Logic and Paradox

This logically goes into the IMHO forum, yet paradoxically it is about books, so it could also go in this forum…

What are some good books that explain (in an easy/interesting manner) logic? A book filled with good examples would be ideal.

What are some good books that deal with paradoxes (paradoxi?paradoxies?)? I am looking for a book with classical paradoxs and maybe some modern ones. I am not looking for “business, environmental, non-philosophy” paradox books.

Godel, Escher, Bach seems to be a good read so far. I’m not extremely far into it but my take on it is that it’s exactly what you’re looking for. So far I’ve read about Zeno’s paradox, stories within stories converging upon infinite series, and various logic problems dealing with both math and philosophy.

Beat me to it, Enderw24 :slight_smile:

Athough, for elementary principles of logic, G-E-B is a hard read. I’ll have to try and think of something additional that’s easy/interesting and isn’t super technichal.

Mathematical Fallacies and Paradoxes by Bryan Bunch.

Labyrinths of Reason: Paradox, Puzzles, and the Frailty of Knowledge by William Poundstone.

Forever Undecided: A Puzzle Guide to Godel by Raymond Smullyan (and a number of Smullyan’s other books)

A number of articles on paradoxes scattered throughout the collections of Martin Gardner’s Mathematical Games articles from Scientific American.

There’s a book entitled Encyclopedia of Paradox or something like that that’s probably good.

Do you mean Vicious Circles and Infinity: an Anthology of Paradox?

I haven’t read this one, but I like the title: What is the name of this book?, by R.M. Smullyan.

It isn’t strictly about logic and paradox, but it does present them in historical context (along with other topics): Bertrand Russell’s Wisdom of the West.

Since everyone else has recommended the standard “popular” books on logic I’ll suggest a couple of slightly more technical ones.

Wilfrid Hodges, Logic: yes it’s a textbook, with exercises and stuff, but it is a very easy one, an easier read than G-E-B for most people, I’d say.

Patrick Suppes, Introduction to Logic: More technical and more difficult than Hodges, I’d say this is the best introductory textbook on the subject.

Jabba has a good point. It may not be glamorous, but a solid logic textbook is the best place to start.

I can also vouch for Huxley’s Introduction to Logic (no, not Aldous).

Can’t add any to the existing list (other than to further the recommendation for Gödel Escher Bach), but I can tell you thatthe plural of “paradox” is “paradoces”.

I strongly recommend against G-E-B. It is long winded, rambling and obtuse. A half decent science writer could have said the same thing in two chapters and made it much clearer. Hofstadter’s columns in Scientific American were also long and pointless. They canned him quickly. It’s one of those “the emperor has no clothes” kind of things.

Go with Smullyan and check the “what other people bought who bought Smullyan” lists at Amazon.

Um, Chronos, in English the plural is “paradoxes”. Perhaps you are referring to some other language?


Each to their own, but I just wish to respectfully and strongly disagree. I think GEB is a terrific book and a wonderful achievement. It has much to recommend it, and amply rewards careful reading. Not to be too polemical, but I feel ftg’s comment tells me more about ftg than it does about the book.

However, since ftg sees fit to pronounce on what is, and is not, fine writing, it is perhaps acceptable to point out a few things.

‘Long winded’ should be ‘long-winded’.

‘Half decent’ should likewise be hyphenated.

‘They’ in ‘They canned him quickly’ is ‘obtuse’ since it refers to no antecedent noun. The same is true of ‘It’ in ‘It’s one of those…’

Perhaps when ftg has studied a while, and learned how to write correctly, he or she will be better placed to bestow upon us the benefits of his or her judgement about Douglas Hofstadter’s work.

Hofstadter’s book is good for explaining the central themes of mathematical logic and theoretical computer science, as well as tying them to other disciplines. I read it after studying both of those subjects, and enjoyed it thoroughly.

ftg seems to think that it’s not a good book because it doesn’t just present the facts. It was never intended to; there are other books that do that.

Thanks for the information people. Before I posted this I was actually considering Amazoning the G-E-B book. Is there any books that deal with scientific paradoxes? Or maybe problems with the modern understanding of science?

I figure whilest I’m amazon’n it I might as well stock up…

Meatros writes:

> Is there any books that deal with scientific paradoxes? Or
> maybe problems with the modern understanding of science?

Could you explain a little what you mean by these topics? It’s not clear what you want here.

How do you spell “petty”?.. & the last two points are wrong to boot.

For what it’s worth: the Hodges book is fine–I used it once in a course–but what I’ve always found most useful & entertaining are the Smullyan books, which work through basic matters of logic, truth tables, paradoxes, logic games & puzzles, &c, all the way up to matters like Gödel’s theorem & the Turing stopping problem. (I’m also fond of his books of retrograde chess problems (which are another form of logic problem: from a current position on the board, deduce what happened earlier in the game), which are cast in the form of parodies of the Holmes stories & the Thousand and One Nights. Worth checking out, if this is your speed. It’s one of the few things I can do in chess without actually being a good chess player.)

But ‘paradox’ comes from the Greek [symbol]para[/symbol] + [symbol]doxa[/symbol], ‘beyond expectation’.

G-E-B is too much of a summary of other’s theories. Rambling, unoriginal, uninsightful.

“Introduction to Logic” Irving M. Copi is amusing and profesional, but logic is one of those subjects you’re better off taking a class on. The subject can have rather delicate nuances. And you’ll find other student’s opinions will considerably startle you.

I recommend against starting with a book specifically about paradox. To understand why a logical statement is invalid/false/improperly formed, it’s necessary to understand what’s meant by sound logic. This lack of undertanding of the basics is responsible for perpetuating grammar school arguments such as “If God can do anything, can he move an immovable objects?” Start with basic formal logic, there are plenty of interesting things to chew on…

As for a book about the modern problems of science, which does have numerous sections about fallacies in reasoning, Morris Kline’s “Mathematics: The Loss of Certainty” is well-written, scholarly, easy to read (at least the first half), and a real page-turning eye-opener. If you can’t find a logic class, that would be a great book to start with.

Then I was in error, and Chronos may be wrong as well. I don’t remember how to make Greek plurals.