Search results
Results from the WOW.Com Content Network
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...
The argument from reason is a transcendental argument against metaphysical naturalism and for the existence of God (or at least a supernatural being that is the source of human reason). The best-known defender of the argument is C. S. Lewis .
Forms of logical reasoning can be distinguished based on how the premises support the conclusion. Deductive arguments offer the strongest possible support. Non-deductive arguments are weaker but are nonetheless correct forms of reasoning. [28] [29] The term "proof" is often used for deductive arguments or very strong non-deductive arguments. [30]
A standard view is that whether an argument is valid is a matter of the argument's logical form. Many techniques are employed by logicians to represent an argument's logical form. A simple example, applied to two of the above illustrations, is the following: Let the letters 'P', 'Q', and 'S' stand, respectively, for the set of men, the set of ...
Given a structure or interpretation, a sentence will have a fixed truth value. A theory is satisfiable when it is possible to present an interpretation in which all of its sentences are true. The study of algorithms to automatically discover interpretations of theories that render all sentences as being true is known as the satisfiability ...
Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. [7] It is likely that the idea of demonstrating a conclusion first arose in connection with geometry, which originated in practical problems of land measurement. [8]
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
Ethics in mathematics is an emerging field of applied ethics, the inquiry into ethical aspects of the practice and applications of mathematics.It deals with the professional responsibilities of mathematicians whose work influences decisions with major consequences, such as in law, finance, the military, and environmental science. [1]