book reviews
## Books on logicreviewed by T. Nelson |

Bo Bennett

Archieboy, 2018, 383 pages

Reviewed by T. Nelson

The dictionary defines ‘fallacy’ as a mistaken belief, especially one based on unsound argument. But it turns out, according to Bo Bennett, that using the dictionary as proof in an argument is itself a fallacy.

We often encounter arguments that are very hard to dissect. We know they're invalid; the concept of fallacy can help us pin down why. This book, a compilation of fallacies from the Internet, teaches how to recognize them in a light, amusing way.

Of course, a fallacy is only one class of logic error. There are many others that we
don't think of as fallacies. The Internet is a rich source of these as well. Teaching
people basic facts about logic, like the opposite of `X and Y`

being ```
not X
or not Y
```

, would be great for the blood pressure of folks who read their stuff on
the Internet.

Or how 'bout this one: If ten climate simulations predict Arctic ice will stay constant and ten predict it will drop to zero, can we just average them and say it will drop by half? Some people seem to think so, but it's invalid. My bp shot up just thinking about it.

Maybe someday mathematicians will tell us whether the number of ways logic can be screwed up is infinite. But coming up with a valid taxonomy of fallacies isn't easy. If I point out that many of the ones in this book are identical to each other, so there aren't really 300 of them, it's not a fallacy either.

Never mind then. Here's a typical example from the book illustrating the *Appeal to
Fear* fallacy:

Timmy: Mom, what if I don't believe in God?

Mom: Then you will burn in Hell forever. Why do you ask?

Timmy: No reason.

The exception, says Bennett, is when fear is not used to support the argument, then it's not a fallacy.

Timmy: Mom, what if I don't believe in God?

Mom: Then I would hope that you don't believe in God for the right reasons, and not because your father and I didn't do a good enough job telling why you should believe in him, including the possibility of what some believe is eternal suffering in Hell.

Timmy: That's a great answer, Mom. You are so much better than my mom in the other example.

Bennett's general solution is to say “may be” instead of “is,” which may be a good solution, but he has an even better one: no index. That way, if there are duplicates, logical flaws, or fallacies in the book, we'll never find them. Which, just coincidentally, is the real reason I'm not pointing any of them out.

This book is no substitute for a course on formal logic—for that, you'd need Sider (reviewed at right) or one of the introductory textbooks. But it's a fun read, he doesn't take sides or take himself too seriously, and best of all he has an infinite supply of material to work from. Read it quick before his website goes all Snopes on us. One star off for PC language and for no index.

*dec 09, 2018*

Alan Jacobs

Currency, 2017, 157 pages

Reviewed by T. Nelson

This little popular-style book is included here because when we misuse logic, or use strawman arguments, or put words in people's mouths, it's usually not because we don't know better; it's because we're not thinking. Instead, we're expressing emotion and signaling to our friends. We use strawman arguments because we see our opponents as straw men.

It may seem strange, then, to claim that emotions help us to think. Despite the author's grating writing style, he makes an interesting point: learning to think empathetically, says Jacobs, will give you a model for how to think of your adversary as a real person, and, maybe, convert them instead of just trying to score points. So what the book is really about is not how to think, but how to stop fighting.

We instinctively defend our sunk costs, which leads to escalation of commitment. This, he says, leads to intellectual bankruptcy. He backs this up with a number of stories about how people overcame it. Yes, they lost all their friends, but they gained . . . well, he doesn't say exactly what; I guess a little truth and a lot more peace and quiet. As Slim Pickens would say: shee-it, I got one of those already.

*dec 09, 2018*

Graham Priest

Cambridge, 2008, 613 pages

Reviewed by T. Nelson

In non-classical logic, philosophers change one or more of the rules of regular logic to see what happens. Usually what happens is not good: you get combinatorial explosions of inconsistencies or logics that contradict themselves.

Yet it can be very useful. Years ago I found three-valued logic to be essential
in understanding how neural networks can form higher-order concepts. Before I left
the field, I even wrote a paper on it in *Biol. Cybern.* as a grad student
way, way back in 1983.

Another example is intiutionist logic, where instead of asking whether something is true we ask whether it has been proved. This is popular with mathematicians and some physicists such as Nicolas Gisin are using it as a way to understand time.

These new forms of logic can also be useful in helping us understand why the rules of real (i.e. classical) logic are what they are. Are they baked into the universe or are they part of our brain? Philosophers think the former, which is why Graham Priest treats them as offshoots of modal logic, which uses the symbols ◻ and ◇ to represent ‘necessary’ and ‘possible’. Imagining the existence of possible worlds can be useful in helping to prove logical statements, such as statements about whether things exist.

