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Roderick Fitts

Reblogged:William Whewell's "Discoverer's Induction" (Part 3)

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The Structure of Knowledge

Before Whewell can fully articulate the details of how induction works in scientific methodology and in theory-formation, he needs to explain several related issues. He has to express his views on the source(s) of knowledge, on how knowledge builds up, and on how we can justify what we’ve learned. In short, he has to first construct his epistemology (theory of knowledge) to then discuss how his theory of induction builds on that foundation. In Part 3 of this series on Whewell, we will cover his controversial notion of fundamental ideas, on how we produce conceptions and the complementary processes of explication and colligation.

Fundamental Ideas

As mentioned in his exposition on the fundamental antithesis of philosophy, knowledge has an inseparable dual nature, a nature that we can conceptually and philosophically analyze and investigate: sensations and ideas, the objective and ideal elements of knowledge. “Without our ideas, our sensations could have no connexion; without external impressions, our ideas would have no reality; and thus both ingredients of our knowledge must exist” (Philosophy I, 54–55). Knowledge has certain subjective and objective background conditions or givens: external objects, our bodies, our minds and their capacity to form thoughts. An important condition or given that falls on the subjective, ideal side of our knowledge is the class he refers to as fundamental ideas.

Fundamental ideas include terms such as space, number, time, resemblance, symmetry, substance and cause. These ideas are exclusively supplied by the mind itself, and thus they are not derived from experience (Philosophy I, 74). Our sensory organs take in sense data from external objects, but it is the fundamental ideas within our minds that structure and organize the disparate sense data to give us our perceptual experiences. Being neither sensations nor things, Whewell remarks that they could be termed relations of things or of sensations (Philosophy I, 43). The fundamental ideas structure our sensory data through unconscious inferences and relations, making the perception and observation of external objects possible. “Perception is Sensation, along with such Ideas as make Sensation into an apprehension of Things or Objects” (Philosophy I, 43).

For Whewell, the fundamental ideas are axiomatic, granted to us in some form by God, the Divine Mind and Creator of all objects, all events and the laws that express how the world works (On the Philosophy of Discovery, 360). As we gain more experiences and make more observations about the world, we will inevitably figure out certain necessary implications of the fundamental ideas, further elaborations of what makes our experiences possible. Axioms are self-evident statements that express certain aspects of these fundamental ideas, while axiomatic definitions identify the laws that clarify these fundamental ideas and how the world operates. “Thus the Axioms of Geometry express the necessary conditions which result from the Idea of Space; the Axioms of Mechanics express the necessary conditions which flow from the Ideas of Force and Motion; and so on.”(Philosophy I, 67).

Each science (as they develop and become more formalized) is organized around a certain fundamental idea: cause is the fundamental idea of mechanics; substance is the fundamental idea of chemistry; space is the fundamental idea of geometry. All fundamental ideas have their respective conceptions, which for Whewell are “special modifications” of the ideas, special applications to particular sets of conditions or circumstances (Snyder, “William Whewell,” para 5). The history and the progress of both knowledge and science could be seen as progressively unpacking, unfolding the conceptual information and implications contained in each science’s axioms and fundamental ideas. (We will return to this idea about science a bit later in this Part.)

Conceptions and Technical Terms

Conceptions for Whewell are cognitive tools that we use to connect and unify our perceptual experiences. Ideas are broader conceptions that could be used to bind together the facts and information contained in less-abstract conceptions (Philosophy I, 51). Words are invented to record, fix and make these conceptions available for more efficient and widespread use; meticulously-honed words that are employed in scientific research and theorizing are known as technical terms (Philosophy I, 51). The regular and cyclical use of concept-formation (i.e. building conceptions from other conceptions) leads to a contextual hierarchy of conceptions: for instance, the conception “electricity” is an idea in Whewell’s sense when compared to “direct current (DC),” but it would be considered a conception when compared to our postmodern idea of “energy,” which is more abstract and broader in scope than “electricity.” Of course, at the apex of this conceptual hierarchy are Whewell’s fundamental ideas, the class of the most abstract ideas that are possible to the human mind.

According to Whewell, scientific discoveries are not usually made when scientists discover new facts; rather, new discoveries tend to be made when a scientist applies a conception that is appropriate for the observed facts. For instance, both Kepler and Tycho Brahe (1546–1601) had the Martian orbital data points (collected by Brahe), but it was only Kepler who thought to apply the conception of an ellipse/elliptical curve to the data (after 5 years of meticulous research and curve-fitting). In doing so, Kepler discovered the true orbital path of Mars (and of the other planets) as a type of ellipse, the first of his three laws of planetary motion.

