|
Closed Concept
A closed concept is a concept where all the necessary and sufficient conditions required to include something within the concept can be listed. For example, the concept of a triangle is closed because it is a three-sided polygon, and only a three-sided polygon, is a triangle. All the conditions required to call something a triangle can be, and are, are listed. Its opposite is an "open concept". See also * Continuum fallacy The sorites paradox (; sometimes known as the paradox of the heap) is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a sing ... References External links Open and Closed Concepts and the Continuum Fallacy- More on open and closed concepts - A guide to the usage and application of necessary and sufficient conditions Concepts in epistemology {{Philosophy-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessary And Sufficient Conditions
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of is guaranteed by the truth of (equivalently, it is impossible to have without ). Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false. In ordinary English (also natural language) "necessary" and "sufficient" indicate relations betw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non-Collinearity, collinear, determine a unique triangle and simultaneously, a unique Plane (mathematics), plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. Types of triangle The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Fallacy
The sorites paradox (; sometimes known as the paradox of the heap) is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a single grain does not cause a heap to become a non-heap, the paradox is to consider what happens when the process is repeated enough times that only one grain remains: is it still a heap? If not, when did it change from a heap to a non-heap? The original formulation and variations Paradox of the heap The word ''sorites'' ('' grc-gre, σωρείτης'') derives from the Greek word for 'heap' ('' grc-gre, σωρός''). The paradox is so named because of its original characterization, attributed to Eubulides of Miletus. The paradox is as follows: consider a heap of sand from which grains are removed individually. One might construct the argument, using premises, as follows: :'' grains of sand is a heap of sand'' (Premise 1) :''A heap of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
