Thursday, September 27, 2012

Whewell on Newton's Laws I: Induction

"Science is his forte and omniscience is his foible," Sydney Smith famously said about William Whewell. And knowing a bit about everything was indeed Whewell's most obvious characteristic. Professor of mineralogy from 1828 to 1832, professor of moral theology and casuistical divinity from 1838 to 1855, Master of Trinity College in Cambridge thereafter, Whewell corresponded with many of the great scientific names of the day, including Faraday and Darwin. (Faraday, for instance, once wrote Whewell asking for advice in naming new scientific concepts; Faraday had thought of 'eastode' and 'westode', but Whewell suggested that he use 'anode' and 'cathode' instead, which Faraday did.) He was old college friends with John Herschel and Charles Babbage, and together with a number of other notable names of the day they had advocated reforms in mathematical education -- in particular, bringing a more continental approach to calculus to England. He wrote textbooks on mathematics and physics, advocated improvements in mineralogical classification, did extensive research on the tides, assisted other scientists (particularly George Airy) in their work, tanslated poetry from the German, got involved in major contemporary debates on political economy, contributed to the revival of Gothic architecture, and wrote his massive and influential History of the Inductive Sciences, which he followed with Philosophy of the Inductive Sciences. He was a busy man, William Whewell, right up to the day he was thrown off his horse and died.

What I particularly want to look at is Whewell's assessment of Newtonian physics, because there are very few people who have ever looked in such detail at the philosophical implications of Newtonian physics. And perhaps the best way to do that is to focus in particular on how Whewell interprets Newton's famous three Laws. In order to do this, however, it's necessary to say a few things about Whewell's approach to two major preliminaries: science in general and causes. In this post I'll only look at the first.

The rough-and-ready summary people often give of the difference between deduction and induction is that in deduction we descend from general propositions to particulars and in induction we ascend from particulars to general propositions. There are any number of things wrong with this if we take it as rigorous, but it does raise the basic issue of how you can have scientific knowledge if you start with particular experiences. Whewell refers to this problem in a number of different ways; for our purposes it will be handy to have a single label for it, so I will call it the modal disparity problem. What we immediately learn from our experiences is particular, contingent, and approximate; in sciences like physics and chemistry, however, we draw conclusions that are clearly none of these things -- they are extraordinarily precise, indeed, sometimes far more precise than our prior experience could warrant, they are at least general and often universal, and at least sometimes they seem to be necessary. The modalities of our starting point and ending point are very different. The process by which we get one from the other is what Whewell generally has in mind when he talks about induction.

For most of his philosophical career, Whewell is fighting a very strong prejudgment in his contemporaries that the sciences work by accumulating facts and then through comparison ascending to general ideas; this is associated with Sir Francis Bacon, and it's a commonplace in England when Whewell comes on the scene that Bacon provided, at least more or less, the best account of scientific inquiry. Whewell will try to shake this up, and his approach is noticeably more 'German' in character. We cannot simply pull ideas from experiences, Whewell thinks, precisely because of the modal disparity. No number of particular cases will get you universal propositions; no number of contingent truths will get you necessary ones. Something else must be going on -- something must be added to the mix in order to make the process of induction possible. And Whewell's answer to what this extra element is, is in a sense straightforward: what you add is the mind itself, which formulates ideas and applies them to experience. We do not get the idea of Number from our experience; it is, so to speak, something in our minds already, that we just have to clarify and impose on the experiences so as to be able to make sense of them. Or to put it in other words, it is our way of looking at experience that imparts necessity, universality, and precision to our conclusions. This is not to say that there is no sense in which we get general propositions from particular experiences. As he often says, we superinduce the ideas on the facts we've discovered; we need both to come together for us to have knowledge. As he puts it in Of Induction, which is his critical response to Mill (who writes more in the Baconian tradition): "Induction is experience or observation consciously looked at in a general form. This consciousness and generality are necessary parts of that knowledge which is science" (p. 15). It is the particular facts we discover through experience that make our knowledge knowledge of something; and it is the mind's way of looking at it through ideas that organize these facts that make it knowledge at all. As he says (p. 13):

But the elements and materials of Science are necessary truths contemplated by the intellect. It is by consisting of such elements and such materials that Science *is* Science.

And a little later (p. 14): "Induction for us is general propositions, contemplated as such, derived from particulars." When we put it all together we get a fairly robust and multi-faceted view of scientific discovery (pp. 29-30):

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;--the Ideas of Time, of Force, of Number, of Resemblance, of Elementary Composition, of Polarity, and the like. But in all cases, the mind performs the operation by the apprehension of some such relations; by singling out the one true relation; by combining the apprehension of the true relation with the facts; by applying to them the Conception of such a relation.

In a very simplified example he gives at one point, he notes that ancient astronomers discovered that the planets had recurring periods; in discovering this they applied the idea of Time to astronomical phenomena. Later they began to organize them according to the idea of Space as well, which was refined by Kepler's use of extensive data and repeated attempts to come up with a clearer and more powerful organizing idea than had previously existed. Afterward, Newton was able to add an even greater degree of organization by organizing them by the idea of Force, as well, in his theory of gravitation. Inductive sciences like physics, then, require several different strands of inquiry to come together. We need to gather new facts; we need to clarify our ideas and conceptions; we need to think through the implications of these ideas for the possible ways in which the facts can be organized; we need to test and compare; and by this joint and simultaneous progress along two fronts, that of pure concept and definition and that of observation and experimental fact, we get progress in the sciences. We do not merely observe nature; we interpret her.

There are many Ideas that organize science, but arguably there are three that Whewell thinks particularly important: Space, Number, and Cause. It is the last that is the most important for our purposes, and we will look at Whewell's account of the Idea of Cause in the next post in this series.


  1. Arsen Darnay7:53 AM

    More, more! (as they say). Delighted by these series. Lady
    Mary Shepherd is still luminous in my memory—very much a contemporary of
    Whewell. If there are choirs of angels, so there must be choirs of
    philosophers, and it seems to me that the more obscure of those hold more
    light, oddly, than the most luminous. 

  2. branemrys8:14 AM

     That's often true; there are often hidden treasures in these names who were very respected in their day but faded out afterward.


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