Helmut, John, List ... I'll answer Helmut's question first as I can think of something right off to say about it, whereas JFS and I have had this same discussion every 3 or 4 years for going on the last 20 and I'll need a while to see if I can think of anything new to say on it.
<TL;DR> I confess I have never found going on about Firstness Secondness Thirdness all that useful in any practical situation. Firstness means one has some monadic predicate in mind as relevant to a phenomenon, problem, or other subject matter, Secondness means one has a dyadic relation in mind to the same end, and Thirdness means one has a triadic relation in mind as bearing on the situation at hand. After that one can consider the fine points of generic versus degenerate cases, and that is all well and good, but until you venture to say exactly *which* monadic, dyadic, or triadic predicate you have in mind, you haven't really said that much at all. </TL;DR> What I really think is interesting in all this is the fact that Peirce, from 1865 on, maintains in the background of his thought the idea that information is the solid substance born by concepts and symbols, while comprehension and extension are its complementary aspects, its shadows. I have been studying this integration of comprehension and extension in the form of information for quite a while, and there is my set of excerpts and comments on this page: Information = Comprehension × Extension http://intersci.ss.uci.edu/wiki/index.php/Information_%3D_Comprehension_%C3%97_Extension But I just ran across a shorter sketch of the main ideas that I must have begun some time ago but not yet finished: Peirce's Logic Of Information http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_Logic_Of_Information It has the advantage of having a nicely self-explanatory figure right up front. At any rate, try taking a look at that ... Regards, Jon On 4/20/2017 4:47 PM, Helmut Raulien wrote: > Jon, John, List, > Is it reasonable to say that a relation has an intension and an extension, the > intension is firstness, and the extension secondness (of the relation, which is > secondness)? > Best, > Helmut > 20. April 2017 um 15:14 Uhr > *Von:* "John F Sowa" <s...@bestweb.net> > Jon, > > That is an extensional definition of a relation: > >> Following the pattern of the functional case, let the notation >> “L ⊆ X × Y” bring to mind a mathematical object specified by >> three pieces of data, the set X, the set Y, and a particular >> subset of their cartesian product X × Y. As before we have >> two choices, either let L = (X, Y, graph(L)) or let “L” denote >> graph(L) and choose another name for the triple. > > Nominalists prefer extensional definitions. But Peirce would > usually state intensional definitions (rules) for the functions > or relations he was considering. > > Alonzo Church (1941) stated the intensional definition: >> A function is a rule of correspondence by which when anything is >> given (as argument) another thing (the value of the function for >> that argument) may be obtained. That is, a function is an operation >> which may be applied on one thing (the argument) to yield another >> thing (the value of the function). > > For further discussion of the distinction between intensions > extensions, see pp. 1 to 3 of Church's book: > http://www.jfsowa.com/logic/alonzo.htm > > By the way, Church was not a nominalist. See the transcript of his > talk "On the ontological status of women and abstract entities": > http://www.jfsowa.com/ontology/church.htm > > John > -- inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey isw: http://intersci.ss.uci.edu/wiki/index.php/JLA facebook page: https://www.facebook.com/JonnyCache
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