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This is a reference request. I'm looking for a modern, rigorous, and intelligently written introductory book on informal logical reasoning and critical thinking, aimed at a non-mathematical audience (think lawyers, the general educated reader).

Here is what I mean by these criteria:

  • "modern": ideally but not necessarily written in the last 10 or 15 years; this rules out Stephen Toulmin's books, for example (his jargon, e.g. the particular meanings he attaches to "grounds" and "warrants," is outdated and idiosyncratic, and no one teaches Toulmin in any U.S. philosophy department)
  • "rigorous": the book should be carefully and precisely written, ideally by someone with a PhD in philosophy or JD, at least someone familiar with the way arguments are analyzed in contemporary language; the book should also ideally include a list of references or recommended further reading
  • "intelligently written": the prose of the book itself should be sophisticated and challenging, not written at a middle-school level; this rules out most of the dime-a-dozen textbooks on "informal logic" and "critical thinking" from publishers like Cengage
  • "for a non-mathematical audience": the book should do little symbolic logic, only as much as is necessary to convey a feeling for logical form and deductive validity; it should entirely avoid the modern syntax, semantics, and proof systems of propositional and predicate logic; it should not give a tiresome enumeration of Aristotelian syllogisms; it should focus on analyzing arguments written in English prose without formalizing them symbolically, and with an eye to the distinction between rhetorical suggestion/conversational implicature and strict deductive implication

I have graduate-level training in philosophy and am surprised I cannot find a book that meets these criteria to use with students who don't need to learn any mathematical logic, so I'm hoping this forum can help! To simplify the statement of the problem: if you were stranded on a desert island, which one introductory book on reasoning would you wish you had with you? Of course this way of asking the question makes it subjective, but I hope it will rule out responses of truly second- or third-rate writing.

If you asked most mathematicians the same question regarding an introductory calculus book, a very large proportion would probably say Spivak's Calculus. I'm looking for the analog for basic reasoning. I'm afraid it might not exist.


Some books that come close to meeting these criteria deal, specifically, with fallacies. Here are a two I would consider rigorous and intelligently written:

  • C. L. Hamblin, Fallacies (very sophisticated prose)
  • S. Engel, With Good Reason: An Introduction to Informal Fallacies

But these are too specialized: they don't do enough, and the Hamblin is too old, even though it is a good example of what could qualify as "sophisticated prose."

Here are examples I think fail to meet some of these criteria:

  • Irving Copi, Introduction to Logic
  • David Kelley, The Art of Reasoning

Some books that are useful, but still not ideal:

  • Armstrong and Fogelin, Understanding Arguments
  • Munson and Black, The Elements of Reasoning
  • Walton, Informal Logic (too long, too meandering)

I've had to settle by using the Armstrong and Munson, but I'm hoping there's something better.

  • May not be anti-math enough. It is obviously not for a non-mathematical audience, but it is a classic: Polya's Mathematics and Plausible Reasoning -- books.google.com/books/about/… – jobermark Feb 15 '18 at 16:06
  • That's certainly a beautiful book, but it's not about analyzing arguments in English prose; it's about mathematical problem-solving. – symplectomorphic Feb 15 '18 at 16:23
  • Per wikipedia, I think the problem is that the field of argumentation is split across philosophy, mathematics, sociology, psychology, political science, etc. No single author can be expected to authoritatively cover the wide range of people appear to be reasoning (or failing to reason) in all these contexts: en.wikipedia.org/wiki/…. Thanks for the book list, I'm adding them to my "to read" list. – MatthewMartin Feb 18 '18 at 17:52
  • @MatthewMartin: I don't quite buy your explanation of the problem. The subject area is well-defined enough: the sort of arguments an average educated reader is likely to encounter in ordinary English prose, such as the arguments given on the LSAT. Yes, this touches on a wide range of argumentative phenomena (deduction, induction, abduction, statistical thinking, rhetoric and implicature), each of which can be formalized in much greater detail in a particular domain, but the elements are pretty well-agreed upon. I did say an "introduction," not an exhaustive authoritative treatment. – symplectomorphic Feb 18 '18 at 21:31
  • Why exactly do you think that Copi's book fail to meet some of the above criteria (and what are they precisely)? – user 170039 Mar 30 '18 at 3:42
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I've taught Critical Thinking for about 20 years, and I have to agree that there is no good textbook.

