Monday, December 9, 2019

William Whewell's "Discoverer's Induction" (Part 6/Final Part)


This final part of my series on Dr. William Whewell will discuss the four tests he believes can determine the veracity and applicability of a true colligation, an induction. I have named these four tests as (1) Deductive Consistency, (2) Prediction of Past and Future Phenomenal Events, (3) Consilience of Inductions, and lastly, (4) Simplicity and Unity. Additionally, this part will discuss what Whewell termed the “Logic of Induction.” Whewell’s “Logic of Induction” will cover how inductive generalizations can be expressed in Inductive Tables and how they can represent the criterion of truth. Lastly, this part will provide a summary of what Whewell believes scientific induction to be.

Tests for Hypotheses

In both these speculations [phenomenal and causal hypotheses] the suppositions and conceptions which occur must be constantly tested by reference to observation and experiment. In both we must, as far as possible, devise hypotheses which, when we thus test them, display those characters of truth of which we have already spoken;—an agreement with facts such as will stand the most patient and rigid inquiry; a provision for predicting truly the results of untried cases; a consilience of inductions from various classes of facts; and a progressive tendency of the scheme to simplicity and unity. (NOR, 128)

This section will discuss Whewell’s tests for inductive, scientific hypotheses and theories. He held that science has progressed through the conceptualizing, and often reconceptualizing, of certain groups of facts. For Whewell, a part of this progress meant that the administration of certain tests would be necessary to ensure that our selected conceptions and hypotheses were not improperly or hastily abstracted. In the chapter “General Rules for the Construction of the Conception,” he describes the third step of colligation as the following: “The Independent Variable, and the Formula which we would try, being once selected, mathematicians have devised certain special and technical processes by which the value of the coefficients may be determined” (Philosophy II, 389).

First Test: Deductive Consistency

The first test for an induction is that it must be consistent with the observed facts. In section 11 of Novum Organum Renovatum, Whewell states that while testing our hypotheses, we must determine “whether the Facts have the same relation in the Hypothesis which they have in reality;—whether the results of our suppositions agree with the phenomena which nature presents to us” NOR, 67). The scientific reasonings and suppositions that we craft to explain some class of phenomena has to be either confirmed or contradicted by subsequent observations and experiments. When the arguments of the hypothesis match our observations and experimental results, with due appreciation for the margin of error or other conditions at present unknown, then we hold that there’s probative evidence for the hypothesis’ truth. When a hypothesis’ deductive conclusions sufficiently matches up with scientific observations made and testing results, Whewell holds that the hypothesis “answers its genuine purpose, the Colligation of Facts” (NOR, 68).

Once we discovered a legitimate colligation, a “true Bond of Unity” that conceptually binds phenomena and facts together, we can begin a series of more precise tests of the hypothesis’ deductive consequences and consistency. Whewell notes that these subsequent, more minute tests are typically conducted more formally and technically than the original tests of the hypothesis. With the wider range of facts already colligated by an inventive genius or sagacious mind, Whewell remarks that the subsequent, intensive and extensive testing of the hypothesis may not require the same level of genius (NOR, 69).

Dr. John McCaskey notes that for Whewell, this consistency must have an astounding level of applicability to our observations, but it does not have to a universal, absolute match. For instance, Whewell once made this remark about the orbit of Uranus: "If we find that Uranus...deviates from Kepler's and Newton's laws, we do not infer that these laws must be false; we say that there must be some disturbing cause" (McCaskey, 2014, 173; see note 52 for references to this point). While Whewell believed that deductive consistency was a necessary condition and a good indication of a hypothesis’ veracity, he thought it should do much more than this. The hypothesis’s applicability must extend beyond attempts to test it in the mere present. This is what Whewell’s second test was designed to investigate.

Second Test: Prediction of Past of Future Phenomenal Events

Passing the first test requires a substantial verification of a scientific hypothesis’ deductive consistency. Whewell would regard this as a basic condition or test of its status as a true theory or a true colligation. To pass the second test, an inductive hypothesis must do more than this. According to Whewell, such hypotheses “ought to foretel phenomena which have not yet been observed; at least all phenomena of the same kind as those which the hypothesis was invented to explain” (NOR, 86). Beyond predicting the observational and experimental results of present tests, the hypothesis should predict the results of both past and future events. Such a theory would “predict the results of new combinations, as well as explain the appearances which have occurred in old ones” (NOR, 86).

