Jon, John, List ...
The question of how many characters, marks, or predicates there are
has an easy but exorbitant answer. If X is the universe of discourse
then there are 2^|X| possible predicates in all. In practice we tend
to have a more limited number in mind and include their enumeration in
the specification of our universe of discourse.
See the following page of selections and comments
from earlier discussions. I will try to organize
the material better over the next few days.
http://intersci.ss.uci.edu/wiki/index.php/Limited_Mark_Universes
This section looks like a later rendition:
http://intersci.ss.uci.edu/wiki/index.php/Limited_Mark_Universes#Another_Version_.2B_Comments
Regards,
Jon
On 1/19/2017 11:50 AM, Jon Alan Schmidt wrote:
John, List:
JFS: In logic (Peirce's as well as everybody else's), the universe of
discourse is the set over which the quantifiers range.
This is an interesting and helpful way of putting it, since Peirce often
discussed the concept of a continuum within the context of his theory of
collections. Consider this passage.
CSP: Whether the constituent individuals or units of a collection have
each of them a distinct identity of its own or not, depends upon the nature
of the universe of discourse. If the universe of discourse is a matter of
objective and completed experience, since experience is the aggregate of
mental effect which the course of life has forced upon a man, by a brute
bearing down of any will to resist it, each such act of brute force is
destitute of anything reasonable (and therefore of the element of
generality, or continuity, for continuity and generality are the same
thing), and consequently the units will be individually distinct ... Then,
I say, as long as the discourse relates to a common objective and completed
experience, those units *retain *each its distinct identity. If you and I
talk of the great tragedians who have acted in New York within the last ten
years, a definite list can be drawn up of them, and each of them has his or
her proper name. But suppose we open the question of how far the general
influences of the theatrical world at present favor the development of
female stars rather than of male stars. In order to discuss that, we have
to go beyond our *completed *experience, which may have been determined by
accidental circumstances, and have to consider the possible or probable
stars of the immediate future. We can no longer assign proper names to
each. The individual actors to which our discourse now relates become
largely merged into general varieties; and their separate identities are
partially lost ... The possible is necessarily general; and no amount of
general specification can reduce a general class of possibilities to an
individual case. It is only actuality, the force of existence, which bursts
the fluidity of the general and produces a discrete unit. (CP 4.172; 1897)
The *actual *("completed experience," that which exists) consists of
discrete individuals; but the *possible *(future experience, that which may
be or would be) is always general, and therefore continuous. Furthermore,
Peirce applied this notion of "universe" not only to subjects, but also to
predicates.
CSP: But besides its universe of objects, our discourse also refers to a
universe of characters. Thus, we might naturally say that virtue and an
orange have nothing in common. It is true that the English word for each is
spelt with six letters, but this is not one of the marks of the universe of
our discourse. (CP 2.518; 1893)
My understanding of Peirce's scholastic realism is that every "universe of
characters" is a continuum of possibilities, rather than a discrete
collection of individuals as nominalism holds. Is that right? Is there a
connection or analogy between "universe of objects" and "universe of
characters" in logic vs. "domain" and "range" in mathematics?
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
On Thu, Jan 19, 2017 at 9:19 AM, John F Sowa <[email protected]> wrote:
Jon A. and Clark,
JA
Already by 1870 Peirce ... shifts individuality from a category
of being to a category of description, relative to a particular
discourse situation...
That's an important observation.
CG
I think really what we’re getting at is Peirce’s notion of the
Universe of Discourse. The question then becomes what distinguishes
or differentiates one universe of discourse from an other?
In logic (Peirce's as well as everybody else's), the universe of
discourse is the set over which the quantifiers range. Two UoDs
are distinct iff the sets are distinct.
Peirce also said that one might have more than one UoD in
a single sentence. An example would be a language L with some
UoD U1, and a metalanguage L2 that talks about L and about
the relationship of L to some particular subject.
CG
We can of course distinguish two universes such as the universe
in which Superman exists and the universe (such as our own)
in which he does not.
Yes, consider the following sentence:
"I think that Tom believes Superman is real, but
Mary knows he's just a character in a story."
This sentence would have four UoDs: (1) the world that includes
Tom, Mary, and me; (2) the UoD of my thought; (3)the UoD of Tom's
belief, and (4) the UoD of Mary's knowledge.
John
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