As noted earlier, I've been reading Subjective Probability: The Real Thing by Richard C. Jeffrey. It's a short book, but I've been distracted by other things, and I've also been slowed by the condition of the book; it's full of errors. For example,

It seems evident that black ravens confirm (H) All ravens are black and that nonblack nonravens do not. Yet H is equivalent to All nonravens are nonblack.

Uhm, no: (X ⇒ Y) ≡ (¬X ∨ Y) = (Y ∨ ¬X) = (¬¬Y ∨ ¬X) = [¬(¬Y) ∨ ¬X] ≡ (¬Y ⇒ ¬X) In words, that all ravens are black is equivalent to that all non-black things are non-ravens.[1]

The bobbled expressions and at least one expositional omission sometimes had me wondering if he and his felllows were barking mad. Some of the notational errors have really thrown me, as my first reäction was to wonder if I'd missed something.

Authors make mistakes. That's principally why there are editors. But it appears that Cambridge University Press did little or no real editting of this book. (A link to a PDF file of the manuscript may be found at Jeffrey's website, and used for comparison.) Granted that the book is posthumous, and that Jeffrey was dead more than a year before publication, so they couldn't ask him about various things. But someone should have read this thing carefully enough to spot all these errors. In most of the cases that I've seen, I can identify the appropriate correction. Perhaps in some cases the best that could be done would be to alert the reader that there was a problem. In any case, it seems that Cambridge University Press wouldn't be bothered.

[1]The question, then, is of why, say, a red flower (a non-black non-raven) isn't taken as confirmation that all ravens are black. The answer, of course, lies principally in the difference between reasoning from plausibility versus reasoning from certainty.

I have been reading Gut Feelings: The Intelligence of the Unconscious by Gerd Gigerenzer. Gut Feelings seeks to explain — and in large part to vindicate — some of the processes of intuïtive thinking.

Years ago, I became something of a fan of Gigerenzer when I read a very able critique that he wrote of some work by Kahneman and Tversky. And there are things in Gut Feelings that make it worth reading. But there are also a number of active deficiencies in the book.

Gigerenzer leans heavily on undocumented anecdotal evidence, and an unlikely share of these anecdotes are perfectly structured to his purpose.

Gigerenzer writes of how using simple heuristics in stock-market investment has worked as well or better than use of more involved models, and sees this as an argument for the heuristics, but completely ignores the efficient-markets hypothesis. The efficient-markets hypothesis basically says that, almost as soon as relevant information is available, profit-seeking arbitrage causes prices to reflect that information, and then there isn't much profit left to be made, except by luck — unpredictable change. (And one can lose through such change as easily as one might win.) If this theory is correct, then one will do as well picking stocks with a dart board as by listening to an investment counselor. In the face of the efficient-markets hypothesis, the evidence that he presents might simply illustrate the futility of any sort of deliberation.

Gigerenzer makes a point of noting where better decisions seem often to be made by altogether ignoring some information, and provides some good examples and explanations. But he fails to properly locate a significant part of the problem, and very much appears to mislocate it. Specifically, a simple, incorrectly-specified model may predict more accurately that a complex, incorrectly-specified model. Gigerenzer (who makes no reference to misspecification) writes

In an uncertain environment, good intuitions must ignore information

but uncertainty (as such) isn't to-the-point; the consequences of misspecification are what may justify ignoring information. It's very true that misspecification is more likely in the context of uncertainty, but one system which is intrinsically less predictable than another may none-the-less have been better specified.

I am very irked by the latest chapter that I've read, Why Good Intuitions Shouldn't Be Logical. In note 2 to this chapter, one reads

Tversky and Kahneman, 1982, 98. Note that here and in the following the term logic is used to refer to the laws of first-order logic.[1]

The peculiar definition has been tucked behind a bibliographical reference. Further, the notes appear at the end of the volume (rather than as actual foot-notes), And this particular note appears well after Gigerenzer has already begun using the word logic (and its adjectival form) baldly. If Gigerenzer didn't want to monkey dance, then he could have found an better term, or kept logic (and derivative forms) in quotes. As it is, he didn't even associate the explanatory note with the chapter title.

Further, Gigerenzer again mislocates errors. Kahneman and Tversky (like many others) mistakenly thought that natural language and, or, and probable simply map to logical conjunction, logical disjunction, and something-or-another fitting the Kolmogorov axiomata; they don't. Translations that presume such simple mappings in fact result in absurdities, as when

She petted the cat and the cat bit her.

is presumed to mean the same thing as

The cat bit her and she petted the cat.

because conjunction is commutative.[2] Gigerenzer writes as if the lack of correspondence is a failure of the formal system, when it's instead a failure of translation. Greek δε should sometimes be translated and, but not always, and vice versa; likewise, ∧ shouldn't always be translated as and nor vice versa. The fact that such translations can be in error does not exhibit an inadequacy in Greek, in English, nor in the formal system.

[1]The term first-order logic refers not to a comprehensive notion of abstract principles of reasoning, but to a limited formal system. Perhaps the simplest formal system to be called a logic is propositional logic, which applies negation, conjunction, and disjunction to propositions under a set of axiomata. First-order logic adds quantifiers (for all, for some) and rules therefor to facilitate handling propositional functions. Higher-order logics extend the range of what may be treated as variable.

[2]That is to say that