Re: Roles and dependence (Pat Hayes)
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Date: Tue, 26 Sep 1995 14:19:38 -0600
To: (John F. Sowa),,,
From: (Pat Hayes)
Subject: Re: Roles and dependence
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(Remark: last message from me in this particular flamage. I've made my
position as clear as I possibly can in previous messages.)

At  1:32 AM 9/26/95 +0500, John F. Sowa wrote:
>>   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 ...
>If that was what he meant, he would have said so.

Well then what the hell DID he mean. (On second thoughts, dont answer that
here. Write a book about it. :-)

>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.

As I said above, it is the CONCEPT of being. Theres a subtlety here. Every
language or representation makes some conceptual assumptions. When we are
talking about the representation, we are discussing these. In the language
itself, of course, these assumptions are taken for granted. Thus, speaking
in the metalanguage, we can accurately say that the existential quantifier
encodes the concept of something existing; when we use that quantifier, we
assert that something exists. I've been following a common convention where
we all understand that this entire discussion is about concepts, but I
'use' the conceptual language to make the discussion more readable. Perhaps
I should be more careful in future. 

>>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?...... but
>>then the Second itself has become an object!
>No.  ....<history omitted>.
>The second of Secondness is the other entity of the relation. 

Then that IS an object!

The Peircian quote didnt use words ending in 'ness': he simply talks about
'Second', etc.. I took his use of 'Second' here to mean what we have been
calling 'Secondness', etc.; but if that is a mistake, I dont see how a
Second can differ from a First; or at the very least, *some* Seconds must
be Firsts. (Eg, my mother is a woman; or, to be more precise: my CONCEPTION
of my mother is, in part, a conception of her as (being) a woman.)

If Peirce means by 'Second' simply the other argument of a relation, why
does he need Thirds? Why cannot a relation introduce itself to its own
arguments (or perhaps introduce its arguments to one another)? I can scent
a hint here of what I suspect to be a fundamental limit of Peirce's
thinking, which is that he really couldn't believe in both things and
relations. Rather than say that a relation held between two things, he
insists either the things have some kind of 'attitude' towards one another,
or that there only are relations, and 'things' are characterised as
identity relations. This may be because he was writing before there was a
securely accepted set theory to give an extensional account of relations.

>>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?
>........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.

I refer you to earlier arguments that this is true for ANY concept. (I will
resist demonstrating how it works for 'woman' because of the growing
concern about pornography on the internet.)

Also, I am genuinely confused here. Surely you should say that the concept
type of Hole is being a second of something of type Secondness, according
to what you wrote above.

>> 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!!!

Oh, give me a break. So 'Thirdness' is just denotation! What was all the
fuss about? We seem to be back on Fregean ground rather firmly.

In any case, theres something wrong here. There are two different ideas
being smudged together: (a) the relationship(?) of a relation to its
arguments (or, between the arguments) (see earlier Peirce quote), and (b)
that between a sign, a user of the sign, and the thing that the user of the
sign intends it to denote (or, the meaning of the sign for the user). These
are most definitely not the same thing!

>.... Quality, Reaction, and Representation. .... Firstness, Secondness, and
>Thirdness..... "prehension" .... "nexus".

Your historical scholarship is impressive, but none of this is any clearer
than any of the rest of it. 

A story. When Boyle was investigating the properties of gases he went
through a whole series of odd ideas about the true nature of gases,
temperature, etc., which influenced his experiments and his interpretations
of them, and there was lots of discussion among the scientists of his day
about the real meaning of his data. Boyle himself never accepted the atomic
theory of matter, even though the laws are now named after him. It makes
fascinating historical reading, but it is of no use to the modern
physicist. Similarly here, I suggest.

>>(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

All credit to him, then. However, this is not a very good argument
*against* modern logic ;-)

>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

Mother(x) iff ( (exist y)(Mother-of(x,y) & Human(x) )

is monadic. This is trivial unless very strong conditions are put on 'can
be expressed' (Can be expressed without using quantifiers? This will
probably rule out the natural numbers.)

>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.

I'll agree. Lets see some applications of these ideas which do more than
simply exhibit the ideas. I'll concede defeat when you do something that I
can't represent in Lww within a few minutes in such a way that the model
theory performs an adequate job of explanation.


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