“To enrich science with a new general truth”: Mill and Whewell on induction

Introduction

In the Preface to the first edition of his A System of Logic, Ratiocinative and Inductive, published in 1843, John Stuart Mill emphasized his indebtedness to certain authors who before him wrote on the topic of induction (Strong 1955). Mill made a special mention of William Whewell, who had, besides providing studies in history of science that were crucial for Mill, frequently expressed “differences of opinion” (Mill in Strong 1955, 209) about induction. Mill explored these differences in the part of his A System of Logic, dedicated to induction, and attacked Whewell’s theory. Whewell did not respond instantly,[1]Although, as it is apparent from his letter to Comte, Mill was hoping that his opponent would (Snyder 1997a, 161). but only after the publication of the second edition of Mill’s System in 1849, with an essay titled On Induction, with especial reference to Mr. J. Stuart Mill’s System of Logic. Mill then answered him again in the third edition, not, as was careful to notice, “from any taste for controversy” (Mill in Strong 1955, 209), but rather because “[t]ruth, on these subjects, is militant, and can only establish itself by means of conflict” (ibid.). Their controversy, now usually referred to as the Whewell-Mill debate, remained an important source of discussions in the field of philosophy of science in the later centuries, which is shown by the number of papers still written of the subject.

That said, the fact is that both authors agreed about the importance of induction for gaining new knowledge. In his The Philosophy of the Inductive Sciences, Founded upon their History, first published in 1840, Whewell writes about “the mental process of Induction […] which is usually and justly spoken of as the genuine source of all our real general knowledge respecting the external world” (2014b, 212). Furthermore, Whewell saw reforming an inductive method of science as his main philosophical project (Snyder 2008, 164). He understood his work as a continuation and correction of Bacon. This is best illustrated by the fact that in the third edition of his The Philosophy of the Inductive Sciences, published as three separate works,the second work is titled Novum Organon Renovatum, as a direct reference to Bacon’s 1620 work Novum Organon (ibid., 177). Mill also understood inductive inference as a legitimate source of knowledge. In A System of Logic, he states that “all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions: that all our knowledge, not intuitive, comes to us exclusively from that source” (2011, 345). For Mill, this holds for scientific discovery as well as for everyday and professional life, since he argued that his rules of inductive inference can be used in any case, “whether the result be to give A an estate, or to enrich science with a new general truth” (ibid.: 349).

Nevertheless, they presented quite different accounts of induction. In this paper, I will try to establish what sets them apart and argue that it is not the frequently supposed distinction between inductivism (Mill) and hypothetic-deductivism (Whewell) about the scientific method. First, I will analyze their disagreement about the role and nature of concepts in induction. Whewell argued that in scientific discovery, e.g., when Kepler discovered his law of planetary motion, a new concept, in Kepler’s case that of an ellipse, is provided by the mind and then “superinduced” upon empirical facts. In contrast to this, Mill argued that the concept of an ellipse was present in the facts themselves, therefore nothing new was added by the mind. In other words, what Whewell calls “colligation of facts” and understands as a crucial part of his theory of induction, Mill dismisses as a mere description of observed facts. I will show that the argument about colligation of facts ends in a disagreement about their underlying epistemological views. Given their different epistemological commitments, the two authors’ respective theories have different emphasis. Mill’s theory is a theory of inductive inference – he hopes to provide a rigorous, logically sound, method of verification of generalizations. Whewell, on the other hand, thinks about induction as a method of scientific practice and thus puts emphasis both on the discovery of an appropriate concept (or a theory) and on its verification. Rather than accepting that Mill is an inductivist and Whewell a deductivist about the scientific method, I will argue that they differ in their understanding of philosophy of science, its scope and aims.

Induction improperly so called?

