Helmut,
The distinction between intesion and extension is
important for every version of logic since antiquity. The oldest example
is "rational animal" vs. "featherless biped" -- those
are two terms with different intensions, but the same extension. Diogenes
the Cynic plucked a chicken and
Terry, I completely agree with what you wrote (copy below).
But
I emphasized database relations because they are the most commonly used
examples of relations that are defined by extension.
However, the
meaning of the data is specified by the rules or axioms that state the
intensions. Those
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
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
Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 5
http://inquiryintoinquiry.com/2021/01/15/sign-relations-triadic-relations-relation-theory-discussion-5/
Re: Cybernetics
( https://groups.google.com/g/cybcom/c/Wyz1oRmturc )
::: Cliff Joslyn
(
Dear Jacob,
I am very sorry to hear this. Along with John, I send my condolences.
I spoke with your father in a couple of very long phone calls about 2 years
ago, when I was beginning my research on Peirce. He was extremely helpful,
generous, and kind.
All my best to your family,
Dan