Let me tell you where I'm coming from: Yes, I've seen all the textbooks with their unending treatments of logic ... Ugh! Sure, logic is important, but why the insistence on formal logic proofs? We have logic courses for that. Indeed, just the fact that the focus is on deductive logic seems rather silly. Most real life reasoning is not deductive and so all this logic has very limited applicability. Yes, logic teaches one to be careful and organized in one's reasoning, but let me put it this way: when it comes to people coming to bad beliefs and making bad arguments, logic is probably the least of our problems. Much more problematic are our cognitive and social biases. When you cover fallacies, you'll find that they can almost all be traced back to those biases, rather than to any logical reasoning impairment.

I suppose I should also that say that I define Critical Thinking basically as "thinking about beliefs (especially your own!) and seeing if they make sense". Or: how to not get caught up in bullshit and be an actual truth-seeker! That of course already goes far beyond merely analyzing some prose... it about developing a critical mind-set ... and the many, many psychological and social barriers that exist both inside and outside of us that prevent us from being genuine truth-seekers.

So, when I teach Critical Thinking, I spend a few weeks on each of the following:

Arguments: basic analysis and evaluation

Fallacies: the usual suspects ... though I emphasize rhetorical flim-flam and emotional trickery

OK, so far so good, but then:

Statistical/inductive reasoning: really important stuff! And by the way: I take a very 'anti-math' approach here as well: you can do all the probability theory and statistics you want, but in the end so many people are still convinced by some hasty generalization of refutation based on one piece of personal experience or anecdotal evidence: that's the kind of crazy thinking that I want my students learn to prevent.

Causal reasoning: super important! The way we think the world causally works translates in how we act. And my oh my, are there a great number of pitfalls in causal reasoning!

Cognitive biases and social biases: as the great philosopher Clint Eastwood said: "A man's gotta know his limitations". Socrates reportedly mumbled something to that effect as well :)

Perception and memory: lots of crappy beliefs come from crappy perception and crappy memory

'Authorities': Media (esp. internet!), culture, science, pseudo-science, religion, etc.

Oh, and in case you think I'm all anti-math and don't like logic: I teach Introduction to Logic, Intermediate Logic (meta-logic; soundness, completeness, etc) and Computability and Logic (undecidability of logic, Godel results), and I love it! ... So yes, I could certainly teach a whole critical thinking course all around logic ... it would certainly be a lot easier for me to teach (and assess!) than what I do now ... I just don't think logic has all that much to offer as far as critical thinking goes.

So, what book do I use? None. All ingredients can be found on the internet. It's not rocket science. Though I can point to a few books that have provided some valuable material:

"How to think about Weird Things"

"How we know what isn't so"

"How to Lie with Statistics"

and there's always Carl Sagan's classic "The Demon-Haunted World"

Sorry, all more than 15 years old I'm afraid, but at least they go beyond mere arguments: there is a lot of psychology and sociology behind the formation of our beliefs, and you have to instill awareness of that in the students, or else in my eyes it fails to be a critical thinking course. If there is one key to critical thinking, it's independent thinking!

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I am currently studying critical thinking using Critical Thinking, A Concise Guide, 4th edition by Tracy Bowell and Gary Kemp. I find this book well-balanced and it has good examples and exercises. I really enjoy studying it and it has already started making a positive difference in my everyday conversations. However, my opinion is subject to the following caveats:

  1. I have a background in mathematics, so I am not well-positioned to judge if the book is good for non-mathematical audience.
  2. So far, I have read only 4 chapters out of 8.
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Step 1: Read Chapter 1 of Bertrand Russell's Introduction to Mathematical Philosophy, where the series 1, 1/2, 1/4, 1/8, ... is shown to satisfy Peano's five axioms. (Page 7)

Step 2: Read Chapter 2 of Terrence Tao's Analysis I. Hindustan Book Agency 2015, where, on page 20, Tao proved that no natural number defined by Peano's axioms can be a half-number.

Step 3: Ask yourself whether you have any reason to trust any textbook, any university or any person's advice.

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    More readers will follow up on this answer if you describe in at least a sentence or two what insights they can expect from these readings. – Mark Andrews Mar 22 '18 at 17:37

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