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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.
Natura non facit saltus [1] [2] (Latin for "nature does not make jumps") has been an important principle of natural philosophy.It appears as an axiom in the works of Gottfried Leibniz (New Essays, IV, 16: [2] "la nature ne fait jamais des sauts", "nature never makes jumps"), one of the inventors of the infinitesimal calculus (see Law of Continuity).
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]
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.
Omniscience is the capacity to know everything. In Hinduism, Sikhism and the Abrahamic religions, this is an attribute of God. In Jainism, omniscience is an attribute that any individual can eventually attain. In Buddhism, there are differing beliefs about omniscience among different schools.
Omnipotence is the quality of having unlimited power. Monotheistic religions generally attribute omnipotence only to the deity of their faith. In the monotheistic religious philosophy of Abrahamic religions, omnipotence is often listed as one of God's characteristics, along with omniscience, omnipresence, and omnibenevolence.
The claim of existence of omniscience by Jains, who deny the existence of a creator god, is a unique phenomenon. [8] The Sutrakritanga text of the Svetambara school, elaborates the concept as all-knowing and provides details of his other qualities. [9] Another text, the Kalpa Sūtra, gives details of Mahavira's omniscience