While at least some of the fundamental ideas are with us from the beginning, they cannot be cognitively used in their initial forms. Whewell notes that “the Ideas, the germs of them at least, were in the human mind before [experience]; but by the progress of scientific thought they are unfolded into clearness and distinctness” (On the Philosophy of Discovery: Chapters Historical and Critical, 1860, 373). In Whewell’s view, the development of both the sciences and of scientific conceptions involve discovering more and more aspects of each science’s respective fundamental idea, along with their respective axioms and definitions. In connection with this, discovering the appropriate conceptions to apply to facts is a fundamentally important goal in all fields of science, as they can be used to further flesh out the axioms and definitions within the all-important fundamental ideas.

We’ve now discussed our particular, perceptual observations about the world, the progressively abstracted conceptions and ideas, technical terms and the fundamental ideas that are the highest, most general abstractions in our minds. However, it’s still an open question how we can reach an understanding of, and expand upon, both fundamental ideas and reach more informed observations, let alone form theories. To give Whewell’s answer to this question, we’ll have to penetrate his “Discoverer’s Induction.”

The Philosophy of Discovery

Briefly, it’s possible to sum up Whewell’s “Discoverer’s Induction,” his view of our knowledge’s structure, the inductive process and scientific theorizing with two complementary processes: the explication of conceptions and the colligation of facts. Explication is a process of conceptual analysis that is a precondition for scientific discovery and is used extensively within the development of scientific theories. Colligation is a complementary process of conceptual synthesis that typically completes a given scientific discovery and is equally crucial to the advance of science. A fuller treatment of these two terms will occupy us for the remaining sections in this series on Whewell.

Explication of Conceptions

Explication is Whewell’s philosophical name for this process of “unfolding” of ideas and of conceptions. There can be multiple goals in a given explication: to gain a clearer understanding of the conception to facilitate further research, to create a more exact definition, and/or to assist in a subsequent colligation of facts.

Many actions can be involved when a scientist explicates a conception. A usual start is for a scientist to survey a given scientific field for examples and to examine them thoroughly. McCaskey notes that Whewell explicates symmetry by making a list of symmetrical examples: for instance, the three faces at the pyramid-like summit of certain crystals and a comparison of the different sides of animals (2014, 171). In his explication of symmetry, Whewell notes that pentagonal symmetry appears abundantly in many vegetables, but never truly on the faces of crystals (Philosophy I, 441). Identifying the types of a conception is another type of explication. Whewell notes that the types of symmetry are found to be triangular/“trigonal,” tetragonal, pentagonal, simple and oolong (Philosophy I, 441).

Explication can also involve the search for and articulation of implications of the conception. Whewell announces an implication of symmetry that applies to the fields of zoology, phytology/botany and crystallography: symmetrical members are impacted in the same manner by the same factors or circumstances. “The parts which we have termed symmetrical, resemble each other, not only in their form and position, but also in the manner in which they are produced and modified by natural causes” (Philosophy I, 445).

Determining in what way the conception is an example or a modification of a more abstract idea is another task in explication. In the case of symmetry, Whewell notes that this idea is either a fundamental idea or that it includes one. He remarks that some people could claim that symmetry is a modification of certain other fundamental ideas such as space and number, but he notes that with symmetrical arrangements there is implied a “Fundamental Idea of regularity, of complete
ness, of complex simplicity, which is not a mere modification of other ideas” (Philosophy I, 444–445).

Some, but not all, explications lead to a concept’s definition. Definitions state the essential nature of the facts subsumed under a conception or idea, with the exception of fundamental ideas. They can be very helpful in determining the truth or falsehood of propositions relating to a given conception.

The establishment, therefore, of a right Definition of a Term may be a useful step in the Explication of our Conceptions; but this will be the case then only when we have under our consideration some Proposition in which the Term is employed. For then the question really is, how the Conception shall be understood and defined in order that the Proposition may be true. (Novum Organum Renovatum, 36)

Definition can be the final step in an explication, but it doesn’t always have to be, and it is certainly never the first or initial step. McCaskey notes that for Whewell, the conception must logically be formed before it can have a valid definition (2014, 171). Whewell states: “Definition and Proposition are the two handles of the instrument by which we apprehend truth; the former is of no use without the latter” (Philosophy II, 13). It is possible for a science to advance with sufficiently clear conceptions that nonetheless lack a formal definition: Whewell gives examples in mechanics, polarization, minerology and geology in which advances occurred even without scientific definitions of the major conceptions used in those sciences (Philosophy II,  14–15).

