# Re: Roles and dependence

sowa@west.poly.edu (John F. Sowa)
```Date: Tue, 26 Sep 1995 01:32:52 +0500
From: sowa@west.poly.edu (John F. Sowa)
Message-id: <9509260532.AA03193@west>
To: cg@cs.umn.edu, phayes@ai.uiuc.edu, srkb@cs.umbc.edu
Subject: Re: Roles and dependence
Cc: p.m.simons@leeds.ac.uk, phismith@ubvms.cc.buffalo.edu
Content-Length: 5309
Sender: owner-srkb@cs.umbc.edu
Precedence: bulk
```
```Peirce:

>   First is the conception of being or existing independent of anything
>   else.  Second is the conception of being relative to, the conception
>   of reaction with, something else.  Third is the conception of mediation,
>   whereby a first and a second are brought into relation.

Pat Hayes:

>Let me try to understand this and illustrate why I can't. Lets suppose that
>the idea of First is clear; it is the concept of *being*, pure and simple:
>it corresponds more or less to the existential quantifier, I presume.

Most definitely not!  Peirce was the first person to publish a paper
that used the term "quantifier" and "existential quantifier" in its modern
sense.  If that was what he meant, he would have said so.

Please note the word "conception".  He is not talking about what something
is or about whether it exists.  He is talking about how we conceive
of it.

>Third is where a first and a second are brought into relation..?? But a
>second IS a relation, right? So what does this 'mediation' mean? It sounds
>like Peirce has the idea that a relation is someTHING, a kind of
>second-order entity, and that to assert that it holds between some Firsts
>is to somehow 'introduce' it to them (to plug them into its tinkertoy hub,
>or to make the reaction happen). I can even follow that, more or less; but
>then the Second itself has become an object!

No.  Whenever Peirce wanted to talk about a reified relation, he said so.
In that same 1885 paper in which he introduced the word "quantifier", he
also introduced the terms "first-intentional logic" for quantification
over concrete things and "second-intentional logic" for quantification
over relations.  Schroeder translated "intentional" into "Ordnung" and
when it came back into English, we got first and second-order logic.

The second of Secondness is the other entity of the relation.  For the
conception of a person as "woman", there is no implicit other.  For the
conception of the same individual as "mother" there is an implicit child.

>Its very ambiguous, in any case, since it depends on what 'intrinsic' and
>'structure' are taken to mean. What is the intrinsic structure of a hole in
>a wall (not that hole, the other one. Remember, you can't refer to the
>wall!), or the number two?

we think we mean.  If you are asking me how I would classify the concept
type Hole, I would say that it is Secondness because I can't define it
except in reference to the wall or other entity in which it is a hole.

> But in any case, your example of Thirdness seems
>different from Peirce's. This example, like most of those you have
>produced, involves the idea of a representation and the thing it denotes or
>describes. I agree this is an important concept that needs careful
>description. But (a) I see nothing in Peirce's account to suggest that this
>is what he had centrally in mind.

Wonderful!  By Jove, you've got it!!!  Peirce's original terms for his
distinction were Quality, Reaction, and Representation.  He later decided
that those terms were not general enough and that they had too many
informal associations that could be misleading.  Therefore, he later
switched to Firstness, Secondness, and Thirdness.

But if it helps you to get a glimpse of the idea, you can consider the
term Quality to be very close to Firstness.  Reaction is one of the
words that he often used in trying to describe Secondness.  Representation
is always an example of Thirdness, but he also wanted to consider other
kinds of Thirdness.

If it helps, Whitehead's term for Secondness is "prehension" and his
term for Thirdness is "nexus".

>(b) theres nothing here to suggest
>that we have to go beyond conventional logic, which understands these
>matters very thoroughly.

Please remember that Peirce invented predicate calculus in its modern
form.  The only difference between the version he published in the
American Journal of Mathematics in 1885 and the modern form is in the
choice of symbols:  Peirce used Sigma for the existential quantifier,
Pi for the universal, + for or, times for and, and less-than-or-equal
for implies -- because in p->q, the truth value of p is always less
than or equal to the truth value of q.  As I said in an earlier note,
the Germans were using Peirce's symbols as late as 1910.  Zermelo used
Peirce's notation for all of his work on set theory.  Even Goedel (1931)
used Pi for the universal quantifier.  As Casey Stengel said, "You could
look it up."

His discussions of Firstness, Secondness, and Thirdness were about
ontology, not logic.  He was just trying to give an explanation of how
these "conceptions" were related to the complexity of the relations
needed to define an instance of one of these categories.

Perhaps that may be a way of explaining the difference:  Firstness
or Quality is not a synonym for "monadic", but a way of saying that
the Firstness or Quality of something can be expressed by a monadic
relation.

In any case, I think that it may be better to drop the idea of trying
to give definitions without giving applications.  As I said before, the
power of Peirce's distinction is in the way he uses it to explain
other conceptions.

John

```