Wednesday, December 22, 2010

Advances in Baconian Induction: John Herschel (Part 1 of 3)


John Frederick William Herschel (1792-1871) was an important 19th Century scientist, arguably the most important. (I currently put William Whewell and Herschel on nearly the same footing, with Whewell having a slight edge.) He studied and made applications to the fields of astronomy, mathematics, chemistry, botany, and electricity. He was also one of the first modern "philosophers of science," and an advocate of the use of inductive reasoning in scientific investigations, particularly a version of Francis Bacon's method of induction, informed by the discoveries of science since the early 17th Century (Bacon died in 1626). To promote and encourage the activities of the "men of science," Herschel published the work A Preliminary Discourse on the Study of Natural Philosophy (1830), a treatise on the scientific method, detailing the elements of science, scientific subjects that had been and were being studied, and the procedures that a good man of science should utilize. (This book would be influential for many later scientists, notably Charles Darwin.) Most importantly, Herschel proposed in this work an enhancement of Francis Bacon's philosophy of induction, discussing both the nature of inductive reasoning and the value that should be placed upon it in science. Indeed, the very progression of science from the state of pre-science speculations and collections of facts is a progression of inductions, Herschel would remind us.

This three part essay will detail the elements and rules of Herschel's view of induction, starting with his empiricist view of experience being the source of all knowledge, working our way through his rules for inductive reasoning and ways for verifying inductions made, and the role of analogy, hypothesis, and the complimentary relation of induction and deduction in science. As a result, it isn't a complete discussion of all the important points about science made by Herschel in his Preliminary Discourse, such as the role of precise measurement in describing laws of nature, and I would suggest that the reader takes some time to read the book itself.

Experience as the Source of All Knowledge

Experience is the source of all human knowledge of nature and its laws. (p. 75) By “experience,” he doesn’t just mean the sensory experience, but the accumulation of all the experience of mankind, including the observations made in books or other works. There are two ways to acquire such experience. The first is “observation”—noting the facts as they happen without human interference, without influencing the frequency of its occurrence, or varying the situations under which the facts occurs. The second is “experiment”—to influence nature to make things happen, by controlling certain factors of an event, and taking note of the results. (p. 76)

Observation and experiment, in this light, are the foundations of all natural science.

(Something of interest to Objectivists, who understand the theory of “measurement-omission”—Herschel states that observation and experiment are not really different kinds of experience, but simply differ in measurement and degree. Stressing the similarity, he calls the two “passive observation” (observation) and “active observation” (experiment).)

The significant difference of the two is due to their results: passive observations led to unfruitful catalogs of phenomena with no means of organizing them, or with no way of determining what causes the phenomena. Active observation can lead to advances in knowledge and applications unheard of by the method of passive observation and these advances become the “natural course.” (p. 77)

Classifying Phenomena and the Laws of Nature

Phenomena are what we observe and what we experiment on. They are natural events insofar as they account for us perceiving certain objects doing certain things. Phenomena are literally appearances: they are what we sense due to processes that occur amongst external objects, or because of secret processes within the objects. We can make these processes sensible: we can analyze them and show them to consist of motions or changes to the sensible objects, although many cases exist in which we are incapable of such analysis and are left with the sensible impressions we have of objects. (Page 85)

Analyzing complex phenomena and resolving them into simpler phenomena—laws—is the proper aim of investigating nature; there is little chance that we’ll discover “ultimate causes,” and so we must content ourselves with determining the laws and causes by which complex phenomena are produced and are made sensible to us. Herschel gives the example of the “phenomenon of sound.” Analyzing sound leads to the inquiry into two causes, those being the excitement and propagation of motion and the production of sensation (in this case, of hearing), which are simpler (also more general or elementary) than the complex phenomenon of sound. A subsequent inquiry into the propagation of motion would in turn lead to simpler phenomena and further inquiries into more laws of motion (or laws of nature more generally). (pp. 90-91)

Ideally, we would already possess or could easily ascertain what things are the ultimate phenomena, the basic ones into which all the composite, complex ones can be broken down or resolved into. But there is no way to ascertain these à priori (independently of experience): rather we must explore nature, and “we must account every phenomenon an elementary or simple one till we can analyse it, and show that it is the result of others, which in their turn become elementary.” (p. 92) By this meaning then, “cause” is a relative term, meaning a proximate cause between an elementary/simple/general phenomenon, and its production of a more complex phenomenon. This process of analyzing phenomena leads to the discovery of laws, which allows us to form general axioms (principles/generalizations), or “forms of words” (I take Herschel to mean “conceptions”), either of which will include all of these laws.

