Book review: Logic made easy. How to know when language deceives you?

Logical thinking is high on the list of qualities expected from any Information Developer. But what exactly is “being logical”? If my writing is seemingly clear and makes sense to anyone who reviewed it, am I thinking logically? My layman’s definition of “logical” used to be “making sense”, but recently the book Logic made easy has come my way and added a lot to my understanding.

The book’s full title is “Logic made easy. How to know when language deceives you?”, and it is the “language” part of the title that immediately drew my attention.

The author, Deborah J. Bennet, is a math professor, logician, and excellent writer who, in a friendly and conversational manner, explains how logic and language sometimes contradict each other.

“We get away with being imprecise in normal discourse and make assumptions about how we will be understood, but we should be on our guard. The conventions and rules of everyday language, which depend enormously on context, are occasionally at odds with the language of logic.”

Observing her students, Bennet noticed that common logical mistakes tend to follow similar patterns. This tendency is caused by the fact that “the language of logic employs simple everyday words—words that we use all the time and presumably understand.” Namely, logical errors are often caused by the use of the logical operators (quantifiers), such as “all“, “some“, “none“, and “not all“. These tricky words and various limit-setting constructions are at the focus of the book, making it a great read for Information Developers, because we are especially interested in avoiding ambiguity in our writing. Below, I quote some of the Bennet’s examples of the language trickiness.

Tricky constructions: choose wisely!

Example 1: OR—do we have a choice?

As Bennet notes, in logic, “or” meanseither … or”, but in our everyday speech it “can have two different meanings, and we generally rely on context to decipher what the speaker intends”. This has a great potential for confusion. Compare:

  • Coffee or tea? (Not both)
  • Cream or sugar? (Both are OK)
  • Are you coming or going? (You can’t do both)
  • Can you play the guitar or the banjo? (You could play both)
  • I will get an A in math or history. (I would like to do both)

Think twice before writing “The X menu helps you install or delete Y” if you can both install and delete an entity.

Example 2: AND…OR in one statement

The author states that constructions with both “and” and “or” “are the most problematic”. See for yourself:

“How would you interpret “Sylvester is mean and Spike is lazy or Tweety-bird is smart”? … It could mean that Sylvester is mean and either Spike is lazy or Tweety-bird is smart. On the other hand, it could mean that either both Sylvester is mean and Spike is lazy or Tweety-bird is smart.

Let’s avoid using “and… or” in one statement. For example, in sentences like “With the new feature, you can create or edit and save the datasets”, pay attention to what actions exclude other actions. Here, you should either use “and” (“create, edit, and save”) or restructure the sentence (“you can either create and save or edit and save the datasets”).

Example 3: ALL/ANY/A meaning a 100% of something

In logic, the words “all” and “every” are called “universal quantifiers” because they are used to “indicate the totality (100 percent) of something”. Sometimes, “any” and “a” are also used as universal quantifiers. Compare:

  • All persons are treated equally under the law
  • Any person who can show just cause why this man and woman should not be joined in holy wedlock…
  • A library is a place to borrow books

The author concludes that the universality of the word “all” is clearer than the universality of “any” and “a”, so “all” is preferable to avoid confusion.

Example 4: incomplete statements that seem obvious

Sometimes, in our everyday speech, we use incomplete constructions that are logically incorrect but still convey the needed meaning because people understand what the speaker has in mind anyway.

For example, a teacher says, “All those who sit quietly during the test may go outside and play afterward.” As Bennet points out, the teacher’s statement means that “those who will get to go out and play will definitely include the quiet sitters, but might well include those who make noise… her statement says nothing at all about the noisemakers”. However, the students still understand what the teacher means because the human mind can derive the meaning of a statement from the context.

We tend to use logically incomplete statements because everyone understands it anyway, but can we always rely on this assumption in writing?

Consider this sentence, for example: “The files smaller than 64 MB are stored in RAM and can be previewed in the Preview pane”. However, particular users might be specifically concerned with the RAM being overloaded with large files. Are they loaded but not previewed, or are they not loaded at all?

To avoid misinterpretations, you could do the following:

  • Set clear restriction
    Use “Only” to emphasize the exclusiveness of the described group: “Only the files smaller than 64 MB are stored in RAM and can be previewed in the Preview pane” (Only X belongs to the A group).
  • Explain other options
    Explicitly state what happens to all other files beyond the exclusive group: “The files larger than 64 MB are not stored in RAM and cannot be previewed in the Preview pane”. (Y does not belong to the A group).
    If possible, describe the unique properties of the other group: “To preview files larger than 64 MB, you must open them in the Editor”. (Y belongs to the B group).

Conclusions

Of course, there is much more to this book than the few examples demonstrated above. All in all, the 256-page book consists of 13 chapters each dedicated to a particular notion such as logical quantifiers (“all”, “not”, and “some”), conditions (“if-then” constructions), syllogisms, fuzzy logic statements, fallacies, and paradoxes. All that is coupled with vivid examples, multiple historical references, and brain-teasing puzzles. I guess that some readers may try to skip particular chapters, but I strongly advise reading the “Introduction” section carefully, because many important recurring concepts are introduced there.

I would say that “Logic made easy” is a gentle introduction to logic for non-logicians. It is a great read for all those (see what I did here? Universal quantifier!) who deal with words professionally and are interested in being as clear and unambiguous as possible.

Be sure to revise your writing and make it more logical!

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