How to Read a Book: the classic guide to intelligent reading

by Mortimer J. Adler

The author may himself express the same proposition in different words in the course of his writing. The reader who has not seen through the words to the proposition they convey is likely to treat the equivalent sentences as if they were statements of different propositions. Imagine a person who did not know that “2 + 2 = 4” and “4 – 2 = 2” were different notations for the same arithmetic relationship—the relationship of four as the double of two, or two as the half of four. You would have to conclude that that person simply did not understand the equation. The same conclusion is forced on you concerning yourself or anybody else who cannot tell when equivalent statements of the same proposition are being made, or who cannot himself offer an equivalent statement when he claims to understand the proposition a sentence contains.