This scientific process is very important in Herschel’s view: the ability to conceptualize laws of nature into conceptions or axioms allows us to perform the cognitive feat of reasoning about phenomena à priori, without reference to phenomena that exist currently or in the past. By reasoning from generals to particulars, the propositions reached apply to a vast number of cases, which were not originally conceived of during the initial formation of the axioms—when these propositions are made as detailed as possible, they represent individual facts, facts which we wouldn’t have known from ordinary experience. These axioms and conceptions allow us to not only explain all known facts, but lead to the discovery of previously unknown facts—to predict facts before they are discovered by trial. One example Herschel cites is the axiom (or law) of gravitation, which predicted that, “the earth, instead of being an exact sphere, must be compressed or flattened in the direction of its polar diameter, the one diameter being about thirty miles shorter than the other; and this conclusion, deduced at first by mere reasoning, has been since found to be true in fact.” (p. 98)

Unlike the analysis of phenomena, we have a guide for the creation of axioms of nature, and they follow the general pattern of abstract or general reasoning. A law of nature states what will happen given certain factors or contingencies, and is no different from announcing a whole group or class of phenomena. This is, therefore, very similar to the natural process of abstraction and proposition formation:
[W]e perceive that two or more phenomena agree in so many or so remarkable points, as to lead us to regard them as forming a class or group, if we lay out of consideration, or abstract, all the circumstances in which they disagree, and retain in our minds those only in which they agree, and then, under this kind of mental convention, frame a definition or statement of one of them, in such words that it shall apply equally to them all, such statement will appear in the form of a general proposition, having so far at least the character of a law of nature. (pp. 98-99)
There are thus two meanings of a “law of nature”:

1. A general proposition stating abstract facts about the actions of natural things under purported circumstances.
2. A proposition stating that a whole class or group of individuals which agree in one respect/character agree in another respect as well. (p. 100, sec. 91)

The first meaning shows a law as little more than an “artificial memory,” and thus has little use, but the second meaning influences our minds profoundly, allowing us to consider a potential proximate cause, if not an ultimate one, Herschel remarks. The second meaning of a law has this impact because, “whenever two phenomena are observed to be invariably connected together, we conclude them to be related to each other, either as cause and effect, or as common effects of a single cause.” (p. 101, sec. 92)

In this connection, a third meaning can be given to a law of nature: a proposition asserting the mutual connection, or even identity, of two classes of individuals, whether objects or facts. An example would be the connection Newton drew between falling objects and objects in orbit and their relation to the gravitational force of objects. (My example; Herschel uses the example of double refraction and polarized light exhibiting what we would call the visible light spectrum in streaks and bands. (pp. 101-102, sec. 93))

We can now appreciate the benefit of classifying phenomena: one of the proper goals in science is to accurately classify particular facts or objects under well considered headings or points of agreement (i.e. the simple phenomena which were discovered by investigating the initial facts). The result of such a process is that this simple phenomena or head of classification,
becomes not a particular but a general fact; and when we have amassed a great store of such general facts, they become the objects of another and higher species of classification, and are themselves included in laws which, as they dispose of groups, not individuals, have a far superior degree of generality, till at length, by continuing the process, we arrive at axioms of the highest degree of generality of which science is capable. (p. 102, italics in original)
This process of methodically reaching higher and higher generalities from a study and comparison of nature is what Herschel means by induction. (p. 102, sec. 95)

The Two Types of Induction

Before discussing the rules by which we should inductively reason, I’ll note that he discusses two kinds of induction:

(1) Juxtaposing and comparing already known classes, and taking note of their similarities and differences/agreements and disagreements (the early comparisons of electricity and magnetism, or the acceleration of horizontal and vertical motion—my examples, or swinging around a sensible material force (a string) and swinging around with no visible force (the force of gravity)).
(2) Investigating the individuals of a class, and attempting to discover what particular feature or quality they all share in common, besides whatever led us to group them together under a concept (Herschel’s “principle of classification”) in the first place. (p. 102)

The first method is better suited when facts are numerous, well observed, and methodically arranged. The second method is better for the “infancy” of a science, while the first is better for the “maturity” of a science. In (1), facts are already numerous and well-documented and organized, but in (2) the exact opposite is the case. The first method exploits the scientific "division of labor," where individuals benefit immensely from the thinking and observations of past thinkers; (2) mainly occurs in the hands of a single individual on a quest for understanding, requiring a union of many areas of knowledge within that person. (p. 103)

(An example of both (1) and (2) is Sir Isaac Newton, particularly his works on optics and gravitation. He once considered how he benefited from the thinking and observations of previous scientists/philosophers, relating himself to a person standing on the shoulders of giants in order to see further regarding nature. And his scientific work united ordinary perception with mechanical philosophy, mathematics, astronomy, and dynamics.)

Part 2 will cover Herschel's characteristics of causation, his "rules of philosophizing," and the 3 methods of verifying inductions.

(Next posts: Advances in Baconian Induction: John Herschel (Part 2 of 3)
Advances in Baconian Induction: John Herschel (Part 3 of 3) )

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