In the second chapter of Book III of A System of Logic, named “Of Inductions Improperly So Called”, Mill analyzes three accounts of induction that, in his opinion, wrongly characterize it. He first defines induction as a process of inferring that 1) a predicate that is true for known individuals is true for all known and unknown individuals of the same class, or that 2) a predicate that is true for an individual at a specific time will under similar circumstances stay true (Mill 2011, 352). Mill then provides his critique of the accounts of induction that extends over or otherwise oppose this definition. Firstly, he criticizes an account of induction, found in “the common books of Logic” (ibid.), that characterizes the process as an inference that proceeds from a less general term to a more general one, but in which the latter is already included in the former.[2]An example he gives: “All the Apostles were Jews, because this is true of Peter, Paul, John, and every other apostle” (Mill 2011, 353). This kind of induction does not include inference to any unknown individuals. Therefore, Mill calls it “a mere shorthand registration of facts known” (ibid., 353). Secondly, he criticizes a process, sometimes called induction by “mathematicians”[3]This should not be confused with what we now call mathematical induction. Nevertheless, neither what Mill is referring to nor mathematical induction do not conform to his definition of inductive … Continue reading (ibid.), in which something is proven to hold for one mathematical entity and is then generalized to all entities of the same class.[4]An example he gives: “… when we have proved, with respect to the circle, that a straight line cannot meet it in more than two points, and when the same thing has been successively proved of the … Continue reading Although this conforms to his definition, at least at face value, he does not take it to be an instance of valid inductive inference. He argues that the general conclusion is not assented to because individual instances support it, but because it follows from a demonstrative proof of these instances (ibid.). In other words, the proof is conducted for a type of entity, not particular entities. Therefore, there remain no unknown individuals to which the proven property must then be inferred. Thirdly, he criticizes Whewell’s account of induction, with which “the error in question is that of confounding a mere description of a set of observed phenomena, with an induction from them” (ibid., 357). I will analyze this critique thoroughly in this part of the paper.

But before Mill’s critique can meaningfully be presented, I must put forward Whewell’s account that he is attacking. Whewell presents it in Book XI of his The Philosophy of the Inductive Sciences. More specifically, Mill is mostly referring to the contents of Chapter five of the book, named “Of certain Characteristics of Scientific Induction.” Here, Whewell further elaborates on his idea that for a scientific discovery, both observed facts and concepts provided by the mind are required (2014, 213). He argues that, in order to infer a general proposition from the facts, a new element must be added to them, namely a concept that unites them (ibid.). Only in this way can empirical facts be viewed as members of the same class. E.g., the concept of inverse-square attractive force can unify different experimental facts such as ones about falling bodies and those about planetary motion under one class (Snyder 2008, 186). Whewell calls this process “the Colligation of Facts” and defines it as “superinducing upon [facts] a new conception” (2014b, 217). As an example of a successful colligation of facts that resulted in scientific discovery, he presents Kepler’s discovery of the law of planetary motion (ibid., 216).

However, before I turn to Whewell’s analysis of Kepler’s discovery and Mill’s critique of it, I will use my own example of a superinduction of a concept to explain the process in more detail. To propose a more pedestrian example: a drop of rain, a book that I accidentally dropped, and a basketball that fell through a hoop a moment ago, can be, although these being quite different phenomena, unified under a concept of falling bodies.[5]But it is important to keep in mind that this would not yet constitute a colligation of facts as defined by Whewell. As Snyder points out, for a genuine colligation to happen, the concept used should … Continue reading Now, Whewell would insist that the mind provides this concept (Whewell 2014b, 213) and it is not just “transformed sensation” (Whewell 2014a, 30), a claim which is not obvious when applied to my example of falling bodies. In my view, Whewell’s statement can be interpreted as a stronger, metaphysical claim, or as a weaker claim, primarily about how we can carve up the world in different ways. 

(William Whewell by James Lonsdale in 1825, source)

I will explore the stronger version first. Not unlike Kant,[6]Despite the fundamental similarity between the two, namely that Whewell’s fundamental ideas functionally resemble Kant’s forms of intuition and categories of understanding, there are … Continue reading Whewell held that human knowledge is always constructed of two heterogeneous elements, namely ideas and sensations (Snyder 2008, 168). He calls this the “Fundamental Antithesis” of knowledge (ibid.); therefore, his view is usually referred to as antithetical epistemology. Central to his view is the claim that the mind possesses fundamental ideas (that of space, time, cause, and likeness among others (Whewell 2014a, Aphorism XVIII)) that form human perception of the world. In other words, humans perceive everything in space, not because the things themselves are that way, but because perception is an act of the mind that always forms perceptions according to the fundamental idea of space (Whewell 2014b, 195). In other words, fundamental ideas provide relations between phenomena and therefore function as conditions of having any knowledge of the world (Snyder 2008, 168). The sensations of drops of rain, the book, and the basketball as falling bodies are possible because of this fundamental idea of space. Furthermore, fundamental ideas also supply the mind with many subordinate conceptions[7]“As we have said, space limited by boundaries gives rise to various conceptions which we have often to consider. Thus limited, space assumes form or figure; and the variety of conceptions thus … Continue reading which provide a more detailed texture of perception (Whewell 2014a, 37). Therefore, the concept of “falling bodies” can be understood as such, i.e., an ideal concept, derived from fundamental ideas, that the mind used in forming a perception.

