Useful (adjective) “Able to be used for a practical purpose or in several ways”
http://www.oxforddictionaries.com/
What is true is not always useful; what is useful is not always true.
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The statement "people are either over six feet tall or not over six feet tall" is an example of a true statement. It is, in fact, an example of tautology. Is it useful? Probably not. Statements perpetuating negative stereotypes of religious or cultural groups are examples of statements that may be useful but are not true; examples of propaganda to be precise. Such statements may be useful for people who want to achieve particular political and economic ends by playing on people's anxieties about their own material and existential security.
Of course, it's not that simple. Even though I cannot think of a use for the proposition about people's heights, I can't altogether rule out the possibility that it could be useful in some context. Tautologies, as a class of propositions, are extremely important to logicians, mathematicians and computer scientists. Indeed, they have been critical to the formation of modern computing.
As for the case of propaganda, we can argue that ascribing this proposition the quality of usefulness is also questionable: it is certainly not useful for those people who are harmed by its consequences, in terms of prejudice and marginalisation. It's probably also not useful for the people who are being encouraged to harbour hatred.
What if, instead of propaganda, we think of more positive examples of the usefulness of propositions that are not true. What about the diverse sources of inspiration many influential thinkers are informed by? Sources like art, literature, music, imagination or nature. Here, elements of human experience where it is not even sensible to discuss 'truth' can be useful in generating associations and stimulating thinking that leads to the production of true propositions. In cases where a truth value is questionable, as where people indulge in a degree of mysticism or magical thinking to inform their views, it is helpful to remember that the production of true propositions is not contingent on the truth of the arguments that gives rise to them: true conclusions can arise from false premises.
Perspective, context, and happenstance shape the class of things that are true and the class of things that are useful. And, the class of things that are true and the class of things that are useful grow over time as new truths come to light (or are debunked), and new ideas evolve. True and useful propositions inform one another - they are entwined in their causes and consequences. But, while some ideas are both true and useful, truth and usefulness are not the same thing.
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