Priest uses the tableau notation throughout, which I quite dislike, but it's not particularly difficult provided that you can bring yourself to care about systems of arbitrary logical rules that conflict with common sense. Beginners might benefit from reading up on modal logic before starting this book.

You might think that spinning fantastical logical systems would be a useless academic exercise, and that's largely true. But they might come in handy someday if we encounter aliens from another dimension where, for instance, ¬ ¬A is not equal to A, or if we find some weird species that thinks that ‘invisible purple unicorn’ ≠ ‘invisible purple unicorn’ if invisible purple unicorns do not exist. Things like this are how wars get started.

*mar 27 2020. edited apr 08 2020*

Rod Girle

McGill-Queen's, 2009/2017, 248 pages

Reviewed by T. Nelson

A good introduction to modal logic is *Modal Logics and Philosophy*
by Rod Girle. Part 1 describes the formal systems, much like Priest above.
Part 2 has interesting discussions of alethic logic (logic relating to truth),
temporal logic (logic dealing with past and future), and epistemic and deontic
logic (logic of knowledge and logic of what is obligated and permissible).

There's also a discussion of logic's relationship to ordinary language. For instance, this sentence is logically valid:

If William of Normandy won the Battle of Hastings, then if the world is flat then William of Normandy won the Battle of Hastings. (P⊃(Q⊃P))

(William did win that battle). Or how about this famous one, from Priest:

If it does not rain tomorrow we will go to the cricket. So, if it doesn't rain tomorrow and I am killed in a car accident tonight then we will go to the cricket.

Both of these are logically valid, and they illustrate some of the challenges logicians face when they take their work home with them.

*apr 08 2020*

Patrick J Hurley, Lori Watson

Cengage, 2018, 728 pages

Reviewed by T. Nelson

This is an undergraduate-level textbook on logic that includes fallacies, formal logic, predicate logic, and propositional logic. Tends to talk down to the reader. Starts out at a low level (truth tables don't come up until page 341), but it's reasonably well written, and it gradually works up to an excellent exposition of predicate logic. Readers will need this knowledge to understand much of modern-day analytic philosophy, and this book makes it easy to absorb.

Later chapters on statistical reasoning and scientific reasoning don't say much of value. The statistics chapter, for example, repeats a myth commonly held by pharma industry haters: suppose there's a clinical trial where 100 subjects get a drug and 100 get a placebo. Two in the placebo group have heart attacks and one in the treatment group gets a heart attack. Does this cut the rate by 1% or 50%?

The authors say the answer is 1% and big corporations are lying when they say 50%, but 50 is the correct answer—or it would be, if the difference was statistically significant, which it's not (a simple Chi-square test tells us this: it gives p=0.56. With such a low N, they'd need 7 heart attacks in the control group, not 2, to reach significance). Statistical reasoning is all about saying things precisely. Unless the company's statistician is incompetent, they'd state the results correctly.*

What it really shows are the risks of letting factors besides logic influence your reasoning. There might be others; in all honesty, I skipped most of the narrative stories (which are all a little contrived) and focused on the exposition. What else can you do with a “concise” book that goes on for 728 pages?

*dec 28, 2018*

* To make it 1% they'd have to say the rate of *non*-heart
attacks was increased by one percent. But this wouldn't make sense, because
nobody cares about the rate of non-heart attacks.

Of course, there are very few philosophers running clinical trials. And maybe that's something we can all be grateful for.

Theodore Sider

Oxford, 2010, 289 pages

Reviewed by T. Nelson

I found Sider's *Logic for Philosophy* to be, if not exciting, certainly one of the
most interesting books I've read in a long time. Part of that is his writing style.
It is, as you might expect, very logical. After struggling through books that were
full of uninteresting digressions or self-assured prolixity, I found Sider's utter
devotion to explaining the logic, the whole logic, and nothing but the logic to be
refreshing.

Many problems crop up in our daily lives that we describe easily in English but which create conundrums when expressed in predicate logic or modal logic. For example, how do you depict “the dog” as opposed to “some random dog” using logic? Or if somebody said, “The round square does not exist,” does this mean that there is a round square somewhere that has the property of not existing? This is the sort of thing that philosophers deal with every day. It's got to take a toll.

And what about parallels to A→B→C where time is a factor? For instance, you could say that A eats B and B eats C implies that A eats C, but if you said that A kills B and B kills C implies that A kills C, it would be impossible. Sider discusses different schemes, of increasing complexity, that philosophers have proposed to deal with these sentences. It does get technical in places; some readers may wish to read an intro logic text first.

*dec 09, 2018*