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In philosophy and the arts, a fundamental distinction is between things that are abstract and things that are concrete. While there is no general consensus as to how to precisely define the two, examples include that things like numbers , sets , and ideas are abstract objects, while plants , dogs , and planets are concrete objects. [ 1 ]
Those abstract things are then said to be multiply instantiated, in the sense of picture 1, picture 2, etc., shown below. It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and ...
An example of this abstraction process is the generational development of programming language from the machine language to the assembly language and the high-level language. Each stage can be used as a stepping stone for the next stage. The language abstraction continues for example in scripting languages and domain-specific programming languages.
In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. [1] For example, suppose there are two chairs in a room, each of which is green.
An abstract data type that represents a sequence of values, where the same value may occur more than once. Data order maintenance, implementation of stacks, queues, etc. Stack: A collection that supports a last-in, first-out access pattern. Function calls/recursive calls, undo mechanisms in applications. Queue
Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. For example, the first steps in the abstraction of geometry were historically made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the ...
A convenient example of what constitutes a non-physical entity is a ghost. Gilbert Ryle once labelled Cartesian dualism as positing the " ghost in the machine ". [ 9 ] [ 10 ] However, it is hard to define in philosophical terms what it is, precisely, about a ghost that makes it a specifically non-physical, rather than a physical entity.
Mathematical constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then ...