Whewell gives numerous examples of past inductions that enabled scientists to predict the actions of different phenomena under investigation. The theory of oxygen (c. late-18th century) included enough facts about the relative weights of the elements and their compounds that it allowed chemists to predict the relative weights of elemental combination even in untried cases. The theory of Electromagnetic Forces (c. early to mid-19th century) allowed physicists to correctly predict many types of motions by materials and machines that had yet to be observed (NOR, 86–87).

He has high praise for those discoverers who can truly predict the events that match their hypotheses before they occur.

Those who can do this, must, to a considerable extent, have detected nature’s secret;—must have fixed upon the conditions to which she attends, and must have seized the rules by which she applies them. Such a coincidence of untried facts with speculative assertions cannot be the work of chance, but implies some large portion of truth in the principles on which the reasoning is founded. (NOR, 87)  

Passing the first test is a good sign of the truth of an inductive hypothesis, but passing the second is an even better indication of its veracity. “The prediction of results, even of the same kind as those which have been observed, in new cases, is a proof of real success in our inductive processes” (NOR, 87). As we shall soon see, passing the second test is a powerful determiner of a hypothesis’s truth, but even this is not the most impressive test in Whewell’s arsenal.

Third Test: Consilience of Inductions

Scientific discoverers have certainly hit upon some element of the truth when their hypotheses’ conclusions match the present observations and experimental results of phenomena they are investigating (first test). They have penetrated the truth of nature at a deeper level when they can correctly predict both past and future events that have not been scientifically tested yet (second test). But these two tests of a hypothesis pale in comparison to the evidential strength conferred to an induction that can pass the third test: consilience. Known as both “the Consilience of Inductions” and as a jumping together of inductions, Whewell introduces the topic through contrasting it to the second test, the prediction of phenomena: 

We have here spoken of the prediction of facts of the same kind as those from which our rule was collected. But the evidence in favour of our induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis. (NOR, 87–88)

In Whewell’s view, the fact that a hypothesis can explain both the class of facts and phenomena it was originally designed to explain and an entirely different, unrelated class of facts can be no work of accident. It also cannot be the work of a false hypothesis. “No false supposition could, after being adjusted to one class of phenomena, exactly represent a different class, where the agreement was unforeseen and uncontemplated” (NOR, 88). That inductions from one field could match up to inductions made in an unconnected field, “can only arise from that being the point where truth resides” (NOR, 88). Successful consiliences of inductions have only occurred with the best theories that the fields of science have constructed; some of the greatest scientific discoveries ever made are the results of these jumping together of inductions (NOR, 88).

In a Consilience of Inductions, or consilience, an inductive hypothesis causally unifies and explains different classes of phenomena, including phenomenal and/or causal laws. Two theories that Whewell believes were truly consilient were Newton’s theory of universal gravitation (a causal law) and Huyghens’ undulatory theory of light (a causal law). Newton’s inverse square law of gravitation was able to explain and connect a variety of seemingly unrelated classes of facts: the orbits of the moon and the planets around the sun, Kepler’s phenomenal laws of elliptical planetary motions and the precession of the equinoxes (NOR, 88). His theory could also explain the relative weights of objects on Earth; it made improvements on projectile trajectory calculations; it could explain tidal wave motions to some degree; lastly, it connected Kepler’s laws of planetary motion with Galileo’s (phenomenal) law of falling bodies through the unifying cause of universal gravitation.

Whewell thought that it was plausible that scientists could create one or several hypotheses to explain the same class of facts with a known law, adjusting the hypotheses to new circumstances to account for them as well. What Whewell considers implausible is for a scientist to use a hypothesis to phenomenally and/or causally explain one class of facts and to stumble upon the law operating in an entirely different class.

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, we have a criterion of its reality, which has never yet been produced in favour of falsehood. (NOR, 90).

Whewell believed that passing the test of consilience made what was once merely an inductive hypothesis a true theory, confirmed beyond the shadow of a doubt. “No example can be pointed out, in the whole history of science, so far as I am aware, in which this Consilience of Inductions has given testimony in favour of an hypothesis afterwards discovered to be false” (NOR, 90). This test would lead to a fourth and final test, which in a way summarizes what a good scientific induction and theory should do in its respective field of science.

Fourth Test: Simplicity and Unity

The last criterion that is a definitive mark of a true theory is that new and additional suppositions should cause the theory to become further unified and should move the theory to greater simplicity. This is a notable difference between true and false theories. With a true theory,

the new suppositions resolve themselves into the old ones, or at least require only some easy medication of the hypothesis first assumed: the system becomes more coherent as it is further extended (NOR, 91)

Such is not the case with false theories. False theories tend to be inadequate for handling new suppositions. These theories have to grapple with the new facts and suggestions, resulting in a more complicated theory with new facets and features to account for the new suppositions and combinations. Eventually, the false hypothesis crashes under the weight of its many elements and additions, and “is compelled to surrender its place to some simpler explanation” (NOR, 91).

