The Inductive Attitude: A Moral Basis for Science and Comprehensivism

06 January 2021 in Resource Center.

Comprehensivism is an emerging practice that takes seriously Buckminster Fuller’s observation that we want “to understand all and put everything together”. In this practice, we value learning from other traditions of inquiry and action, all our communicated experiences, and the Ethnosphere, our all-encompassing cultural zone. To assess this learning, we value accumulating and comparing many working hypotheses, conjectures, guesses, theories, and explanations so we can evaluate our vast inventory of knowledge comprehensively.

With these aspirations and values in mind, this resource will consider inductive reasoning as a moral basis for science as examined by George Pólya (1887–1985) in his 1954 public domain book “Mathematics and Plausible Reasoning: Volume I: Induction and Analogy in Mathematics”. We will also explore the implications of Pólya’s ideas for our comprehensivity, our efforts at learning that are broad in scope and deeply incisive or cutting. For diligent readers who want to assess the relevant parts of Pólya’s book on their own, at the end there is a section with links to its most important and most accessible sections on inductive reasoning.

Induction as The Moral Basis of Science

In a previous resource on The Value of Multiple Working Hypotheses, we learned the value of considering multiple working hypotheses to sharpen our assessments in investigations, learning, civic life, and for our comprehensivity, the quality of our learning that is ever more extensive and ever more intensive and ever more integrated. Since the extensive learning of comprehensivism pulls in so much from Humanity’s vast cultural heritage, we need epistemic virtues, criteria for good knowledge, to aid us in making sense of and assessing all that we have accumulated. What other epistemic virtues might we adopt?

Let’s consider George Pólya’s 1954 book “Induction and Analogy in Mathematics” which states, “Strictly speaking, all our knowledge … consists of conjectures.” Conjectures are statements or assertions that claim to understand something. They are hypotheses. Pólya emphasizes that they are guesses.

Pólya invites us in: “let us learn guessing”. He demonstrates his point, “mathematics in the making resembles any other human knowledge in the making. You have to guess a mathematical theorem before you prove it; you have to guess the idea of the proof before you carry through the details.” In this book, mathematics is not a bunch of ex post facto (after the fact) theorems, it is the art of guessing patterns that have not yet been formulated. Pólya claims that all other human knowledge is guessed at and secured in the same way. The question is clear: How can we guess? How can we devise conjectures? How can we hypothesize? This is the art of induction.

Pólya writes, “observe that inductive reasoning is a particular case of plausible reasoning”. Reasoning is about how to assess or secure our knowledge. Inductive reasoning uses experience to secure our knowledge. Pólya adds, “we support our conjectures by plausible reasoning”. So, plausible reasoning is any way to support our knowledge whether it uses experience or not. However, as far as I can tell, inductive and plausible reasoning are synonymous as all reasoning is based on experience.

Pólya’s objective in “Induction and Analogy in Mathematics” is to curate and explore examples in mathematics than can teach us skill in the practice and understanding of induction. Indeed he goes further, he suggests that mathematics provides a laboratory for “investigating induction inductively”.

But this book, the sequel to Pólya’s delightful and very accessible 1945 book “How To Solve It”, is significantly more demanding of the reader’s mathematical skills. I have organized 28 Meetup events over the past six years, to explore just the first seven chapters, a mere 120 pages, of the book. Despite its many advanced parts, “Induction and Analogy in Mathematics” makes many accessible and interesting observations about induction. We will focus on the accessible parts of the book that might provide insights into the epistemic virtues we seek.

Pólya provides a powerful but succinct definition of induction:

[Induction is the endeavor] to extract the most correct belief from a given experience and to gather the most appropriate experience in order to establish the correct belief regarding a given question.

— George Pólya, Chapter 1, p. 3

This is a powerful and incisive statement. Induction has two aspects. First, to extract or guess or infer a conjecture from experience. Second, to survey, seek out, or design experience to establish or support a conjecture. In both cases it is about assessing the correctness of our beliefs, conjectures, hypotheses, guesses, theories, explanations, and descriptions.

