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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.
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]
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).
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.
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.
The problem of free will has been identified in ancient Greek philosophical literature. The notion of compatibilist free will has been attributed to both Aristotle (4th century BCE) and Epictetus (1st century CE): "it was the fact that nothing hindered us from doing or choosing something that made us have control over them".
God could not, for example, create square circles, act contrary to his nature, or, more relevantly, create beings with free will that would never choose evil. [8] Taking this latter point further, Plantinga argued that the moral value of human free will is a credible offsetting justification that God could have as a morally justified reason for ...