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}John, thanks for a great post. I think that we don't pay enough
attention to relations.
Edwina
On Wed 18/10/17 12:06 PM , John F Sowa s...@bestweb.net sent:
Kirsti and Gary R,
If a debate doesn't converge, the traditional solution (since
Socrates) is to find which words are causing confusion and either
(a) avoid using them or (b) define them more precisely.
Kirsti,
> Possibilities may be real, but they do not exist until they
> become actual.
In that sentence, three words raise debatable issues: 'real',
'exist', and 'actual'. To analyze the issues, I suggested Quine's
dictum: "To be is to be the value of a quantified variable."
(And by the way, I apologize for typing 'Kirstima'. I wrote
'Kirsti'
in my previous notes. I blame my fingers for typing too many
letters.)
> But claiming existence to possibilities just does not hold.
In Peirce's article of 1885, he introduced the algebraic notation
for predicate calculus. For "first intentions", he used quantified
variables to range over individuals. For "second intentions", he
used quantified variables to range over relations among individuals.
Every possibility or general that we talk about in ordinary language
can be represented by a relation in logic.
For first intentions, the domain may be the physical world or the
domain of mathematical entities, such as numbers, sets, and
geometrical shapes.
For second intentions, the domain is relations, which may represent
generals of any kind. Those generals include possibilities, among
which are sign types.
If we restrict the word 'actual' to physical, Generals and possibles
aren't actual, but they exist in a domain of second intentions.
For example, let's consider a relation TallerThan. As a general,
it doesn't exist in the first-intentional world of actual entities.
But there could be a particular instance TallerThan(Bob,Bill)
which does exist in the physical world.
However, we could use second-intentional logic to say that the
relation ShorterThan is the inverse of the relation TallerThan.
We can use quantified variables to refer to those relations
in the domain of second intentions.
Gary (quoting excerpts from CP 5.503)
> [Reality and existence] are clearly not the same. Individualists
> are apt to fall into the almost incredible misunderstanding that
> all other men are individualists, too -- even the scholastic
> realists, who, they suppose, thought that "universals exist."
> [But] can any such person believe that the great doctors of that
> time believed that generals exist? They certainly did not so
opine.
In the excerpt that precedes that quotation, Peirce wrote about
what "many a logician" would consider:
> reality means a certain kind of non-dependence upon thought, and
so
> is a cognitionary character, while existence means reaction with
the
> environment, and so is a dynamic character; and accordingly the
two
> meanings, he would say, are clearly not the same.
Since Peirce was talking about logicians, he would expect them to
use
logic to represent both reality and existence. But the domains
would
be different. Logic about physical existence is first intentional;
it refers to things that react with the environment. Logic about
reality is second intentional; it has a "cognitionary character"
that does not react with the environment. But both first
intentional
logic and second intentional logic use quantified variables.
Summary: For actual things that interact with the environment,
Peirce used first-intentional logic. For relations that represent
generals and possibilities, he used second intentional logic,
which may refer to anything that has a "cognitionary character"
in thought. By Quine's dictum, the verb 'be' may be use to
talk about either domain.
John
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