Also known as the confirmation paradox, it was discovered by Carl Gustav Hempel (1905-1997).
The statement ‘All prime ministers live at 10 Downing Street’ tends to be confirmed by finding a kennel containing a dog, because this is an example of a dwelling that is not 10 Downing Street which is the home of a non-prime-minister; which is a logically equivalent statement.
However, the same process could be used to prove that all the roses in a large garden have green leaves by observing that all the plants with other-colored leaves are not roses, a much easier process.
The resolution of the paradox is to restrict the universe in which the search is made. However, the paradox is not a total surprise because non-mathematical induction is not a logical proof.
For example, the assertion that water is a compound of hydrogen and oxygen is based on a study of a tiny proportion of the extant water, and it is conceivable that most of the rest is a compound of carbon and manganese.
Utilitarianism is a family of normative ethical theories that prescribe actions that maximize happiness and well-being for all affected individuals. Although different varieties of utilitarianism admit different characterizations, the basic idea behind all of them is to in some sense maximize utility, which is often defined in terms of well-being or related concepts. For instance, Jeremy Bentham, the founder of utilitarianism, described utility as “that property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness…[or] to prevent the happening of mischief, pain, evil, or unhappiness to the party whose interest is considered.”
Utilitarianism is a version of consequentialism, which states that the consequences of any action are the only standard of right and wrong. Unlike other forms of consequentialism, such as egoism and altruism, utilitarianism considers the interests of all humans equally. Proponents of utilitarianism have disagreed on a number of points, such as whether actions should be chosen based on their likely results (act utilitarianism), or whether agents should conform to rules that maximize utility (rule utilitarianism). There is also disagreement as to whether total (total utilitarianism), average (average utilitarianism) or minimum utility should be maximized.
Though the seeds of the theory can be found in the hedonists Aristippus and Epicurus, who viewed happiness as the only good, and in the work of the medieval Indian philosopher Śāntideva, the tradition of modern utilitarianism began with Jeremy Bentham (1748-1832), and continued with such philosophers as John Stuart Mill, Henry Sidgwick, R. M. Hare, and Peter Singer. The concept has been applied towards social welfare economics, the crisis of global poverty, the ethics of raising animals for food, and the importance of avoiding existential risks to humanity.