Customer Reviews

Paradoxes from A to Z

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Let me begin by saying that I am happy that I own this book. The price was right and I use it to look up paradoxes with which I am not familiar. That said, the treatment is brutally bad in spots, and does not convey a sense of the true recalcitrance of many of the paradoxes. As one example, take the first entry is the book, Achilles and the Tortoise. Clark seems to take the line that since we can sum infinite series, there is no more paradox:

"So the sequence of partial sums is 1/2, 3/4, 7/8,... It goes on for ever, getting closer and closer ('converging') to 1. In this case 1 is the limit, and so the sum, of the series. Achilles gradually closes in on the tortoise until he reaches it."

What? The "explanation" continues by simply explaining limits. This is inane hand waving. Worse still, Clark cites Salmon's excellent collection of articles on Zeno's paradoxes (of which Achilles and the Tortoise is one). A main theme of many of the articles in Salmon's book is that limits do NOT dissolve the paradox.

In the same entry as Achilles, Clark discusses Thomson's Lamp, where the dominant line taken today is that there is no spatio-temporal continuity through an infinite sequence of tasks. "But the description of the supertask entails nothing about the lamp's state at one minute..."

So be it. But then in "explaining" Achilles, Clark writes, "Why then is Achilles at the limit, 1? ... The answer is that, if he is anywhere, as surely he is- he must be at 1."

The problem is the "as surely he is." This echoes Thomson's own, "Surely the lamp must be on or off." If there is no (spatio-temporal) continuity through an infinite task, as was just explained to dissolve Thomson's Lamp, how is there continuity in the case of Achilles? Put differently, why does a limit process tell us about Achilles but not the Lamp? That Thomson's sequence (0,1,0,1...) i.e. (off, on, off, on...) does not have a limit is precisely his point.

There may be a response involving discrete versus continuous tasks, or some other explanation. But the reader is not told this. In general, my problem with the book is that the treatment is superficial and often presents the paradoxes as though they no longer present problems, when in fact they do. An intelligent reader may also be left bewildered by some of Clark's "explanations."

I wonder for whom this book is intended. I think that this book would make a terrible introduction to paradoxes, but may very well serve as a good reference book for those already acquainted with many of the paradoxes.

And that is the problem. The picture of the chicken and the egg on the cover is the most entertaining aspect of the book. The explanations are alphabetical, easy to understand, the collection reasonably complete - and reading it is boring.

Paradoxes are supposed to be fun. The contradictions should gobsmack you at the back of your head and turn you upside down looking for a way to get out. This is more like the guidance councilor talking to you about sex - after listening to her talk you wonder what all the fuss was about and you lose all interest.

A useful reference for schools or public libraries. Since I love self referential conundrums I'll keep it around, but for more fun try Vicious Circles and Infinity: An Anthology of Paradoxes, This Book Does Not Exist, Paradoxes (by Sainsbury), Martin Gardiner's aha! Gotcha: Paradoxes to Puzzle and Delight or anything at all by Raymond Smullyan.

I had high hopes for this book, but found it disappointing. First, it is a comprehensive resource for the most well known paradoxes, and it strikes a good balance between accessibility and the technical aspect of this subject. For paradoxes involving math (Cantor's/Galileo's/Monty Hall/Two-envelope) it serves as a good primer.

After reading a few of the entries I got the feeling that this author dismisses the concept of paradox out of hand. That's over-simplifying it a bit, but pretty close to the mark. Of course, not all paradoxes are worthy of serious consideration - some fall under the "amazing but true" (Simpson's/Placebo) or the "complete BS" (Buridan's) categories - but most, especially those which have been debated for thousands of years, are perplexing for good reason.

Take for example the "Heraclitus/Ship of Theseus" paradox, which the author proclaims as fallacies in the book. At the end of the chapter the issues they raise persist... the question of what makes a thing the same thing after undergoing changes through time is not resolved by stating that the premises are flawed.

Same with "The Heap". Determining at what point something changes from one thing in to something else during a gradual process is not a mere exercise in abstraction, it is crucial in sociology, economics, legal theory, biology... to say nothing of one's fundamental outlook on the universe. Other important fallacies given just a cursory glance include the paradox of "Knowability" (AKA Meno's) and the paradox of "Analysis". The latter is especially threatening, as it proposes that all deductions are trivial which would have grave implications for logic itself.

To the author's credit, he does mention at some point that paradoxes generally point toward a more comprehensive view of a given subject (see Zeno's), but by that time it's too little too late.

I'm nitpicking a bit here - this book is OK, but it needs a much broader context. It seems to have been written to appeal to skeptics. If you get a chance, read through the "Paradoxes" chapter, which is a good indication of the author's viewpoint, and if you're still sold then you will enjoy the rest.

24 short (1-3 page) treatments of various paradoxes. The main problem with this book is the unequal quality from one description to another. My best guess as to the target audience would be under graduate philosophy students.

'Gould, Escher and Bach' is a better book for those interested in paradoxes.