In Chapter 1 §4, Pólya explains the inductive attitude. The text is very good and it’s in the public domain, so I will quote it at length:

The inductive attitude. In our personal life we often cling to illusions. That is, we do not dare to examine certain beliefs which could be easily contradicted by experience, because we are afraid of upsetting our emotional balance. There may be circumstances in which it is not unwise to cling to illusions, but in science we need a very different attitude, the inductive attitude. This attitude aims at adapting our beliefs to our experience as efficiently as possible. It requires a certain preference for what is matter of fact. It requires a ready ascent from observations to generalizations, and a ready descent from the highest generalizations to the most concrete observations. It requires saying “maybe” and “perhaps” in a thousand different shades. It requires many other things, especially the following three.

First, we should be ready to revise any one of our beliefs.

Second, we should change a belief when there is a compelling reason to change it.

Third, we should not change a belief wantonly, without some good reason.

These points sound pretty trivial. Yet one needs rather unusual qualities to live up to them.

The first point needs “intellectual courage.” You need courage to revise your beliefs. Galileo, challenging the prejudice of his contemporaries and the authority of Aristotle, is a great example of intellectual courage.

The second point needs “intellectual honesty.” To stick to my conjecture that has been clearly contradicted by experience just because it is my conjecture would be dishonest.

The third point needs “wise restraint.” To change a belief without serious examination, just for the sake of fashion, for example, would be foolish. Yet we have neither the time nor the strength to examine seriously all our beliefs. Therefore it is wise to reserve the day’s work, our questions, and our active doubts for such beliefs as we can reasonably expect to amend. “Do not believe anything, but question only what is worth questioning.”

Intellectual courage, intellectual honesty, and wise restraint are the moral qualities of the scientist.

— George Pólya, Chapter 1, p. 7–8

Should we be ready to revise any of our beliefs? Do you have that much intellectual courage?

Should we change our beliefs whenever we discover they are disputed by experience? Do you have that much intellectual honesty?

Should we refrain from changing our beliefs excessively? Do you have the wise restraint to resist changing your beliefs without a good reason.

Should we all adopt this inductive attitude as an epistemic virtue guiding our assessment of knowledge?

The Inductive Attitude and Comprehensivism

We have learned that the inductive attitude involves boldly having the intellectual courage to reassess our beliefs when new evidence is found, having the intellectual honesty to change our beliefs when presented with disconfirming evidence, and having sufficient wise restraint to resist changing our beliefs without good evidence. Later on, Pólya explains it this way:

Induction: adaptation of the mind, adaptation of the language. Induction results in adapting our mind to the facts. When we compare our ideas to the observations, there may be agreement or disagreement. If there is agreement, we feel more confident of our ideas; if there is disagreement, we modify our ideas. After repeated modification our ideas may fit the facts somewhat better. Our first ideas about any new subject are almost bound to be wrong, at least in part; the inductive process gives us a chance to correct them, to adapt them to reality.…

Adaptation of the mind may be more or less the same thing as adaptation of the language; at any rate, one goes hand in hand with the other. The progress of science is marked by the progress of terminology.

— George Pólya, Chapter 3, Example and Comment #21, p. 55

This is another powerful and incisive explanation of the process of learning couched in the language of induction, the language of science. It seems like a good epistemic virtue for our comprehensivity, our broad learning about our world and how it works. Until we start looking for evidence among the traditions, cultures, and experiences where comprehensivists look for their knowledge. When we start looking, we find that individual beliefs seem to trump the inductive attitude almost everywhere.

As far as I’ve been able to determine, each of us espouses and clings to many core beliefs which we would steadfastly refuse to change regardless of evidence. How many of your beliefs do you hold onto so tightly that you would refuse to change them even if the evidence against them seemed strong? Are human beings constitutionally incapable of adapting to experience, observation, and evidence? Is the inductive attitude unhuman and inconsiderate of our stubbornness?

