# What does “Honor this in the breach” mean?

The text below is from a book for engineers whose content is unimportant: the purpose of my question is only to understand, "honor this in the breach".

I searched this expression on the Internet, but explanations about Shakespeare's uses do not help much.

The scope of this book is supposed to be “everything up to, but not including, partial differential equations.” We honor this in the breach: First, we do have one introductory chapter on methods for partial differential equations (Chapter 19).

To "honor (something) in the breach" bears some similarity to the phrase "the exception proves the rule", a proverb whose meaning is given by oxforddictionaries.com as:

The fact that some cases do not follow a rule proves that the rule applies in all other cases.

In this example, the author is saying that the presence of a chapter on partial differential equations in the book is meant to emphasize, rather than undermine, the point that the book's actual scope is meant to be "everything up to, but not including, partial differential equations." The inclusion of the final, "breaching" chapter makes it clear that the purpose of all the preceding chapters was to lay the groundwork for learning a more advanced subject.

The phrase is from Shakespeare's Hamlet:

Hamlet: Ay, marry, is't, But to my mind, though I am native here And to the manner born, it is a custom More honor'd in the breach than the observance,

Hamlet Act 1, scene 4, 7–16ℹ

E notes makes the following point

MORE HONORED IN THE BREACH Since, to Hamlet's mind, native customs ought to bring honor on a people, it would be more honorable to forego was-sail and "up-spring reels." These customs are, as he puts it, "more honor'd in the breach than in the observance"—breaking tradition is in this case more honorable than observing it.

His words have since been twisted around. Today we mean something like "more often disregarded than adhered to," perhaps taking "honor'd" to mean "observed" (as one "honors" tradition or "honors" a contract). But Hamlet's point is that the custom is observed too often, denigrating its observers rather than conferring honor on them.

Thus, the way the expression is used today is different from the way that Shakespeare intended. A rule which is rarely observed is often said "to be more honoured in the breach than the observance".

The author, it seems, was provided the scope for his book. Although you say "a book for engineers whose content is unimportant", the content actually is important. The author has been asked to treat a subject at a certain level using only certain tools. Apparently, other works treating the subject at this level have introduced PDEs, and he has decided to follow suite. But he is saying the PDE treatment is introductory, hence falls short of how PDEs would be used in more advanced courses. "honored in the breach" appears to be saying that it is now the norn to introduce the student to PDE methods at this point.