Whewell provides an extended example of several false theories in the history of science, including the false theory of eccentrics and epicycles in the field of Astronomy. As astronomers measured planetary positions and motions more accurately (particularly Tycho Brahe), they reached the conclusion that “no combination of equable circular motions would exactly represent all the observations” (NOR, 91). Kepler extensively applied the latest modifications of the epicyclical hypothesis to the best planetary data available. Though the hypothesis and the data agreed with some degree of accuracy, it was not a high enough degree to satisfy Kepler, who then discarded that hypothesis for the much simpler elliptical hypothesis. In time, many other astronomers would also dispense with the epicycle hypothesis and its addition of eccentrics and adopt the elliptical theory of planetary motion. “Astronomers could not but suppose themselves in a wrong path, when the prospect grew darker and more entangled at every step” (NOR, 91–92).

True theories do not grow out of proportion as new classes of facts are introduced to them. Rather, elements within the theory are already capable of explaining these new facts or can be easily modified to accommodate them. For a false theory, new facts and suppositions are threats, to be dismissed or explained away to save the theory. For a true theory, new facts and suppositions are assets, strengthening its elements and identifying implications of the theory that went unnoticed initially. In true theories, the original hypothesis and news suppositions and facts “run together,” resulting in “a constant convergence to unity” (NOR, 91).

Connections Between Consilience and Simplicity

For Whewell, a hypothesis that can pass the toughest tests—consilience and simplicity—gives us an “irresistible” proof of its truth (NOR, 95). The best theories in the fields of science have both of these characters: “the Consilience of Inductions from different and separate classes of facts” and “the progressive Simplification of the Theory as it is extended to new cases” (NOR, 95). In his view, this is because of the fact that these characters of consilience and simplicity are merely two aspects of the same quality of true scientific theories.

For if these Inductions, collected from one class of facts, supply an unexpected explanation of a new class, which is the case first spoken of, there will be no need for new machinery in the hypothesis to apply it to the newly-contemplated facts; and thus, we have a case in which the system does not become more complex when its application is extended to a wider field, which was the character of true theory in its second aspect. (NOR, 95–96)

Dr. McCaskey, philosopher and historian of science, states the relationship between consilience and simplicity in this way:

Consilience gives rise to Whewell’s final criteria, simplicity. One hypothesis that encompasses multiple, seemingly unrelated, phenomena is simpler and better than
multiple independent hypotheses. (McCaskey, 174)

Theories that have these characters are also a scientist’s means of ascending to an even higher level of generality. Consilient theories suggest a new, higher-level induction that can explain the classes of facts that were previously presumed to be unrelated. Theories that can easily accommodate new ranges of phenomena can also suggest that a high-order induction is within reach. In both cases, the inductions and hypotheses formed and verified to be consilient and unifying are then considered as subordinate inductions to a higher-level, more general induction (NOR, 96). This leads us to a very important phase in the development of inductions and in science that will be discussed in the next section: the phenomenon of successive generalizations (NOR, 96).

The Logic of Induction

Throughout Whewell’s books on the philosophy of science, he goes to great lengths to explain the inductive process and how to properly test inductive hypotheses. In the chapter, “The Logic of Induction,” he seeks to resolve the issue of the best form to show the conclusiveness of a given induction. He describes this process, the “Logic of Induction,” as the “analysis of doctrines inductively obtained, into their constituent facts, and the arrangement of them in such a form that the conclusiveness of the induction may be distinctly seen” (NOR, 105).

A “logic” is regarded as a means or method of arranging our reasonings and propositions in such a way that their truth or falsehood could be determined through their form. Whewell notes that we use the form of the syllogism and its deductive rules to determine valid deductive or demonstrative reasoning (NOR, 106). Just as the syllogism provides deductive reasoning a valid form for assessing a given argument’s logic, Whewell believes that his invention of Inductive Tables supply us with a means of determining the truth of our inductive hypotheses and inferences (NOR, 106). The Inductive Tables present the Logic of Induction, or as he states in On the Philosophy of Discovery, Chapters Historical and Critical, “the formal conditions of the soundness of our reasoning from facts” (Whewell, 1860, 207). These Tables present the main theories of a field of science as a “graduated table of co-ordinate and subordinate inductions,” with each step of an induction showcasing the particular facts being explained and the general theory that explains these facts (NOR, 106). (An example of one of his Inductive Tables can be found on page 140 of NOR.)