Pólya observed, “There may be circumstances in which it is not unwise to cling to illusions”. When we are momentarily confused by unusual circumstances, we rely on our core beliefs to reorient us. When we suffer trauma where our autonomy and truth is denied by others, it may be wise to cling to some hopeful illusions about our worth and dignity. Shouldn’t we give people the psychological solace of whatever illusions they may want to cling? Induction should not be a destructive force crushing our psychological cocoons.

From a comprehensivist perspective, before we adapt our beliefs we should take into account all our experiences including those that led us to our current beliefs, including our learning from all Humanity’s traditions of inquiry and action, from all of the cultures that comprise the Ethnosphere, and from all our communicated experiences in Bucky Fuller’s cosmic intellectual conception of Universe. That is, our inductive reasoning should accommodate all our comprehensivist knowing, including any incomplete, intuitive, and ineffable knowing.

I hope that is what Pólya meant, otherwise with a too narrow account of experience, induction can become an imperial force violently separating us from our traditions, our cultural heritage, our friends and family. If we do not want narrowly considered experiences to become a tyranny where induction runs roughshod over people and their cultures, we must take a comprehensive view of experience and soberly accommodate all experience including the often ineffable bases of beliefs.

This is evidence that Pólya’s inductive attitude ought to incorporate the moral reform of T. C. Chamberlin’s method of multiple working hypotheses. Then the full array of conjectures considered by the full scope of comprehensivist learning can enrich the exploration and refine our judgment fortified by the discriminative edges of multiple working hypotheses. In my interpretation of Pólya, this is what wise restraint entails.

Now we are starting to realize powerful benefits from our comprehensivist approach. Our broad outlook warns us to the dangers of interpreting Pólya too narrowly. Our broad outlook gives us access to more conjectures and more experiences to include in our inductive assessments. Our ready affinity to intensively engage this complexity in depth gives us the wherewithal to practice the wise restraint Pólya recommends.

In considering this comprehensivist context including our practice of engaging multiple working hypotheses and honoring the full breadth of comprehensivist experience, should we adopt Pólya’s inductive attitude of adapting our beliefs to our experience as an epistemic virtue providing a moral basis for the practice of comprehensivism?

This essay was written to provide ideas in support of the 13 January 2021 session of “Comprehensivist Wednesdays” at 52 Living Ideas (crossposted at The Greater Philadelphia Thinking Society).

Addendum: 1h 24m video from the 13 January 2021 event:

Reading about Induction in Pólya

In case a diligent reader would like to consider reading Pólya’s material on induction directly, I recommend the Preface §1–4 and Chapters 1 & 2 as accessible for all readers, except you might skip Chapter 2 §6 unless you are familiar with elementary calculus. Chapters 3 and 4 are excellent but would require a bit of mathematical application to fully appreciate. Regardless, all readers would benefit from reading Chapter 3, Examples 21 & 41 and Chapter 4 §6–7 & Example 26. Although Chapter 5 is advanced mathematically, §5 and the beginning of Example 15 are important and accessible. The rest of the book does not directly address induction, but the subject is always in the background. The book will reward both diligent and casual study: it is a masterpiece of world literature.

Here are links to the relevant sections of the book for readers who just want the highlights (50 pages in total or 30 pages if you skip most of Chapters 3 & 4 as recommended above): §1–4 of the Preface on pages v–viii introduces Pólya’s objectives; Chapter 1 on pages 3–8, including Examples 9–14 on pages 9–11. Chapter 2 on pages 12–22, including Examples 5, 7, 10, 11, and 18–20 on pages 23–30, and #46 on page 34. Chapter 3 on pages 35-52 especially Example Problems 21 and 41 in Chapter 3 on pages 55 and 58. Chapter 4 on pages 59-70 especially §7–8 on pages 68–69 and Example 26 on page 73. Chapter 5 §6 “the role of the inductive phase” on pages 83-84 and the first paragraph of Example 15 on p. 87.

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Posted by CJ Fearnley

Explorer in Universe.

1 comment

Kirby Urner

I’ve appreciated some of our follow-up conversation on social media. Here’s a snapshot:

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