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In constructive mathematics, the limited principle of omniscience (LPO) and the lesser limited principle of omniscience (LLPO) are axioms that are nonconstructive but are weaker than the full law of the excluded middle. They are used to gauge the amount of nonconstructivity required for an argument, as in constructive reverse mathematics.
It provides a challenge to the knowability thesis, which states that every truth is, in principle, knowable. The paradox states that this assumption implies the omniscience principle, which asserts that every truth is known. Essentially, Fitch's paradox asserts that the existence of an unknown truth is unknowable.
In international law, the principle is known as the Lotus principle, after a collision of the S.S. Lotus in international waters. The Lotus case of 1926–1927 established the freedom of sovereign states to act as they wished, unless they chose to bind themselves by a voluntary agreement or there was an explicit restriction in international law ...
The usual statement of the Sylvester–Gallai theorem is not valid in constructive analysis, as it implies the lesser limited principle of omniscience, a weakened form of the law of excluded middle that is rejected as an axiom of constructive mathematics. Nevertheless, it is possible to formulate a version of the Sylvester–Gallai theorem that ...
Other means of reconciling God's omniscience with human free will have been proposed. Some have attempted to redefine or reconceptualize free will: God can know in advance what I will do, because free will is to be understood only as freedom from coercion, and anything further is an illusion. This is the move made by compatibilistic philosophies.
What exactly al-Farabi posited on the question of future contingents is contentious. Nicholas Rescher argues that al-Farabi's position is that the truth value of future contingents is already distributed in an "indefinite way", whereas Fritz Zimmerman argues that al-Farabi endorsed Aristotle's solution that the truth value of future contingents has not been distributed yet. [3]
The equidistance principle is a methodology that has been endorsed by the United Nations Convention on the Law of the Sea but predates that treaty and has been used by the Supreme Court of the United States, states, and nations to establish boundaries equitably. [1]
Epicurus was not an atheist, although he rejected the idea of a god concerned with human affairs; followers of Epicureanism denied the idea that there was no god. While the conception of a supreme, happy and blessed god was the most popular during his time, Epicurus rejected such a notion, as he considered it too heavy a burden for a god to have to worry about all the problems in the world.