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seeking demonstration of Rand's algebra

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Selkc

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Selkc is referring to this:

Two links between the conceptual and the mathematical fields are worth noting at this point, apart from the obvious fact that the concept “unit” is the base and start of both. 1. A concept is not formed by observing every concrete subsumed under it, and does not specify the number of such concretes. A concept is like an arithmetical sequence of specifically defined units, going off in both directions, open at both ends and including all units of that particular kind. For instance, the concept “man” includes all men who live at present, who have ever lived or will ever live. An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence. The same principle applies to concepts: the concept “man" does not (and need not) specify what number of men will ultimately have existed —it specifies only the characteristics of man, and means that any number of entities possessing these characteristics is to be identified as “men.” . The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition. The relationship of concepts to their constituent particulars is the same as the relationship of algebraic symbols to numbers. In the equation 2a = a + a, any number may be substituted for the symbol “a” without affecting the truth of the equation. For instance: 2 X 5 = 5 + 5, or: 2 X 5,000,000 = 5,000,000 + 5,000,000. In the same manner, by the same psycho—epistemological method, a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes. Let those who attempt to invalidate concepts by declaring that they cannot find “manness" in men, try to invalidate algebra by declaring that they cannot find “a—ness” in 5 or in 5,000,000.

Question is, what about the above is unclear? Edited by Plasmatic
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  • 1 month later...

Rand is not advocating a new kind of math.  She is demonstrating how massively complex hierarchies of percepts and concepts can be (MUST be) condensed in the form of new concepts - be it calculating incomprehensible numbers or deconstructing erroneous assumptions in a therapy patients mind.  

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