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Some view opinions held by all people to be valid criteria of truth. According to consensus gentium, the universal consent of all mankind (all humans holding a distinct belief), proves it is true. There is some value in the criterion if it means innate truth, such as the laws of logic and mathematics. If it merely means agreement, as in a ...
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:
Base articles on reliable, independent, published sources with a reputation for fact-checking and accuracy. Source material must be published, on Wikipedia meaning made available to the public in some form. [f] Unpublished material is not considered reliable. Use sources that directly support the material presented in an article and are ...
The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something about everyday life, or when data used in an argument is numerical. It is sometimes also used to mean a "statistical proof" (below), especially when used to argue from data.
Proofs need not be verbal. Before Copernicus, people took the apparent motion of the Sun across the sky as proof that the Sun went round the Earth. [19] Suitably incriminating evidence left at the scene of a crime may serve as proof of the identity of the perpetrator. Conversely, a verbal entity need not assert a proposition to constitute a ...
A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants.
The first condition is logical as people compare new information with what they already know to be true and consider the credibility of both sources. However, researchers discovered that familiarity can overpower rationality—so much so that repetitively hearing that a certain fact is wrong can paradoxically cause it to feel right.
So if any true sentence could possibly be believed by a rational person, then that sentence is believed by one or more rational persons. Some anti-realists advocate the use of intuitionistic logic; however, except for the last line, which moves from there are no unknown truths to all truths are known, the proof is, in fact, intuitionistically ...