I am moving now to the weaker version of Whewell’s claim. Regardless of the source of the concept of falling bodies, it can be argued that this concept is not the most obvious description of the three phenomena. Therefore, it required a deliberate act to understand the phenomena in exactly this way. In other words, the fact that they all fall may indeed be in the objects themselves, but there is nothing in them that discriminates this property over all others. In this weaker sense, Whewell’s can be understood as making the following argument: 1) it is not trivial how we group different facts, 2) but the criteria for this operation are not provided by the facts themselves, 3) therefore, some mental content is involved in the process. This aligns well with some of his statements, for example: “We take a standard, and measure the facts by it; and this standard is constructed by us, not offered by Nature” (Whewell 2014b, 214).

Now, I can turn to Whewell’s example of the colligation of facts, namely that of Kepler’s discovery of the law of planetary motion. He begins by noticing that, in former accounts of induction, the act of inventing the appropriate concept was often ignored (Whewell 2014b, 215). He references to Aristotle’s account of inductive syllogism and provides his own example of it: “[1] Mercury, Venus, Mars, describe ellipses about the Sun; [2] All Planets do what Mercury, Venus, Mars, do; [3] Therefore all Planets describe ellipses about the Sun” (ibid.). He criticizes Aristotle because he focused only on providing “the evidence of the inference” (ibid., 216) and overlooked “the invention of the second extreme term” (ibid.). Whewell’s point is that Kepler’s act of bringing the concept of an ellipse into the inductive inference was not a trivial step,[8]It escapes Whewell’s notice that the same can be said for the first extreme term, namely “planets.” That does not necessarily work against him; it only shows that even when scientists are … Continue reading but a laborious one that a theory of induction should account for. He points out that Kepler tried many other alternatives of planetary motion,[9]E.g., “various combinations of epicyclical constructions” (Whewell 2014b, 216). before settling with ellipses. Furthermore, Whewell does not diminish the role of proving the inductive inference,[10]“The Invention of the Conception was the great step in the discovery; the Verification of the Proposition was the great step in the proof of the discovery” (Whewell 2014b, 217). rather he is pointing out that this is not the only step in the inductive inference that needs to be explained by a comprehensive theory of induction (ibid., 217). In other words, for Whewell, the colligation of facts under a concept already constitutes a genuine act of induction. Understood either in the weaker or the stronger sense analyzed above, the process of superinducing a concept to facts results in a new combination of facts and conceptions that can then be tested. If the newly found combination is well corroborated, then the process of colligation expands knowledge, which can be understood as a feature of induction that separates it from a mere description or a deductive inference.

Mill strongly opposed this claim that unifying some observations under a concept already constitutes a genuine act of induction. More specifically, he argued that Kepler did not superinduce a concept of an ellipse upon Mars’ orbit around the sun, but that he only observed it. To argue this, Mill first compares Kepler to a navigator sailing around a piece of land, observing its coast, and, after returning to the same spot a couple of days later, describing it as an island (2011, 357).[11]It should be noted here that this example does not serve Mill all that well. For details, see below. Although he admits that Kepler’s operation “was far from being as easy as that of the navigator” (ibid., 358), he conceives them as essentially the same. He sees only one difference between them: navigator could observe the coast directly, while Kepler had to use indirect observations of Mars’ position relative to the Earth’s position.[12]Mill does not explain what kind of data did Kepler use. For an overview of how Kepler arrived at his calculations of Mars’ orbit, cf. Forster (2011). To solve this disagreement between examples, he presents the following counterfactual argument: 1) If the path of the planets were visible and Kepler had a privileged position to see it fully, the law of elliptical orbits could be arrived at only with observation; 2) The first part of the counterfactual is not true only accidentally; 3) Therefore, it can be said that Kepler’s law could be arrived at only with observation (ibid., 361). He then concludes that, although a concept is necessary to unify separate facts and reason about them, this conception is not something “pre-existent,” but just “a copy” of something that is already in the facts themselves (ibid.).

