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

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)
William Whewell's "Discoverer's Induction" (Part 4)

William Whewell's "Discoverer's Induction" (Part 5)

Introduction

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.

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

Introduction

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.

Prerequisites for Understanding Bacon's Induction Part 1: Natural Magic

Introduction

In 2006, John McCaskey stated in his dissertation that Bacon's view of induction could not be fully understood without acknowledging the Aristotelian background from which it arises. I'll discuss that in Part 2; for now, I want to discuss the natural magic tradition that Bacon uses for his own purposes. Since Bacon doesn't address any particular magicians in his criticism, neither will I, but I will discuss his general criticism of the practice of magic.

Bacon's "More Certain and Guarded Method" of Induction

"[...]our determination is that of trying, whether we can lay a firmer foundation, and extend to a greater distance the boundaries of human power and dignity."[Bacon, New Instrument, Book 1, Aphorism 116]

"Our only hope, then, is in genuine induction."[ibid., Aphorism 14. See here: The Ideas that Have Influenced Civilization, in the Original Documents]

Sir Francis Bacon (1561–1626) was the first modern philosopher of science, and was instrumental in the development of what we now call the “scientific method.” Here are the essentials of his method of induction, which unfortunately was never completed.

Induction's Bad Reputation

[Originally posted on Facebook]

In my note "Aristotle on Induction," commenter Brian Tinker raised a good question:

Given what you and [Edwin] Locke [in this paper] have said about induction, why does it have such a bad reputation?

I think some of its bad reputation is earned: a very small part, that is. Let me explain.

Most people understand induction to be "by enumeration." Something like: "All of the enumerated cases of swans I've observed are white, therefore all swans are white," or "the sun has always risen, therefore it will rise tomorrow (and the next day, etc.)."

Philosopher Bertrand Russell (1872–1970) gives another example, through parable, of "induction by enumeration" in his book The History of Western Philosophy, page 543. The parable begins: A census officer is questioning homeowners in a village, all of whom seemed to have the same name, William Williams. Finally, the officer decides that every homeowner in the village is named William Williams (an enumerative induction), records the names, and takes a holiday. But he was mistaken: there was one man named John Jones who owned a home there, but the officer had missed him.

This means that the induction is faulty, and illustrates the problem—that inductions by enumeration are never certain; one counter-example can ruin even the strongest of inductive generalizations.

Francis Bacon, the first modern philosopher of science, points out the basic problems with enumerative induction (a criticism which I agree wholeheartedly with):

The induction which proceeds by simple enumeration is puerile, leads to uncertain conclusions, and is exposed to danger from one contradictory instance, deciding generally from too small a number of facts, and those only the most obvious. [Bacon, Novum Organum (New Instrument), Book 1, Aphorism 105.]

Bacon summarizes why most philosophers (in my opinion) denigrate induction, and why it has a bad reputation. Since what he points out about enumerative induction is true, it is my reason for thinking some of induction's bad reputation is earned.

Also, I agree with Dr. Leonard Peikoff's comments on enumerative induction in a lecture course that he presented some years ago:

Induction in my judgment is not in any sense a matter of quantity. There's a type of induction called induction by simple enumeration, which means induction simply by enumerating or counting instances. [...]Now, I regard quantity as such as insignificant. It entirely depends on what happens to that quantity, which can be a good suggestive beginning if you see something happening. What happens when you integrate it with everything else you know that's relevant? (Art of Thinking, Lecture 2)

While enumerating cases can be instructive in forming ideas, noting similarities and differences, and in figuring out how rare or widespread certain phenomena may be (say, meteoroid impacts), I think it's a poor candidate for valid inductive thinking.