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On an interview aired in 1959 Bertrand Russel, talking about religious beliefs said: "...it seems to me a fundamental dishonesty to hold a belief because is useful and not because is true."

The open statement in Jeremy Bentham's book An Introduction to the Principles of Morals and Legislation published in 1789 is the following:

Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do… By the principle of utility is meant that principle which approves or disapproves of every action whatsoever according to the tendency it appears to have to augment or diminish the happiness of the party whose interest is in question: or, what is the same thing in other words to promote or to oppose that happiness. I say of every action whatsoever, and therefore not only of every action of a private individual, but of every measure of government.

My question: Don't the principles of Utilitarianism oppose the view of Bertrand Russel? In fact, as far as I understand the principles of Utilitarianism, that an action is considered "good" or "moral" by its utility, meaning that every action is good and moral if it provides happiness.

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The quote from Russell is in conflict, not with Utilitarianism, but with some versions of Pragmatism, in particular with William James' Pragmatist Theory of Truth.

Note that Bentham's quote refers to the good and the right in actions; while Russell's quote refers to the holding and to the truth of beliefs. Those are two different areas. A rational person is usually supposed to hold a belief in proportion to the evidence that supports that belief, regardless of any practical consequences that the belief may have. And so, utilitarians are not usually expected to hold the view, that Russell's quote opposes, that a belief should be held according to its consequences.

Some others, however, have indeed held that view about beliefs. One such thinker, with whom Russell personally debated, was William James. In the essay The Will to Believe (1897) James developed an argument, according to which it is allowed and justified, in some cases, to hold a belief even when one doesn't have sufficient epistemic evidence in its favor. The main class of beliefs that James had in mind were religious beliefs. The basic idea of his argument was, that if we have to wait for evidence, we are bound to miss the benefits that some (e.g. religious) beliefs could bring about. In later publications, James developed the Will to Believe argument into a general theory of truth. He came to hold that a "true" belief was just a belief which was beneficial to hold, in the long run. This received the title "the pragmatist theory of truth".

Russell opposed James' theories, on various grounds. One of his arguments was that, even if some (e.g. religious) beliefs were beneficial, what gave them their psychological power was the that the believer believed that they were really (i.e. not in the pragmatist sense) true.

Suppose I say there was such a person as Columbus, everyone will agree that what I say is true. But why is it true? Because of a certain man of flesh and blood who lived 450 years ago—in short, because of the causes of my belief, not because of its effects. With James's definition, it might happen that ‘A exists’ is true although in fact A does not exist. I have always found that the hypothesis of Santa Claus ‘works satisfactorily in the widest sense of the word’; therefore ‘Santa Claus exists’ is true, although Santa Claus does not exist. James says (I repeat): ‘If the hypothesis of God works satisfactorily in the widest sense of the word, it is true.’ This simply omits as unimportant the question whether God really is in His heaven; if He is a useful hypothesis, that is enough. God the Architect of the Cosmos is forgotten; all that is remembered is belief in God, and its effects upon the creatures inhabiting our petty planet. No wonder the Pope condemned the pragmatic defence of religion. (History of Western Philosophy p.728)

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    +1. You are clearly spot on. Russell's remarks apply to pragmatism, not to utilitarianism. Anyone would think Mill's 'On Liberty' was written solely in aid of flushing out useful beliefs. Late reply - I have only just come across your answer. – Geoffrey Thomas Sep 10 '18 at 8:56
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I think it helps to include more of the transcript than you provided. For example, when pressed on the practical benefits of moral rules coming from religion, Russell responds:

Yes, but those rules are generally quite mistaken. A great many of them do more harm than good. And they would probably be able to find a rational morality that they could live by if they dropped this irrational traditional taboo morality that comes down from savage ages.

So, Russell seems to be saying that pursuing the truth will lead one to right living/more happiness/more utility.

Just as a contrast, I was recently reading a book by Holly Ordway, who is an author and professor who also has spent a large amount of time investigating similar questions. The attitude that she took when investigating the same questions was what you suggest: even if the truth left her materially worse off, she wanted the truth anyway. Therefore, the attitude you suggest is possible, and has been held by others.

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