This attack can be targeted at both the stronger and the weaker claim contained in Whewell’s account of the colligation of facts. First, I will evaluate it against the weaker claim that the process of grouping facts requires some independent mental content. It needs to be pointed out that Mill would accept that a concept, used to describe a particular set of facts, need not necessarily be collected from the same set (Mill 2011, 362). It can be selected “from among those [concepts] which have been previously collected by abstraction from other facts” (ibid.). In other words, a concept known to a scientist from her past experience can be used as a hypothetical description of a set of facts before her. She can then test if the hypothetical description actually “correctly represents the series of the observed facts” (ibid.). If it does, it can be used as a description of them; if not, it must be discarded (ibid.). In Mill’s view, this additional step of producing and testing hypotheses is required only because we do not have “adequate visual [or other sensual] organs” (ibid., 363). But he fails to provide sufficient support for this conclusion. The counterfactual presented in the paragraph above fails in two points: 1) it fails to disprove that at least in some cases there is some independent content involved in what Mill calls description of facts, 2) it can also be used against Mill account of induction. The first point can be shown more easily with Mill’s example with a sailor. It is questionable if “an island” is just a straight description of the fact that after sailing around it for a couple of hours or days, one will arrive at one’s starting point. The concept of an island only makes sense in opposition to the concept of a continent. In “the facts themselves,” there exists no qualitative difference such as this, only quantitative ones between smaller and larger pieces of land. Therefore, it is not at all evident that this is an example of a description in Mill’s sense of the word. And while Mill’s argument does not address this issue, Whewell’s account of the colligation of facts has fewer problems with it.[13]Although his solution admittedly is not the most elegant, since he would have to argue, that both an island and a continent are a priori concepts that follow from fundamental ideas. Second, it is not clear why our inability to always successfully collect appropriate concepts from the facts is only accidental, while our inability to know something for the whole class of individuals is necessary. The following argument can be made: 1) If we could see all the swans that exist at the same time and would know the past and the future, we would be able to determine that they are all white just by observing them; 2) The first part of the counterfactual is not true only accidentally; 3) Therefore, an inductive inference that all swans are white, is only a description. It may be harder to imagine humans knowing the past and the future at the same time, than Kepler floating in space and observing Mars’ visible path, but that does not make Mill’s argument more convincing.

In addition, Mill does not have much to say about Whewell’ s stronger claim that fundamental ideas and ideal concepts function as conditions of having any knowledge of the world. He only denies this without providing much argumentation. This is expected, given his empiricist view that “all genuine knowledge […] whether theoretical or ethical, must be obtained by observation and experience” (Macleod 2016). He takes the proposition that all concepts originate from observed facts (Mill 2011, 361), as the premise on which his argumentation is built. And the same can be said for Whewell, who uses his antithetical epistemology as a basis for his theory of induction.

Discovery and proof

Considering what has been said so far, one has to acknowledge a disagreement between the two authors’ fundamental epistemological views about the nature of facts.[14]Or, as Walsh puts it: “In the final analysis, the dispute is unresolvable. Setting aside all the lacunae in Mill’s criticism, the fact remains that he seems to suggest that certain properties … Continue reading This strongly affects the scope and emphasis of their respective theories of induction. Since Mill sees the discovery of an appropriate concept as a completely trivial step, his theory of “the operation of discovering and proving general propositions” (2011, 347) focuses entirely on the proving, i.e., finding a logically rigorous method of verifying generalizations. He is not satisfied with a simple enumerative induction of the form “That F is G. That other F is G. Yet another F is G. All observed F are G. Therefore: All F are G” (Wilson 2008, 257) but tries to establish a method of testing enumerative inductions and making them more plausible. These are his so-called “canons of the Inductive Logic” (Mill 2011, 398), consisting of four methods,[15]The methods are: 1) the method of agreement, 2) the method of difference, 3) the method of residues, and 4) the method of variation (Macleod 2016). designed to isolate a real cause of certain phenomena or, in present day terms, sufficient conditions for a phenomenon to arise (Wilson 2008, 258). I will not present the four methods of the canons of induction in detail. However, it is important to understand that they are used for eliminating alternative generalizations of experimental data (ibid.). Let us say that a phenomenon A always co-occurs with phenomena P1, P2 and P3. Simple enumerative induction only allows us to form a general statement “when P1, P2 and P3 occur, A will occur”. Mill’s method of agreement, on the other hand, can be used to design an experiment in which phenomena P1, P2 and P3 can separately be produced to observe in which cases A arises. If we establish that A arises only when both P1 and P3 are present, we can conclude that P1 and P3 are sufficient conditions of A. P2 has therefore been eliminated as a partial cause of A, allowing us to formulate a much more precise and better tested general statement. Mill holds that by application of the canons of induction, scientists “can isolate causes and reveal the laws which govern natural phenomena” (Macleod 2016).[16]As Wilson points out, this method presupposes that 1) one of the co-occurring phenomena is indeed a cause of A, and 2) that it is possible to determine all possible causes of A (Wilson 2008, 259). He … Continue reading

John Stuart Mill by London Stereoscopic Company, circa 1870, source)

