William James lived in a time when philosophy was dominated by metaphysical beliefs that claimed the existence of timeless and absolute truths that could be established by rational arguments, while at the same time science was claiming that all our ideas about the world were provisional and had to pass empirical tests to be considered to some degree true. James, following Charles Peirce's ideas, thought it would be useful to re-interpret the definition of truth in philosophical discourse to be more in line with that of science. That is, a statement about the world is not considered true (or false) until some empirical testing is done to corroborate that the statement corresponds to the world (or not). This is subtly contrasted with the Aristotlean view which says that a statement about the world is true or false regardless of whether tests are subsequently performed to decide which it is.
To demonstrate this distinction, consider a shuffled deck of cards spread face down. One is selected at random but is kept face down. What does it mean to say that the statement "The selected card is the queen of hearts" is true? An Aristotlean would say the statement is true if the card is indeed the queen of hearts. A pragmatist would say that the truth of the statement is the passing of a test (such as turning the card over) to determine if the card is the queen of hearts. To an Aristotlean, there is a distinction between truth and methods for deciding a truth. To a pragmatist, there is no difference.
An Aristotlean would say that "the number formed by 317 repititions of the digit 1 is prime" is a timeless statement of truth (it is either true or false). It depends solely on accepted definitions of "number" and "prime", not the algorithms which determine the primality of a number, or the running of such algorithms.
Both camps agree essentially with the correspondence theory of truth. James would NOT agree, for example, that the card suddenly attains its number and suit at the exact moment it is flipped over. There is instead a lateral shift in the pragmatist description of the correspondence theory, which demands that a statement of truth also include the results of empirical tests. Gardner says "The question here is one of linguistic preference. Is it best to preserve the language of the old correspondence theory, or is something gained by modifying it along the lines proposed by the pragmatists?"
The problems for James started when he became too enamored by this new way of speaking about truth. He would say that truths are made by acts of verification. James' ambiguous writing got himself considerably misunderstood. This is from his Pragmatism: A New Name for Some Old Ways of Thinking:
The truth of an idea is not a stagnant property inherent in it. Truth happens to an idea. It becomes true, is made true by events. Its verity is in fact an event, a process: the process namely of its verifying itself....James is just saying that as science's methods improve, there is more certainty about assertions made about the world. He's not saying, for example, that the Earth's core changes every time scientific tests show something new about its composition. This, however, is the kind of thing fellow philosophers thought he was saying.
How do we know James was being mis-read? Gardner prints a letter written to James by philosopher Charles A. Strong, who registers enormous surprise at what he thinks is an astonishing "change of face" on the part of James, whom he'd considered an idealist. James responded with amiable anger, insisting that "Epistemological realism" had always been the "permanent heart and center" of his thinking.
Gardner sums up his feelings about pragmatism near the end of the chapter:
"...in ordinary discourse pragmatism has now degenerated into a synonym for practical... In this trivial sense everyone is a pragmatist. Even in the more technical sense of insisting that scientific hypotheses can be tested only in experience, every scientist and philosopher is a pragmatist. When I say I am not a pragmatist I mean only that I agree with most philosophers today in seeing no pragmatic reasons for adopting the epistemological language of pragmatism...The notion that a statement can have an absolute, timeless correspondence with the world, whether verified or not, is too useful a notion. Abandon it and at once you have to invent another way to say the same thing."