Saturday, July 6, 2019

William Whewell’s “Discoverer’s Induction” (Part 4)

Previous posts: William Whewell's "Discoverer's Induction" (Part 1) 
William Whewell's "Discoverer's Induction" (Part 2)
William Whewell's "Discoverer's Induction" (Part 3)

Induction as a True Colligation of Facts

Colligation and Induction

William Whewell’s theory of induction and of scientific methodology centers on the explication of conceptions and on the colligation of facts. Induction for him is mainly about what facts, propositions, definitions, and ideas we can draw out of our conceptions, and about how to find new and more productive ways to bind these elements up into a more exact, more appropriate conception. The ancient and prevailing theory of induction has been that it’s enumerative: a general statement or proposition that is applied to a collection of instances.

For Whewell, induction is not merely a collection of certain phenomena, an enumeration of instances. With induction as he sees it, “there is a New Element added to the combination [of instances] by the very act of thought by which they were combined” (Philosophy II, 48). This “New Element,” this “act of thought” is what Whewell calls a colligation. Because the formation of the appropriate conception is of seminal importance in scientific theory-building, Whewell uses induction in a specialized sense to mean a true, successful colligation, a true binding of facts that creates scientific knowledge. “Induction is a term applied to describe the process of a true Colligation of Facts by means of an exact and appropriate Conception”  (Philosophy II, “Aphorisms Concerning Science,” Aphorism 13).

Discovering and employing an appropriately colligated conception in scientific pursuits provides us the, “true bond of Unity by which the phenomena are held together” (Philosophy II, 46). A true colligation allows us to reach two major goals in the field of any science: the discovery of phenomenal and causal laws.  

Phenomenal and Causal Laws

In every department of science, when prosecuted far enough, these two great steps of investigation must succeed each other. The laws of phenomena must be known before we can speculate concerning cause; the causes must be inquired into when the phenomena have been reduced to rule. (NOR, 127–128)

Induction is our means of gaining exact, true knowledge about the world. The goal of any induction is to reach one of two possible goals: a discovery of one of the laws of phenomena or of the laws of causes. Snyder explains the difference between the two this way: “Laws of phenomena are, as their name suggests, laws that express what takes place, while laws of causes explain why it does” (Reforming Philosophy, 51).

The discovery of the laws of phenomena are the first steps involved in gaining the true knowledge required for the advancement of science. Phenomenal laws can be seen as formulas, expressing facts that we observe in general terms using fundamental ideas and their associated axioms (e.g., time, space, position) (Novum Organum Renovatum; hereafter NOR, 120). Examples of phenomenal laws for Whewell include the laws of planetary motion as well as laws regarding the dispersion, refraction and reflection of light (NOR, 118).

Causal laws are explanations for why the facts subsumed under each laws’ respective phenomenal laws are the way that they are. A key example for Whewell when it comes to causal laws is Sir Isaac Newton’s (1642–1726/27) law of universal gravitation, a law which explained the phenomenal laws already known within certain fields of science (e.g. the laws of planetary motion). Not only that, but Newton’s law also explained (or gave future scientists a better starting point for explaining) a host of other facts: some of these facts include the revolutions of moons around their respective planets, tidal waves, and falling objects. The discovery of causal laws requires reaching a true colligation, which may involve redefining past technical terms or words, and tends to lead to new conceptions. Newton’s research into gravitation led to not only a redefinition of the term gravity, but also led to his creation of the idea of mass (McCaskey, 171).

