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There are more extreme examples showing that second-order logic with standard semantics is more expressive than first-order logic. There is a finite second-order theory whose only model is the real numbers if the continuum hypothesis holds and that has no model if the continuum hypothesis does not hold. [5]
The idea of second order predication was introduced by the German mathematician and philosopher Frege. It is based on his idea that a predicate such as "is a philosopher" designates a concept, rather than an object. [2] Sometimes a concept can itself be the subject of a proposition, such as in "There are no Bosnian philosophers".
Second-order cybernetics took shape during the late 1960s and mid 1970s. The 1967 keynote address to the inaugural meeting of the American Society for Cybernetics (ASC) by Margaret Mead, who had been a participant at the Macy Conferences, is a defining moment in its development.
Second order approximation, an approximation that includes quadratic terms; Second-order arithmetic, an axiomatization allowing quantification of sets of numbers; Second-order differential equation, a differential equation in which the highest derivative is the second; Second-order logic, an extension of predicate logic
An example of second-order conditioning. In classical conditioning, second-order conditioning or higher-order conditioning is a form of learning in which a stimulus is first made meaningful or consequential for an organism through an initial step of learning, and then that stimulus is used as a basis for learning about some new stimulus.
Second-order cybernetics: Also known as the cybernetics of cybernetics, second-order cybernetics is the recursive application of cybernetics to itself and the practice of cybernetics according to such a critique. Schismogenesis; Self-organisation; Social systems theory; Syntegrity; Variety and Requisite Variety; Viable system model
A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z 2). Such subsystems are essential to reverse mathematics , a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength.
In contrast, historical significance is an example of a subject specific secondary key concept or "second-order knowledge" also known as a meta-concept, [2] or disciplinary concept, [3] which is typically used to help organize knowledge within a subject area, frame suitable areas of inquiry, provide the framework upon which substantive ...