Choice and Chance. An Introduction to Inductive Logic

by Brian Skyrms

This definitive survey of the hottest issues in inductive logic sets the stage for further classroom discussion.

Genres: Philosophy, Logic, Nonfiction

Paperback

First published January 1, 1966

Reviews

[Happy Reader · Rating 4 out of 5]

Good introductory text

[Jayson Virissimo · Rating 5 out of 5]

This is probably the best entry point to inductive logic on the market.

More consistent, concise, and at least as correct, but not quite as fun as, Ian Hacking's introductory text.

[Brian Powell · Rating 3 out of 5]

"Choice and Chance" is a light but provocative introduction to the problem of induction. First, we’re not talking deduction here, as Skyrms emphasizes: “An argument is deductively valid if and only its conclusion is false when its premises are true; an argument is inductively strong if and only if it is improbable that its conclusion is false when its premises are true.” These definitions emphasize that induction is not the opposite of deduction (as is too often falsely alleged), but instead inductive reasoning applies to a spectrum of inference: from deduction (truth by logical necessity) to the most egregious non sequiturs. Ideally, our inferences should be inductively strong – that they are correct “most of the time” or with “high probability” -- essential for distinguishing the desirable strength of induction, but notoriously difficult to formalize. This is Skyrms’ entre into Hume’s problem of induction – how do we confirm that conclusions assigned high probability by our inductive model actually occur most of the time?

The problem is with the validity of the inductive approach itself. The go-to method for learning new things about the world is induction, whether these things be how to tie a shoe, build a rocket, or conduct scientific inquiry. It’s a bit of a meta-problem: can we use inductive logic to justify the use of induction? No, not unless we wish to commit logical suicide by running round and round in a vicious circle. And we cannot use deduction either, because its conclusions never tell us anything not already implicitly contained in the premises (i.e. we cannot learn from it). Skyrms describes an inductive approach to validating induction that introduces a hierarchy of arguments, wherein the inductive inferences made on one level are justified by the one above it. Acknowledging that I’ve not examined this solution carefully, it’s difficult to see how it succeeds: like a rug that’s too large for the room, we can smooth it out here only at the expense of creating a ripple over there. Skyrms spends some time discussing the other commonly attempted solutions: induction works if any method does (a clever argument and well worth understanding (p. 44), even if it’s not a solution per se), and there isn’t actually a problem and we all need to get over it.

Inductive inference in the natural sciences is generally used to project knowledge of particular cases to knowledge universal. Strong induction in these cases relies on the presumed uniformity of nature, across space and time, that supports extrapolation from known events here and now to unknown events there and then. The degree of relevant uniformity dictates the strength of the induction: that it will rain tomorrow because it has rained all week projects only a temporary regularity and risks being false, whereas the claim that the sun will rise tomorrow projects a firm, well-substantiated regularity.

The problem of induction is how to identify the relevant uniformity in general. Skyrms explores this nuanced challenge in Chapter 3, beginning with the work of Goodman on how regularities depend on the language used to describe events (we’ll discuss Goodman’s work on this and related issues in a later reference). In short, one can perform linguistic shenanigans – words with situation- and time-dependent meanings, to deeply confuse and thwart attempts at establishing regularities. It is not clear from Skyrms’ treatment whether this is actually a problem for the practical sciences or only an academic curiosity. Of more immediate concern to the practicing scientist is how one discovers patterns and regularity in data for the purpose of establishing law-like relationships between quantities. Skyrms has in mind discrete data points represented in 2D: how do we draw a curve through these points? Any way we please! And each such curve will support a different prediction for the value of points lying outside the domain supported by the data (a different extrapolation): “For any prediction whatsoever, we can find a regularity whose projection licenses that prediction (p. 65).” Skyrms closes Chapter 3 without any resolution to this dismal state of affairs, without any pep talk. This is unfortunate because I believe the situation is not so dire, despite the clear challenges so well-articulated by the author. Happily, experimental science augmented with a suitable helping of goodness-of-fit tests goes a far way towards clarifying some of these issues. It’s unfortunate that Skyrms doesn’t mention any of them, but they’ll be covered in other references in this list.

At this point, Skyrms makes a rather abrupt break from his inquiry into induction and discusses Mills methods of identifying necessary and sufficient conditions of observed events; duly interesting but admittedly off topic (Skyrms suggests skipping the rather lengthy Chapter 4 entirely on a first read). In fact, the remainder of the book is seemingly off topic, covering probability theory without making any clear connections back to the deep problems we were left with at the end of Chapter 3. Because the latter portions of the book seem to wither in isolation, I recommend the first three chapters (only 75 pages or so) as a basic introduction to the problem of induction; hence the 3-star review.

[Izlinda · Rating 3 out of 5]

So I'm bad at logic, but for my Philosophy of Science course we had to read several sections from this logic book. (Makes sense, since induction is used in science.)

Uhm. The exercises sometimes helped, but other times Skyrms' writing, though put in layman terms, was still confusing. Looking ahead in the syllabus, it seems we're done with this book for this semester, so...good riddance!

(I'm so glad I'm not required to take the full logic course. I would die otherwise.)