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Author Topic: Intensional vs. Extensional definition - Introduction to Mathematical Philosophy  (Read 546 times)

March 12, 2018, 03:54:04 AM
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A class or collection may be defined in two ways that at first might seem like something quite distinct. We may enumerate its members, as you say, “The collection I mean is Brown, Jones, and Robinson.” Or  we may mention a defining property, as when we speak of “mankind” or “the inhabitants of London.” The definition which enumerates is called definition by “extension,” and the one which mentions a defining property called a definition by “intension.” Of these two kinds of definition, the one by intension is logically more fundamental. This is shown by two considerations: (1)that the extensional definition can always be reduced to an intensional one; (2) that the intensional one often cannot even theoretically be reduced to the extensional one.

This is from page 12 of my Touchstone paperback edition or page 14 of the Kindle version (where I found it by searching.)
Russell explains both cases further, but I think this quote sufficient.
"It is a commonplace that happiness is not best achieved by those who seek it directly; and it would seem that the same is true of the good."
BR, "Mysticism and Logic" in CPBR Vol. 8, p. 48.
June 03, 2018, 10:45:24 PM
Reply #1
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"We cannot enumerate all fractions or all irrational numbers, or all of any other infinite collection. Thus our knowledge in regard to all such collections can only be derived from definition by intension."

IMP, p 13.
"It is a commonplace that happiness is not best achieved by those who seek it directly; and it would seem that the same is true of the good."
BR, "Mysticism and Logic" in CPBR Vol. 8, p. 48.