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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 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 ...
Although the most common translation of the noun "Logos" is "Word" other translations have been used. Gordon Clark (1902–1985), a Calvinist theologian and expert on pre-Socratic philosophy, famously translated Logos as "Logic": "In the beginning was the Logic, and the Logic was with God and the Logic was God".
Omniscience (Kevala Jnana) The first two kinds of knowledge are through indirect means and remaining three are through direct means. [ 4 ] [ 2 ] Indirect means includes inference, analogy, word or scripture, presumption and probability.
The topic of omniscience has been much debated in various Indian traditions, but no more so than by the Buddhists. After Dharmakirti's excursions into the subject of what constitutes a valid cognition, Śāntarakṣita and his student Kamalaśīla thoroughly investigated the subject in the Tattvasamgraha and its commentary the Panjika.
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 ...
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 ...