Definitions only serve a cognitively useful purpose when they make a conception more distinct by clarifying the propositions concerning the given conception such that we can express true principles. If our definitions genuinely clarify the terms used in our scientific propositions, then we’ve made an important advance in our explication efforts and in our search for scientific truth. Snyder notes that for Whewell, explication plays an important role in the history of science: the “history of scientific ideas” is more often than not a series of careful explications succeeded by the colligation of these unfolded, explicated ideas (Snyder, William Whewell, para 9).

For Whewell, explication is a process of “unfolding” a conception, which can mean examining examples, discovering implications, determining the more general idea that subsumes the conception being investigated and/or constructing propositions or a definition. The essential point is that a proper explication clearly and distinctly identifies the facts that are bound within the conception.

The Colligation of Facts

Colligation is the process of “binding” facts together, in many ways doing the opposite of the complementary actions performed in an explication. Anytime that we can create a precise, cognitive connection among the things or facts that we observe in the world through our conceptions, we have properly colligated facts. Whewell is adamant here that the process is an integration of facts, not just the characteristics that certain objects seem to share or have in common. McCaskey echoes the need to be clear on what is meant here by a colligation:

[Colligation] is rather a cognitive binding of the facts themselves—not just the common attributes, not just the definition, but indeed all the attributes and even propositions associated therewith. The conception of universal gravitation, for example, includes the fact of heliocentric motion, includes the fact of the precession of the equinoxes, includes the conception of terrestrial weight, and so on. (2014, 172)

It’s also important to note here that there is no necessary sequential or logical order between colligations and explications. In a sufficiently advanced body of knowledge, an explication could be the unfolding of a conception that has already been bound together, colligated, by past scientists or even by the same person in the past. Science is the accumulation and systematization of the knowledge gained from the conceptual connections made through successful colligations (Philosophy II, 36).

It is in connection with colligation that we can see what Whewell means by induction. For him, the whole process is about creating precise, distinct, properly formed conceptions which allow us to truly understand the facts of the world and advance in our fields of science. Due to this, he generally believes that induction refers to the combination of the methods of explication and colligation:

The two operations spoken of in the preceding chapters, —the Explication of the Conceptions of our own minds, and the Colligation of observed Facts by the aid of such Conceptions, —are, as we have just said, inseparably connected with each other. When united, and employed in collecting knowledge from the phenomena which the world presents to us, they constitute 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. (Philosophy II, 47)

While true, it’s also the case that Whewell believes that colligation is a normative set of actions. We can perform it correctly or incorrectly. Performing a normatively proper colligation is what he really means by an induction. “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). (Whewell also notes in this aphorism that induction is also used to mean the proposition that can be stated as a result of the inductive process. I take it that he means the scientific law, principle, definition or other significant proposition that the induction has warranted to be inferred by properly binding together the relevant facts with an appropriate conception.)

Induction—a true colligation—has three steps. As Malcolm Forster notes:

According to Whewell, “the Colligation of ascertained Facts into general Propositions” consists of (1) the Selection of the Idea, (2) the Construction of the Conception, and (3) the Determination of the Magnitudes. In curve fitting [for example], these three steps correspond to (1) the determination of the Independent Variable, (2) the Formula, and (3) the Coefficients. (“The Whewell-Mill Debate in a Nutshell,” 2006, 5, words in brackets mine)

An exposition on the three steps of colligation will occupy us in the next part of this series on Whewell.


Forster, M. (2006). “The Whewell-Mill Debate in a Nutshell.” [Online] Retrieved from:
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. (2012). William Whewell. E. N. Zalta (ed.) Stanford Encyclopedia of Philosophy.
https://plato.stanford.edu/archives/win2012/entries/whewell/ (Original work published
Snyder, L. (2006). Reforming philosophy: A Victorian debate on science and philosophy.
Chicago: The University of Chicago Press.
Whewell, W. (1847). Philosophy of the inductive sciences, founded upon their
history (2nd ed. in two volumes). London: John Parker.
Whewell, W. (1858). Novum organum renovatum (3rd ed.). London: John Parker.
Whewell, W. (1860). On the philosophy of discovery: Chapters historical and critical. London:
John W. Parker.

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