Cf: Relations & Their Relatives • Discussion 19
https://inquiryintoinquiry.com/2021/08/18/relations-their-relatives-discussion-19/
::: Henry Story
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<QUOTE HS:>
Could one not say that Frege also had a three part relation? I guess:
for singular terms their Sense and Reference. […] His argument could be
explained very simply. Imagine you start with a theory of language where
words only have referents. Then since in point of fact Hesperus = Phosphorus,
The Morning Star = The Evening Star, the simple theory of meaning would not
allow one to explain how the discovery that they both were the planet Venus,
came to be such a big event. So sense cannot be reduced to reference.
Equalities can have informational content.
</QUOTE>
Yes, Peirce's take on semiotics is often compared with Frege's parsing
of Sinn und Bedeutung. There's a long tradition concerned with the
extension and intension of concepts and terms, also denotation and
connotation, though the latter tends to be somewhat fuzzier from
one commentator to the next. The following paper by Peirce gives
one of his characteristically thoroughgoing historical and technical
surveys of the question.
• C.S. Peirce (1867) • Upon Logical Comprehension and Extension
(
https://peirce.sitehost.iu.edu/writings/v2/w2/w2_06/v2_06.htm )
The duality, inverse proportion, or reciprocal relation between
extension and intension is the generic form of the more specialized
galois correspondences we find in mathematics. Peirce preferred the
more exact term “comprehension” for a compound of many intensions.
In his Lectures on the Logic of Science (Harvard 1865, Lowell Institute
1866) he proposed his newfangled concept of “information” to integrate
the dual aspects of comprehension and extension, saying the measures
of comprehension and extension are inversely proportional only when the
measure of information is constant. The fundamental principle governing
his “laws of information” could thus be expressed in the following formula.
• Information = Comprehension × Extension
The development of Peirce's information formula is
discussed in my ongoing study notes, consisting of
selections from Peirce's 1865–1866 Lectures on the
Logic of Science and my commentary on them.
• Information = Comprehension × Extension
(
https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension )
Regards,
Jon