In contrast to Mill’s, Whewell’s theory of induction accounts for both the discovery of appropriate concepts[17]Considering the example given in the previous paragraph, it might not be clear why exactly such concept is needed. The thing is that a given phenomenon usually does not co-occur with only three other … Continue reading (“the colligation of facts”) and its verification. The latter has a less rigorous character then Mill’s canons and it consists of three separate criteria: 1) prediction of the unknown facts, 2) “consilience of induction from different and separate classes of facts” (Whewell 2014b, 238), and 3) coherence of scientific theory which can interpret new evidence without adjustments made to it (Snyder 2008, 185). The first and third criteria are quite straight forward. When Kepler, for example, established that Mars’ orbit is elliptical, this theory should be able 1) to predict other unobserved positions of Mars, and 3) to account for some future evidence of positions of other planes, without significant adjustments made to it. The second criterion, the “consilience of induction,” requires some additional explanation. Whewell characterizes it as a process in which “inductions from classes of facts altogether different have […] jumped together” (2014b, 230). His central example of this is Newton’s theory of gravitation, which consolidated phenomena “such as planetary motion, satellite motion, and falling bodies” (Snyder 2008, 186), under a more general concept of “phenomena caused to occur by an inverse-square attractive force of gravity” (ibid., 187). Newton’s concept of the inverse-square attractive force did not only account for the facts colligated under it, but also for other facts that were before considered to be of a different class. In that way, he achieved a new level of generalization. Whewell saw consilience of inductions as conclusive proof that a theory is true (Whewell 2014b, 233).

Given these two accounts of validating scientific discovery, Mill’s “theory of proof” was seen as promoting an inductivist approach to the scientific method, while Whewell’s “theory of discovery” was seen as a hypothetico-deductivist one (most noticeably Buchdahl 1971; cf. Snyder 1997b, 581 for a more extensive bibliography). It is hardly controversial that Mill is indeed an inductivist. Although his account is sometimes characterized as presupposing several different hypotheses and then eliminating all but one (Wilson 2008, 258), these “hypotheses” should not be understood as guesses or deductive statements, but as generalizations from observations. Let us again take the example used above. A scientist observes that when phenomena P1, P2 and P3 occur, phenomenon A occurs. The hypotheses she needs to be tested are: H1) P1, P2 and P3 cause A to occur, H2) P1 and P2 cause A, while P3 co-occur only accidentally, H3) P1 and P3 cause A, while P2 co-occurs only accidentally, and so on. When hypotheses are established, an experiment that will test them can then be conducted. Hypotheses, as well as a conclusion, established on experimental results, are both drawn from empirical evidence. Mill’s account, therefore, satisfies a criterion for inductivism, presented by Buchdahl (1971), namely, that a conclusion of inference must be drawn from the evidence, not just tested upon evidence. On the other hand, it is not clear if Whewell’s theory satisfies this criterion. Arguing that superinducing a concept upon some fact and then checking, if it satisfies conditions of prediction, consilience, and coherence, equals to deductively establishing a hypothesis which is then tested upon facts, is not, at least at face value, in contradiction with what has been said about Whewell’s theory.

However, labeling Whewell as a hypothetico-deductivist is not uncontroversial. One of the strongest opponents of this characterization of Whewell is Laura J. Snyder (Snyder 1997a; 1997b; 2008; 2019); but cf. also Andersen and Hepburn 2020). She presents a convincing argument that Whewell’s account of the scientific method cannot be described as hypothetico-deductivist (Snyder 1997a).[18]She also argues that Whewell does not present a retroductivist account since he does not think that retroductive inference is the only way to draw hypotheses from data (Snyder 1997a, 166). … Continue reading She presents two defining characteristics of a hypothetico-deductivist account of the scientific method: 1) “only evaluative criterion for hypotheses is that they entail true empirical consequences” (Snyder 1997a, 163), 2) hypotheses can be discovered by “non-rational guesswork”, i.e., without “any particular method” (ibid.). She is right to point out that Whewell would reject them both. He would argue 1) that consequential testing is not enough since hypotheses must be inferred from data, from which also follows that 2) the hypotheses cannot be randomly guessed. In other words, Snyder rejects the premise that superinducing a concept equals to deductively establishing a hypothesis about a set of data, which is, in my view, justified.[19]Also, a more general point can be made: the frivolous “guesswork” suggested by hypothetico-deductivism again suggests a mind that is, although active vis-à-vis empiricist’s passive observer, … Continue reading Although Whewell sometimes talks about “guesses” that a scientist makes about observed data (2014b, 220), these guesses are not non-rational. Instead, they are based on two previous steps, that of “decomposition of facts” and “explication of concepts” (Whewell 2014b, 171, 199; cf. Snyder 2008, 179–81). As already seen above, Whewell holds that the mind always plays an active role in forming sensations, i.e., it provides ideas and concepts that are then used to unify sensations (2014b, 193). He makes an important observation that although a concept has at some point been deliberately used to unite a set of facts, this act of uniting facts in a particular way quickly slips out of notice (ibid., 217). Consequently, scientific observation must first be made possible by making the concepts involved in perception explicit and then by decomposing already unified facts to more simple ones. Therefore, it is not the case that Whewell argues for randomly producing different concepts that can be used to unite the facts. Rather, he argues that after a careful examination of facts, a scientist should try to find concepts that she deems most appropriate for uniting the facts. These concepts (or hypotheses) can then by tested using the criteria of prediction, consilience, and coherence.

