BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}The Church definition of a function is exactly why I define the
semiosic triadic process as a function, where the Object [Argument]
is mediated by the Representamen/Function to provide the Interpretant
[value].
Edwina
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On Thu 20/04/17 9:14 AM , John F Sowa s...@bestweb.net sent:
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 [1]
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 [2]
John
Links:
------
[1]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fwww.jfsowa.com%2Flogic%2Falonzo.htm
[2]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fwww.jfsowa.com%2Fontology%2Fchurch.htm
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