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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.
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.
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. [1] [2] It is one of the three laws of thought, along with the law of noncontradiction, and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens ...
A self-refuting idea or self-defeating idea is an idea or statement whose falsehood is a logical consequence of the act or situation of holding them to be true. Many ideas are called self-refuting by their detractors, and such accusations are therefore almost always controversial, with defenders stating that the idea is being misunderstood or that the argument is invalid.
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Lack-of-fit sum of squares-- Lacunarity-- Lacunary function-- Lacunary value-- Ladder graph-- Ladner's theorem-- Lady tasting tea-- Lady Windermere's Fan (mathematics)-- Ladyzhenskaya–Babuška–Brezzi condition-- Ladyzhenskaya's inequality-- Lafforgue's theorem-- Lag operator-- Lagged Fibonacci generator-- Lagrange bracket-- Lagrange inversion theorem-- Lagrange multiplier-- Lagrange ...
Omniscience, under this view, is the knowledge of necessary facts as necessary, and contingent facts as contingent. Since the future does not yet exist as anything more than a realm of abstract possibilities, it is no impugning of divine omniscience to claim that God does not know the future as a fixed and unalterable state of affairs: that he ...