There is an important, essential connection between the gradual generalization of scientific theories and the construction of Whewell’s Inductive Tables: Inductive Tables are impossible to construct without a sufficiently high degree of inductive generality within a given science. As Dr. Snyder notes in “The Whole Box of Tools": William Whewell and the Logic of Induction,” Whewell’s Inductive Tables,

can be constructed only for sciences which have achieved a large degree of generality, that is, where phenomenal laws have been subsumed under causal laws of greater generality, and these causal laws are themselves seen as instances of laws of even greater generality. (2008, 196)

In Whewell’s time (roughly the mid-19th century), the only sciences that had developed sufficiently to warrant formal Inductive Tables were Astronomy and (to a lesser extent) Optics (Snyder, 196). Whewell believed that successful inductions spur on to try more generalized inductions/hypotheses. The formulation and verification of consilient, unified theories lead to more gradual, careful generalizations. Whewell believed that these gradual generalizations would lead to even more formalized Inductive Tables as science progressed, and that this process would further improve the soundness of our inductive reasonings (Snyder, 197).

Conclusion: Whewell’s View of Scientific Induction

Scientific induction, for Whewell, is a highly technical, slow, gradual interaction between our ideas and the facts of reality. This interaction is principally represented by the explication—the unfolding—of conceptions and the colligation—the binding—of facts. The end-goal of Whewell’s “Discoverer’s Induction” is a range of conscientiously analyzed, successfully tried and tested scientific conceptions, technical terms, which he also describes as “true colligations.” An induction proper is not merely a collection, an enumeration, or an organization of facts, but a new conception superinduced upon the facts, a new element that allows us to see a group of facts “in a new light” (Philosophy II, 85, 87–88). This was a chief insight missed by his philosophical predecessor Francis Bacon, an oversight he intended to correct by naming one of his works after one of Bacon’s: the Novum Organum Renovatum (a reference to Bacon’s Novum Organum).

Whewell’s form of induction uses a variety of logical tools to reach and justify its inductive principles (Snyder, 163). These include enumeration, analogical, and eliminative inference. They also emphatically include deductive, demonstrative reasoning; a notion that may be alarming or confusing to some people. Whewell discusses this crucial interplay between induction and deduction in volume II of his Philosophy:

Deduction is a necessary part of Induction. Deduction justifies by calculation what Induction had happily guessed. Induction recognizes the ore of truth by its weight; Deduction confirms the recognition by chemical analysis. Every step of Induction must be confirmed by rigorous deductive reasoning, followed in such detail as the nature and complexity of the relations (whether of quantity or any other) render requisite. If not so justified by the supposed discoverer, it is not Induction.” (Philosophy II, 93)

This heavy reliance on deduction for the verification of colligations is highlighted by Whewell’s first two tests for scientific hypotheses: (1) Deductive Consistency and (2) Prediction of Past and Future Phenomenal Events. The third and fourth tests, (3) Consilience and (4) Simplicity, are designed to determine which theories can withstand the most stringent and difficult of trials, resulting in theories which we must consent to be incontestably true (at least in his view). The results of all of these labors are observationally and experimentally verified phenomenal and causal laws and significantly improved understandings of various groups of facts, our conceptions, and our ideas. Even more fundamentally, successful uses of Whewell’s “Discoverer’s Induction” would result in real progressions of the state of the sciences. The state of science and its advancement are both subjects that Whewell spent the majority of his adult life studying, chronicling, discussing, and helping to bring about.


McCaskey, J. P. “Induction in the Socratic tradition.” Shifting the paradigm: Alternative
     perspectives on induction, edited by Louis F. Groake and Paolo C. Biondi. Berlin/De
     Gruyter, 2014, pp. 161-192. doi: 10.1515/9783110347777.161
Snyder, L. J. "The whole box of tools": William Whewell and the logic of induction.” British
     Logic in the Nineteenth Century, edited by Dov M. Gabbay, John Woods. Amsterdam/
     North Holland, 2008, pp. 163–228. [Vol. 4 of 11 vols.]
Whewell, W. Novum organum renovatum (3rd ed.). London/John Parker, 1858.
---. On the philosophy of discovery, chapters historical and critical. London/John Parker, 1860.
---. Philosophy of the inductive sciences, founded upon their history (2nd ed.). London/John
     Parker, 1847.

No comments:

Post a Comment