Regardless of Whewell being a hypothetico-deductivist or not, a more general argument can be made against dividing the two philosophers along inductivist and hypothetico-deductivist lines. This distinction simply does not fit well with their philosophies – it cannot capture what differentiates them. As I will try to show in this last part of the paper, they differ on the meta-methodological rather than the methodological level.[20]For the distinction between the two levels and a similar suggestion cf. Andersen and Hepburn (2020). On the one hand, Whewell provides a comprehensive theory of scientific practice that consists of more then just normative standards for experimental testing. Although he prided himself that his philosophy of science is grounded in his studies of its history (already suggested in the title The Philosophy of the Inductive Sciences, Founded upon their History; cf. Cobb 2011), the opposite is also true. Laudan points out that in his writing about history of science Whewell “was concerned with tracing the development of science in terms of certain categories of narration” (1971, 385), provided by his theoretical framework. Furthermore, in his essay “Of the Transformation of Hypotheses in the History of Science” he explicitly tries to answer a question of “how it is possible that, in subjects, mainly at least mathematical, and therefore claiming demonstrative evidence, mathematicians should hold different and even opposite opinions” (Whewell 1856, [139]). That is, he understood that the development and especially success of scientific theories does not depend only on their ability to provide proofs, but involves a more complex process of accounting for existing phenomena and successfully predicting new ones while remaining sufficiently simple. He saw that there is usually more than one scientific theory competing for dominance and argued that the one which satisfies the criteria of prediction, consilience and coherence wins. Therefore, it can be said that Whewell provided a rational reconstruction of scientific progress.  

What left Whewell vulnerable to Mill’s criticism was his conflation of the criteria for a scientifically more desirable theory with a criterion for truth (cf. Lakatos 1976, footnote 114). He states:

“But when the hypothesis, of itself and without adjustment for the purpose, gives us the rule and reason of a class of facts not contemplated in its construction [i.e., when consilience of inductions happen], we have a criterion of its reality, which has never yet been produced in favour of falsehood” (Whewell 2014b, 233).

The assertion that when a theory achieves consilience “we have a criterion of its reality” is not at all obvious. Contrary, it relies on two, rather uncertain arguments. First, the fact that consilience “has never yet been produced in favour of falsehood”, i.e., that is well corroborated by history of science. But this cannot work as an argument: empirical facts about scientific practice cannot justify a normative criterion for evaluating truth-values of scientific theories. And second, on the idea that “MAN is the Interpreter of Nature, Science the right interpretation” (Whewell 2014a, Aphorism I), which, however fundamental to Whewell philosophy it may be,[21]For a discussion of the idea that successful scientific theories are also true in Whewell’s work, cf. Laudan (1971, 382–83). In general, Laudan argues that consilience can psychologically justify … Continue reading clearly begs the question.  

Mill, on the other hand, makes an attempt at providing a rigorous, logically sound, method of verification of generalizations.[22]It is now generally accepted that a good inductive argument can only provide “some degree of support for the truth of the conclusion” (Hawthorne 2020) and cannot prove it. His account can still be seen as “capturing basic intuitions about experimental methods for finding the relevant explanatory factors” (Andersen and Hepburn 2020), but it is too narrow as an account of scientific practice. Most importantly, his epistemological commitments prevent him to consider the description of a set of observations with a concept as a crucial, nontrivial part of science. Therefore, as Whewell complained (Whewell’s letter to Herschel in Cobb 2011), Mill’s theory of induction cannot be used to adequately reconstruct scientific discovery (cf. Cobb 2011 for a partial affirmation of this claim).

I take this to show that the two philosophers cannot be accurately compared using a distinction between an inductivist and a hypothetico-deductivist approach to scientific method. Rather, when writing about induction, they have a different goal in mind. Whewell is interested in a theory that could be used to describe scientific practice, while Mill is primarily concerned with providing a normative standard of testing, to which scientists should conform. It can therefore be concluded that their theories of induction differ in 1) their underlying epistemological commitments and 2) their understating of the aims and the scope of philosophy of science.