In reaching these laws and correctly colligating facts, we often wind up with definitions and propositions. Whewell remarks on the meaning of these discoveries:

In collecting scientific truths by Induction, we often find [...] a Definition and a Proposition established at the same time,--introduced together, and mutually dependent on each other. The combination of the two constitutes the Inductive act; and we may consider the Definition as representing the superinduced Conception, and the Proposition as exhibiting the Colligation of Facts. (Philosophy II, 54)

The Whole Box of Tools

But all who discover truths must have reasoned upon many errors, to obtain each truth; every accepted doctrine must have been one selected out of many candidates. (History of the Inductive Sciences, Vol. I; hereafter History I, 411–412)

Naturally, in the course of discovering phenomenal laws, scientists become wrapped up in devising hypotheses to causally explain the facts and the phenomenal laws that had been previously discovered and investigated (NOR, 126–127). For Whewell, the hypothesis-phase of scientific research and theorizing equates to the search for the appropriate conception to bind the facts together. He admits that forming the right hypothesis is not an easy or simple process. It’s not a matter of baseless or arbitrary conjecturing or guessing. But it’s also not merely just a matter of collecting enough observations and instances.

Colligating facts properly requires a series of inferences, a “train of researches,” as Whewell described it when discussing Kepler’s laborious efforts in calculation and reasoning while preparing Astronomia nova (“New Astronomy”; 1609) (History I, 422). Snyder highlights the fact that induction for Whewell involves several different types of reasoning, which include enumerative, eliminative and analogical reasoning (“William Whewell,” para 10).

Enumerative reasoning is inferring that a property generally belongs to a class of instances based on the observations of some class-members possessing the given property; inferring that all crows are black from observing that some crows are black is an example of enumerative reasoning (Reforming Philosophy, 64). Eliminative reasoning is the inference that one proposed property or theory is likely true due to the elimination of all of the other possible properties or theories. Analogical reasoning is inferring that two or more different kinds of objects or systems have a certain, deeper similarity by noting or highlighting some other shared feature or property.

Kepler stands as a great example of what Whewell means by the “train of researches” needed to colligate facts. In the course of writing Astronomia nova, Harmonices Mundi (“The Harmony of the World”; 1619) and the Rudolphine Tables (1627), among other works, Kepler used all of the above-mentioned forms of reasoning. He used countless numbers of enumerative inferences and measurements concerning the orbital data points of Mars in an attempt to learn the shape of its orbital path. He used eliminative reasoning not just in rejecting the then-prominent epicyclical theory of planetary motion, but also in the testing and the rejection of several other potential shapes for Mars’ orbital motion before successfully matching his data with an elliptical shape; this prompted the development of his elliptical first law, now known as Kepler’s Law of Orbits (Cf. History I, 422, 426). Though without success, Kepler also wrote extensively on the analogous harmony between the celestial heavens and the terrestrial bodies through the relations between music and the angular motions of the planets (History I, 420).

All of these forms of reasoning could be very helpful in the selection of the proper conception to bind together the facts of the world. While Whewell certainly approved of this variety of reasoning methods being used as induction, not everyone in the philosophical and scientific communities of his time agreed. Snyder notes that DeMorgan not-so-subtly complained about Whewell’s liberal use of reasoning methods in his 1847 textbook on logic, Formal Logic: Or, The Calculus of Inference, Necessary and Probable. DeMorgan lamented that some writers use the term “induction” as if it meant “the use of the whole box of [logical] tools” (Reforming Philosophy, 64).


Part 5 will wrap up this series with a discussion of the three steps in colligation/induction for Whewell, including the tests for hypotheses that he views as necessary for the confirmation of our scientific theories.


McCaskey, J. P. (2014). Induction in the Socratic tradition. In L. F. Groarke & P. C.
Biondi (Eds.), Shifting the paradigm: Alternative perspectives on induction (pp. 161-
192). Berlin: De Gruyter. pp. 161-192. doi: 10.1515/9783110347777.161
Snyder, L. (2006). Reforming philosophy: A Victorian debate on science and philosophy.
Chicago: The University of Chicago Press.
Snyder, L. (2012). William Whewell. E. N. Zalta (ed.) Stanford Encyclopedia of Philosophy. (Original work published
Whewell, W. (1837). History of the Inductive Sciences, from the Earliest to the Present
Time (3rd ed., in three volumes). London: John W. Parker.
Whewell, W. (1847). Philosophy of the inductive sciencesfounded upon their
               history (2nd ed.). London: John Parker.
Whewell, W. (1858). Novum organum renovatum (3rd ed.). London: John Parker.

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