Search results
Results from the WOW.Com Content Network
Plausible reasoning can be used to fill in implicit premises in incomplete arguments. Plausible reasoning is commonly based on appearances from perception. Stability is an important characteristic of plausible reasoning. Plausible reasoning can be tested, and by this means, confirmed or refuted.
Mathematics and Plausible Reasoning is a two-volume book by the mathematician George Pólya describing various methods for being a good guesser of new mathematical results. [ 1 ] [ 2 ] In the Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing."
Deductive reasoning plays a central role in formal logic and mathematics. [1] In mathematics, it is used to prove mathematical theorems based on a set of premises, usually called axioms. For example, Peano arithmetic is based on a small set of axioms from which all essential properties of natural numbers can be inferred using deductive reasoning.
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods.
As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting conclusion is false. Statistical methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping .
[a] Occam's razor is used to adjudicate between theories that have already passed "theoretical scrutiny" tests and are equally well-supported by evidence. [ b ] Furthermore, it may be used to prioritize empirical testing between two equally plausible but unequally testable hypotheses; thereby minimizing costs and wastes while increasing chances ...
The American Invitational Mathematics Examination (AIME) is a selective and prestigious 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics examination (formerly known as the AHSME), and starting in 2010, those who rank in the top 2.5% on the AMC 10. Two different versions of the test ...
In economics, Knightian uncertainty or ambiguity may occur. Thus, one must make assumptions about the probabilities, but the expected values of various decisions can be very sensitive to the assumptions. This is particularly problematic when the expectation is dominated by rare extreme events, as in a long-tailed distribution.