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postulate:

see axiomaxiom,
in mathematics and logic, general statement accepted without proof as the basis for logically deducing other statements (theorems). Examples of axioms used widely in mathematics are those related to equality (e.g.
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Postulate

 

(from the Latin postulatum, “demand”), a proposition, condition, assumption, or rule that is accepted without proof because of certain reasons. Generally, however, a postulate is accepted with some substantiation, and this substantiation usually serves as an argument in favor of accepting the postulate. The nature of the acceptance may vary. A proposition is accepted as true, as in meaningful axiomatic theories, or as provable, as in formal axiomatic systems. Some instructions are adopted “for execution” as rules governing the formation of the formulas of some calculus or as rules of inference of the calculus that make it possible to derive theorems from the axioms. Some principles abstracted from the data of repeated experience are made the foundation for physical and other natural scientific theories; examples include principles of the type “laws of conservation.” Some positions, prescripts, and norms (legal, for example) are accorded, as a result of other positions, the status of laws. Some religious, philosophical and ideological dogmas are made the foundation for certain systems of belief. For all the diversity of these examples, there is something common to them all: without sparing arguments designed to convince us of the rationality, or legitimacy, of the postulates that we propose, we ultimately simply demand—hence the origin of the word “postulate”— acceptance. In such cases we say that the propositions advanced are postulated.

Such a broad concept, so rich in shades of meaning, naturally has many concrete, more specialized, and therefore extremely varied realizations. The following is a list of some of the most common realizations.

(1) Euclid, who gave the first known systematic axiomatic description of geometry, distinguished between postulates (αιτηματα), which assert the feasibility of certain geometrical constructions, and axioms proper, which affirm (postulate) that the results of these constructions have certain properties. Moreover, he defined axioms as propositions of a purely logical (and not geometrical) character that he accepted without proof, such as “the part is less than the whole.” The dual and not clearly drawn line of delimitation between these similar concepts persisted beyond Euclid.

(2) The terms “axiom” and “postulate” were and are often used synonymously. In particular, Euclid’s well-known fifth postulate of parallel lines is called the parallelism axiom in Hilbert’s axiomatics.

(3) At the same time, the term “axiom” is used by many authors to denote “purely logical” propositions accepted in a given theory without proof. (See, for example, A. Church, Vvedenie ν matematicheskuiu logiku, vol. 1, subsecs. 07 and 55, Moscow, 1960 [translated from English].) By contrast, the term “postulate” is used in reference to specific concepts of a given (usually mathematical) theory.

(4) According to another tradition in mathematical logic, postulates of a formal system (calculus) include axioms written in the language proper (“subjective” language) of the system and the rules of inference formulated in the metalanguage of the given theory (and therefore belonging to its metatheory). (See, for example, S. C. Kleene, Vvedenie ν metamatematiku, subsecs. 19 and 77, Moscow, 1957 [translated from English].)

(5) “Postulates” is the name given to assertions of deductive and (especially) semideductive sciences that cannot be proved, if only because the arguments and facts supporting them are exclusively experimental and inductive in character. In many such cases we speak of the assertion of the equivalency of some intuitively clear but not clearly formulated assertion or concept that is an explication (refinement) of the former and therefore formulable at a fundamentally higher level of abstraction. Examples of the first type are the fundamental principles of thermodynamics and the principle of the constancy of the speed of light and its limiting character; an example of the second type is the Church thesis in the theory of algorithms.

postulate

[′päs·chə·lət]
(mathematics)

postulate

Logic Maths an unproved and indemonstrable statement that should be taken for granted: used as an initial premise or underlying hypothesis in a process of reasoning
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By design, the Twenty Postulates that emerged from his work reflect the conditions necessary for teacher education such that preservice teachers are (or will be) prepared to meet certain reasonable expectations, as also discussed previously (e.g., enculturating students into a political democracy, providing access to knowledge, forming connections with students, practicing good stewardship; Goodlad, 1990a, 1990b; Goodlad et al., 1990; see also Sirotnik, 2001).
Bradwardine's practice not only justices the attribution of these principles; it helps to clarify (and possibly even correct) Bradwardine's expression of his second postulate: "every sentence signifies or means everything which follows from it" (Bradwardine, 2010, [paragraph]6.3).
Most physicists expect that as triple-slit experiments are conducted with other particles, such as electrons and bucky-balls, the case for Born's postulate will get stronger, Dowker says.
Why did mathematicians feel the need to deduce the parallel postulate from the other axioms of geometry?
Sequence-based identification of microbial pathogens: a reconsideration of Koch's postulates. Clin Microbiol Rev.
Third, there is absolutely nothing about this "postulate" that need necessarily be granted by a secular humanist historian.
The author postulates that the clot in the left internal jugular vein in this patient altered the blood flow dynamics, which led to increased venous pressure and the resultant venous insufficiency in the VPVC.
The answer is that any language is made up of variants, while its fundame ntal logical postulates are really very few in number.
He postulates that if he did a really big favour for someone, and asked the person who received the favour not to "pay it back" but "pay it forward" by doing a big favour for three other people, eventually the world would be changed.
Cruz y Ortiz's architecture of surprise postulates a distinction between exterior and interior, transition, a sense of discovery.
These operations are characterized by certain rationality postulates that determine their behavior on the knowledge level.
Indeed, Koch postulates that 20% of a company's clients account for 80% of its income and then goes on to explain how companies should focus their greatest efforts on the 20% that really matters and exploit the enormous potential of that magic number.