

‘Whewell described the reasoning just as it appeared to a man deeply conversant with several branches of science as only a genuine researcher can know them, and adding to that knowledge a full acquaintance with the history of science. These results, as might be expected, are of the highest value, although there are important distinctions and reasons which he overlooked. John Stuart Mill endeavored to explain the reasonings of science by the nominalistic metaphysics of his father. The superficial perspicuity of that kind of metaphysics rendered his logic extremely popular with those who think, but do not think profoundly; who know something of science, but more from the outside than the inside, and who for one reason or another delight in the simplest theories even if they fail to cover the facts.’

C S Peirce ‘Lessons from History of Science’ in C Hartshorne and P Weiss (ed.), Collected Paper of Charles Sanders Peirce vol I,II, Harvard University Press (1974), p.29