John, List ... That is indeed an extensional definition of a 2-place relation. It can be generalized to k-place relations and then beyond the finite arity case, but k-place relations are enough to cover the triadic case of principal interest to us in semiotics.
But there is nothing remotely nominal going on here, as the definition invokes sets of tuples. Sets and tuples are the very sorts of abstract objects nominal thinkers would eschew if they could — we know they can't but they think they can — which is why they are always inventing square wheels like Russell's no-class theory or Leśniewski's mereology. The more interesting polarity that does arise in this setting of sets is not the one between nominalism and realism but the one that ranges over different cognitive styles or intellectual inclinations, namely, the empiricist and rationalist tendencies of mind. The question is, not which is best, but how best to integrate these dual capacities within the practice of inquiry. Regards, Jon On 4/20/2017 9:14 AM, John F Sowa wrote: > 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 and 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
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
