“Priestley was the first (unless it was Beccaria) who taught my lips to pronounce this sacred truth — that the greatest happiness of the greatest number is the foundation of morals and legislation.”

—  Jeremy Bentham

"Extracts from Bentham's Commonplace Book", in Collected Works, x, p. 142; He credits Priestley in his Essay on the First Principles of Government (1768) or Beccaria with inspiring his use of the phrase, often paraphrased as "The greatest good for the greatest number", but the statement "the greatest happiness for the greatest number" actually originates with Francis Hutcheson, in his Inquiry concerning Moral Good and Evil (1725), sect. 3. In an unpublished manuscript on utilitarianism, written for James Mill, he later criticized this formulation: "Greatest happiness of the greatest number. Some years have now elapsed since, upon a closer scrutiny, reason, altogether incontestable, was found for discarding this appendage. On the surface, additional clearness and correctness given to the idea: at bottom, the opposite qualities. Be the community in question what it may, divide it into two equal parts, call one of them the majority, the other minority, layout of the account of the feelings of the minority, include in the account no feelings but those in the majority, the result you will find is that of this operation, that to the aggregate stock of happiness of the community, loss not profit is the result of the operation. Of this proposition the truth will be the more palpable, the greater the ration of the number of the minority to that of the majority: in other words, the less difference between the two unequal parts: and suppose the condivident part equal, the quantity of the error will then be at its maximum." — as quoted in The Classical Utilitarians : Bentham and Mill (2003) by John Troyer, p. 92;

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British philosopher, jurist, and social reformer 1748–1832

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