Search results
Results From The WOW.Com Content Network
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.
In international law, the principle is known as the Lotus principle, after a collision of the S.S. Lotus in international waters. The Lotus case of 1926–1927 established the freedom of sovereign states to act as they wished, unless they chose to bind themselves by a voluntary agreement or there was an explicit restriction in international law ...
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 ...
The law of most of the states is based on the common law of England; the notable exception is Louisiana, whose civil law is largely based upon French and Spanish law.The passage of time has led to state courts and legislatures expanding, overruling, or modifying the common law; as a result, the laws of any given state invariably differ from the laws of its sister states.
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 ...
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.
This raises the question, similar to the Euthyphro Dilemma, of where this law of logic, which God is bound to obey, comes from. According to these theologians (Norman Geisler and William Lane Craig), this law is not a law above God that he assents to but, rather, logic is an eternal part of God's nature, like his omniscience or omnibenevolence.