John,
yes, but isn´t it so, that in mathematics and symbolic logic, if the extension is known i.e. covered by proofs, an intensional term can be equivalent with an extensional one, and this is called "classical logic"? That is, if I am right, that e.g. "NOT (A AND NOT B)" is extensional, and means the same as "IF A THEN B", which is intensional? I just am still trying to understand the reason for intuitionistic logic, and with your hint towards intension/extension, I suspect having come a bit closer to this quest for understanding: Is it so, that in intuitionistic logic intensional and extensional terms are not equivalent, and it is applied for those cases in which the extension is vague, unknown, or not proved? And what about "NOT A OR B": Is this term also purely extensional, or a bit intensional? I mean, can we classify operators in a scale between intensional and extensional? Like, the "IF-THEN"- operator would be intensional, the "AND"- operator extensional, and the "OR"- operator somewhere between? Though the "OR"- operator may be completely extensional too, I am not sure.
I also think, that intension and extension has to do with Salthe`s distinction between composition and subsumption (classification). If some operators are extensional and this would mean compository, and others intensional, and this would mean classificatory, perhaps there could not be an operator such as "OR" somewhere between, because composition and subsumption are two distinct ways of putting systems in a hierarchy- though there are cases called holarchy, in which both applies, but then in opposite hierarchic subset-directions towards each other. Maybe the "OR"- operator is such a thing?
Warning: I am a-frayed I was thinking while writing, so what I wrote is not an elaborated hypothesis.
Best,
Helmut
17. Januar 2021 um 06:43 Uhr
"John F. Sowa" <s...@bestweb.net>
wrote:
"John F. Sowa" <s...@bestweb.net>
wrote:
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 threw it into Plato's Academy while shouting "Here is Plato's man."
Alonzo Church, who wrote that excerpt I cited, had been the editor of the Journal of Symbolic Logic for many years.
It's just as important for the latest work in computer science for both theory and applications.
John
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