Jon, John,
just a thought: Might it be, that in classical mathematics and logic there is not distinguished between intension and extension, and in intuitionistic logic there is? For example, "NOT (A AND NOT B)" is an extensionistic proposition, or the extension of the relation, but "IF A THEN B" is an intensionistic proposition, or the intension of the relation? For classical logic, both are the same, but for intuitionistic logic not, for some reason I dont understand. I mean, I understand the difference between extension and intension, but I also understand, why for classical (exact) logic the difference does not matter. In a reasonable universe of discourse that is. So, is intuitionistic logic designed for a not-reasonable universe? But why? What would a not-reasonable universe be like then, and why would anybody want to try to reason in such a universe, casting pearls before the swine? On the other hand I think, it is quite a honest thing to do, to try to refute Adorno´s saying, that there is no right life in the wrong life.
Best,
Helmut
16. Januar 2021 um 18:02 Uhr
"John F. Sowa" <s...@bestweb.net>
wrote:
"John F. Sowa" <s...@bestweb.net>
wrote:
Jon A,
It's important to distinguish the intension and the extension of a function or relation. The *intension* is its definition by a rule or set of axioms. The *extension* is the set of instances in some domain or universe of discourse:
JA> We can now define a “relation” L as a subset of a cartesian product.
That is a purely extensional definition. If we're talking about a database, for example, the extension may be constantly changing, but the intension may be the same for all the variations in extension
For the distinction between extensions and intensions, see the discussion by Alonzo Church: http://jfsowa.com/logic/alonzo.htm .
John
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