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Extension

In general semantics, extension is a process that, as in this mathematical example, starts with unique individuals, and gives them unique names, e.g., I, II, III, etc., or 1, 2, 3, etc. The next step if needed generalises or passes beyond extension to infinite-valued higher-order abstractions like 'numbers', and so on. The passing from lower-order abstractions (presented extensionally) to higher orders, e.g., from '1, 2, 3, etc.,' to 'numbers,' is said to follow the 'natural order of evaluation,' so that when one talks about order, extension is implied, and when one talks about extension, order is implied. An example of reversed order is when a particular higher-order abstraction such as race, e.g., 'white', 'black' etc., is projected onto the individuals comprising it. The individuals (each uniquely different by extension, no matter what is being discussed) comprise the 'race' (which exists only on higher-orders), not the other way around. This usage derives from extension (semantics).

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