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The limited principle of omniscience states (Bridges & Richman 1987, p. 3): LPO: For any sequence , , ... such that each is either or , the following holds: either = for all , or there is a with =.
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.
Likewise, God cannot make a being greater than himself, because he is, by definition, the greatest possible being. God is limited in his actions to his nature. The Bible, in passages such as Hebrews 6:18, says it is "impossible for God to lie". [9] [10] A good example of a modern defender of this line of reasoning is George Mavrodes. [11]
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 ...
Markov's principle (also known as the Leningrad principle [1]), named after Andrey Markov Jr, is a conditional existence statement for which there are many equivalent formulations, as discussed below. The principle is logically valid classically, but not in intuitionistic constructive mathematics. However, many particular instances of it are ...
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 a package of bills announced Monday, the Dems want to adjust the legal standard to make it easier to sue a campus that has allowed discriminatory harassment to go unchecked as well as ensure ...
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 ...