Re: Roles and dependence (Pat Hayes)
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Date: Mon, 25 Sep 1995 14:38:42 -0600
To: (John F. Sowa),,
From: (Pat Hayes)
Subject: Re: Roles and dependence
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At 10:33 PM 9/23/95 +0500, John F. Sowa wrote:
>Following is one of Peirce's shortest and simplest statements of the
>   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.
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. (I
don't think that the idea of pure existence with no relationships is
coherent,in fact, but lets leave that aside and be generous..) Now, Second
is the conception of being relative to something else (I presume this means
'relative to in some way', since there are many ways of being relative). So
there are things and there are relations between them; OK so far. Now
however I get lost. 
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! This is a kind of First -
something that exists in its own right - and then this 'Third' is just a
collection of relations - Seconds - between the Second and the Firsts (its
arguments, in modern parlance). Thats just the reification trick we are all
familar with. Indeed. look at what Peirce himself says at the end of this
quote: the first and the second are brought into RELATION. Why should this
particular kind of relation be excluded from its bretheren in the Seconds?
>I will try once more to state my understanding of what Peirce
>was trying to say:
> 1. Firstness classifies an entity by its intrinsic structure, pattern,
>    or form, independent of any relationships it may have to any external
>    entity. 

See my ancient-Rome example for why I consider this idea to be incoherent.
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?

> 2. Secondness classifies an entity according to some relationship it may
>    have to some external entity.  
I'm happy with these, as you might expect.

> 3. Thirdness classifies an entity by its mediating effect in bringing
>    other entities into relation. 

Consider the relation of being taller than. My youngest son, Robin, is
taller than me. Nothing 'mediated' in order to 'bring' us into this
relationship: its just true, thats all. Or consider the fact that the sun
is hotter than my oven,  (etc.)

>As an example, .....
>    As Thirdness, the drawing is a guide for a contractor or builder who
>    translates (or has translated) the pattern of marks to a structure of
>    wood, steel, and concrete.  It would be defined by a triadic predicate
>    that involves the builder x who maps the drawing y to the structure z.
>I hope that this statement is "crisp" and "clear" enough.

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


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