How to Know When Language Deceives You
Interesting enough for this forum that a woman purports to be an expert on logical thinking. She may be, as she apparently teaches the subject. But as I flipped through the pages I noticed a lack of symbols. Just as I feared, this indicated a lack of rigor. For in an effort to make it "easy," the author succeeds in making the subject matter sound confusing. Logic is simplicity itself - to dumb it down merely obfuscates the principles under consideration. (Anyone who has read a "For Dummies" book on a subject in which one is already well-versed has encountered this "muddling effect.")
Let me give a brief example. In a section entitled "Proof by Contradiction," the author uses Euclid's reasoning that there are an infinite number of prime numbers to illustrate proof by contradiction: "To do this, he assumed as his initial premise that there is not an infinite number of prime numbers. Proceeding logically, Euclid reached a contradiction in a proof too involved to explain here."
Firstly, if it were too involved, she should not have chosen it as an example. An example is supposed to be used to demonstrate something, in this case a method of arriving a logical proof. If she is not going to give Euclid's proof, then we must take her word for it that he was employing the method after which she entitled this section of her book.
The actual logic goes like this: If there is not an infinite number of prime numbers, then there must be one prime number which is the largest among the finite set. Let us call this largest prime J. Now take J and multiply it by all the other prime numbers, all of which must necessarily be less than itself. Call this new number K. Now consider K + 1. Obviously, K + 1 cannot be divided by J (since K can be). Nor can it be evenly divided by any other prime, since every prime number is a factor of K. Therefore, K + 1 would be a prime number, contradicting the original premise that J (obviously less than K + 1) is the largest prime. We (after Euclid) have therefore proved there is no greatest prime number.
The above is hardly "too involved." In other words, this author chose a good example, and then did not give it.
Much of the book is fuzzy in a similar fashion.
So one should "not bother" with this book.