Conclusion

In this paper, I analyzed differences between Mill’s and Whewell’s account of induction and argued that the debate between them should be understood as a disagreement on the meta-methodological rather than methodological level. First, I analyzed their disagreement about the role and nature of concepts in induction. By using my example first, I presented Whewell’s idea that the mind always plays an active role in perception. I made a distinction between two different versions of this claim: a stronger, metaphysical one that fundamental ideas function as conditions of human experience, and a weaker one that some mental content is involved in unifying observed phenomena. I evaluated Mill’s critique as directed at both the weaker and the stronger version of Whewell’s claim. As discovered, the critique fails against the weaker claim and does not provide any real arguments against the stronger claim. Therefore, it was shown that the argument ends in disagreement about the role of observation for gaining knowledge of concepts. Then, I analyzed their different theories of validation of hypotheses and the subsequent claim that Mill is an inductivist about the scientific method, while Whewell is a deductivist. I showed that this distinction has two problems: 1) Whewell is not a hypothetico-deductivist and 2) it cannot capture what differentiates their views. Rather, their theories have different aims and scopes. Whewell provides a rational reconstruction of scientific progress, while Mill establishes what he thinks is a rigorous, logically sound method of verification of generalizations. Their theories of induction therefore differ 1) in their underlying epistemological commitments and 2) in their understanding of the role of philosophy of science.

Acknowledgement

I would like to thank Prof. Neil Dewar for his comments on an earlier version of this paper.

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Laudan, Larry. 1971. “William Whewell on the Consilience of Inductions.” Edited by Sherwood J. B. Sugden. Monist 55 (3): 368–91. https://doi.org/10.5840/monist197155318.

Macleod, Christopher. 2016. “John Stuart Mill.” Stanford Encyclopedia of Philosophy. 2016. https://plato.stanford.edu/entries/mill/.

Mill, John Stuart. 2011. A System of Logic, Ratiocinative and Inductive. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781139149839.

Snyder, Laura J. 1997a. “The Mill-Whewell Debate: Much Ado about Induction.” Perspectives on Science-Historical … 5 (2): 159–98. http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:The+Mill-Whewell+Debate:+Much+Ado+about+Induction#0.

———. 1997b. “Discoverers’ Induction.” Philosophy of Science 64 (4): 580–604. https://doi.org/10.1086/392573.

———. 2008. “‘The Whole Box of Tools’: William Whewell and the Logic of Induction.” In Handbook of the History of Logic. Volume 4, edited by Dov M. Gabbay and John Woods, 163–228. Oxford, Amsterdam, Waltham: Elsevier B. V. https://doi.org/10.1016/S1874-5857(08)80008-8.

———. 2019. “William Whewell.” The Stanford Encyclopedia of Philosophy. 2019. https://plato.stanford.edu/archives/spr2019/entries/whewell/.

Strong, E. W. 1955. “William Whewell and John Stuart Mill: Their Controversy about Scientific Knowledge.” Journal of the History of Ideas 16 (2): 209. https://doi.org/10.2307/2707663.

Walsh, Harold T. 1962. “Whewell and Mill on Induction.” Philosophy of Science 29 (3): 279–84. https://doi.org/10.1086/287876.

Whewell, William. 1856. “Of the Transformation of Hypotheses in the History of Science.” Transactions of the Cambridge Philosophical Society 9: [139]-[146].

———. 2014a. The Philosophy of the Inductive Sciences. Volume 1. Cambridge: Cambridge University Press. https://doi.org/10.1017/cbo9781139644662.

———. 2014b. The Philosophy of the Inductive Sciences. Volume 2. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781139644679.

Wilson, Fred. 2008. “The Logic of John Stuart Mill.” In Handbook of the History of Logic. Volume 4, edited by Dov M. Gabbay and John Woods, 229–81. Oxford, Amsterdam, Waltham: Elsevier B. V. https://doi.org/10.1016/S1874-5857(08)80009-X.

