Argument and inference. An introduction to inductive logic (Q2803844)

This textbook introduces students to basics of argumentation and uncertain inference. The author provides numerous examples, exercises and solutions for all eight chapters and the two appendices. Throughout the text, short introductions to current chapters provide good overviews of the covered material and demonstrate how it builds on previously covered material. The author's didactic approach is well-suited for undergraduate students, first-year students in particular.NEWLINENEWLINEThe first chapter covers basic argument forms such as modus ponens, modus tollens, inductive generalisation and analogical inference. Chapter two demonstrates hypothesis generation, data collection and hypothesis confirmation by considering Halley's prediction of a comet reappearing \(75\) to \(76\) years later. The chapter also briefly introduces \textit{affirming the consequent} and Popper's notion of falsification. The next chapter contrasts inductive confirmation with inference to the best explanation. The fourth chapter covers Mill's methods for causal inference.NEWLINENEWLINEThe final four chapters are devoted to probabilistic inference. Chapter five introduces proportions of populations, independences and (strengths of) association. The next chapter introduces probabilities and basic probabilistic inference rules (conditional probability, conjunction and disjunction rule). The penultimate chapter teaches null hypothesis significance testing and confidence intervals. The last chapter is a gentle introduction to Bayes' rule. Two appendices on deductive logic and probability complete the book.NEWLINENEWLINEIt is slightly odd that the book does not have a bibliography. A few references are dispersed throughout the text, none of them refers the student to other introductory textbooks. Furthermore, keen students will miss references to in-depth treatments of examples discussed in this book. It should also be noted that there is no reference and no discussion of contributions made by Rudolf Carnap, George Pólya and David Hume. None of their successors or commentators are mentioned in this book. I hence think that this textbook needs significant supplementation to cover sufficient ground for a well-rounded introduction to induction.NEWLINENEWLINEOverall, I found this textbook to be well-suited for undergraduate students providing many many examples and intuitive explanations -- with the exception of Chapter 7, which I found highly confusing.NEWLINENEWLINEAccepting the usual axioms of probability and an intuitive understanding of randomness and chance, Johnson writes (p. 165) that the following argument is not deductively valid:NEWLINENEWLINEPremise 1: 60\% of the marbles in the jar are red.NEWLINENEWLINEPremise 2: Two marbles are about to be randomly selected from the jar (with replacement).NEWLINENEWLINEConclusion: Hence, there is a 36\% chance that both of these marbles selected from the jar will be red. NEWLINENEWLINEFor him, this argument is by nature inductive and also not a good argument, since the probability 36\% is relatively small. Replacing the conclusion by the logically equivalent argument ``Hence, there is a 64\% chance that at least one of these marbles selected from the jar will not be red'' makes the argument inductively stronger.NEWLINENEWLINEAlso, I was confused by the following passage (p. 201): ``A jar of marbles contains an unknown percentage of green marbles. 250 marbles are selected (with replacement) from this jar. Of these 150 are green the rest is nongreen. What is the proportion of green marbles in the population? In this problem, the observed relative frequency is 60\% \dots, when the sample size is 250, the 95\% probability interval is 0.12 wide. If the observed relative frequency (0.60) is placed at the center of this interval, then the interval is 0.54 to 0.66. With that, we can say the following about the population: there is a 95\% chance that the percentage of green marbles in this jar is between 54\% and 66\%.'' My personal understanding of null hypothesis significance testing and estimating true populations are somewhat different.NEWLINENEWLINEIt is commendable that the author lists errata on his personal website, currently available at \url{http://blog.loighic.net/errata}. The errata currently listed do not apply to Chapter 7.