References

References
1 Although, as it is apparent from his letter to Comte, Mill was hoping that his opponent would (Snyder 1997a, 161).
2 An example he gives: “All the Apostles were Jews, because this is true of Peter, Paul, John, and every other apostle” (Mill 2011, 353).
3 This should not be confused with what we now call mathematical induction. Nevertheless, neither what Mill is referring to nor mathematical induction do not conform to his definition of inductive inference.
4 An example he gives: “… when we have proved, with respect to the circle, that a straight line cannot meet it in more than two points, and when the same thing has been successively proved of the ellipse, the parabola, and the hyperbola, it may be laid down as an universal property of the sections of the cone” (Mill 2011, 354).
5 But it is important to keep in mind that this would not yet constitute a colligation of facts as defined by Whewell. As Snyder points out, for a genuine colligation to happen, the concept used should be new, either “never before used in science” (Snyder 1997a, 174), or new in its specific application (ibid.).
6 Despite the fundamental similarity between the two, namely that Whewell’s fundamental ideas functionally resemble Kant’s forms of intuition and categories of understanding, there are several important distinctions. 1) Whewell does not make a Kantian distinction between forms of intuition and categories; 2) he does not try to make an exhaustive list of the fundamental ideas and concepts that make perception possible; 3) for him, some conceptions can work as conditions for scientific knowledge, but not for perception, which does not hold for Kant; 4) Whewell holds that fundamental ideas represent objective features of the world, since 5) they originate from the mind of a god who also created the world (Snyder 2008, 219).
7 “As we have said, space limited by boundaries gives rise to various conceptions which we have often to consider. Thus limited, space assumes form or figure; and the variety of conceptions thus brought under our notice is infinite. We have every possible form of line, straight line, and curve; and of curves an endless number;—circles, parabolas, hyperbolas, spirals, helices” (Whewell 2014a, 87).
8 It escapes Whewell’s notice that the same can be said for the first extreme term, namely “planets.” That does not necessarily work against him; it only shows that even when scientists are explicit about using certain concepts, they are still implicitly using others. 
9 E.g., “various combinations of epicyclical constructions” (Whewell 2014b, 216).
10 “The Invention of the Conception was the great step in the discovery; the Verification of the Proposition was the great step in the proof of the discovery” (Whewell 2014b, 217).
11 It should be noted here that this example does not serve Mill all that well. For details, see below.
12 Mill does not explain what kind of data did Kepler use. For an overview of how Kepler arrived at his calculations of Mars’ orbit, cf. Forster (2011).
13 Although his solution admittedly is not the most elegant, since he would have to argue, that both an island and a continent are a priori concepts that follow from fundamental ideas.
14 Or, as Walsh puts it: “In the final analysis, the dispute is unresolvable. Setting aside all the lacunae in Mill’s criticism, the fact remains that he seems to suggest that certain properties are sensible, are among the givens of sensation, which Whewell thinks of as being insusceptible of apprehension by the sensory apparatus” (1962, 284). Another way of representing this difference can be found in Lakatos (1976), who makes a distinction between activist and passivist theories of knowledge. Passivists hold that knowledge is “nature’s imprint” on a passive mind (classical empiricism, in our case Mill), while activists hold that nature must be interpreted through our mental activity (e.g., Kantians, in our case Whewell) (cf. Lakatos 1976, 216).
15 The methods are: 1) the method of agreement, 2) the method of difference, 3) the method of residues, and 4) the method of variation (Macleod 2016).
16 As Wilson points out, this method presupposes that 1) one of the co-occurring phenomena is indeed a cause of A, and 2) that it is possible to determine all possible causes of A (Wilson 2008, 259). He calls the two presumptions the “Principle of Determinism” and the “Principle of Limited Variety” respectively (ibid.).
17 Considering the example given in the previous paragraph, it might not be clear why exactly such concept is needed. The thing is that a given phenomenon usually does not co-occur with only three other phenomena, but with many more, most of which a scientist decides to ignore in an experiment. A concept (or a theory) directs her in this decision.
18 She also argues that Whewell does not present a retroductivist account since he does not think that retroductive inference is the only way to draw hypotheses from data (Snyder 1997a, 166). Retodructive inference, or abduction, was first presented by C. S. Peirce (ibid.). It is an inference of the form: “[1] The surprising fact, C, is observed; [2] But if A were true, C would be a matter of course, [3] Hence, there is reason to suspect that A is true” (Peirce in Snyder 1997a, 166).
19 Also, a more general point can be made: the frivolous “guesswork” suggested by hypothetico-deductivism again suggests a mind that is, although active vis-à-vis empiricist’s passive observer, essentially unbounded by its background knowledge, assumptions, affiliations with a research program … I think this is an overly naïve way to look at developing a hypothesis and that it already was such for Whewell.
20 For the distinction between the two levels and a similar suggestion cf. Andersen and Hepburn (2020).
21 For a discussion of the idea that successful scientific theories are also true in Whewell’s work, cf. Laudan (1971, 382–83). In general, Laudan argues that consilience can psychologically justify scientific theories, but not logically as Whewell would want.
22 It is now generally accepted that a good inductive argument can only provide “some degree of support for the truth of the conclusion” (Hawthorne 2020) and cannot prove it.

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