[lit-ideas] Russell's Theory of Relations
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Tue, 7 Aug 2012 18:46:06 -0400 (EDT)
We are discussing Russell's Theory of Relations.
R. Paul quotes from an acquaintance of Russell's: Witters, freely rendering
from "Philosophical Investigations §216."
A preface may be in order.
In strict adherence to the facts, the theory is Whitehead's and Russell's.
They symbolise a "relation" by "R".
"A relation," they hold, "holds between two components, which we'll call
'the relata'" and which they go on to symbolise as
"R (x, y)"
-- The first issue they consider is the axiom freely rendered by R. Paul:
> 'a thing is identical with itself,'
Whitehead and Russell go on to define a special 'relation' for that, which
they symbolise, drawing from Leibnitz, as "=".
= (x, x)
or
x = x
Russell and Whitehead hold that "identity' qua relation is symmetrical and
transitive.
In a message dated 8/7/2012 2:50:03 P.M. Eastern Daylight Time,
rpaul@xxxxxxxx brings in another example:
RELATION (Paul, St. Paul).
Paul's gloss:
-- Paul is trying to check if Whitehead's and Russell's use of 'relation'
is a *stretch*:
"If I say, having been asked, whether the former Saul of Tarsus was any
relation [in Whitehead's and Russell's sense] of mine, that he wasn't, I don't
mean to deny that it would be 'logically possible,' for a clever
[Wittgensteinian] to come up with some relation [call it "R"] which
metaphysically
(so to speak) or biologically linked us -- e.g. that we share the same
blood type, and are 'related' by being members of the
set of humans with O-positive blood."
In other words, R. Paul is submitting that 'relation' has _looser_ uses
than Whitehead and Russell admit.
R. Paul, however, grants:
"Yet the sense in which all the students of Mutton College are related in
virtue of their being students of Mutton College is not the sense in which
some of them might be related as cousins."
Russell and Whitehead refer to the 'subscript' here:
R1, R2.
Suppose two students at Mutton College are called (as they may):
Jack
Jill.
Indeed, for any x and y, Whitehead and Russell write, it is possible to
assume that there is a relation R1 such that
R(x, y).
--- E.g. "Jack and Jill are related in virtue of (both) being current
students at Mutton."
This, to keep using Paul's example, is different from R2, where "R2" is
read as "they are cousin":
COUSIN (Jack, Jill).
-- 'cousin', incidentally, unlike 'mother' is SYMMETRICAL.
R. Paul is suggesting that the _looser_ use of 'relation' has to do with
'kinship' (as when David Ritchie says that he has 'no relation' with Major
Ritchie).
R. Paul goes on:
"While ['everything bears some relation with anything else' -- in
Whitehead's & Russell's symbolism: COROLLARY to Theorem 5*6: "for any x, and
any y,
R(x,y) is an axiom"] may sound like an important notion, it strikes me as
second only to 'a thing is identical with itself,' as being a sentence than
which none more useless can be imagined.* (*Philosophical Investigations
§216, freely rendered) which was our starting point.
When Witters brings in 'imagination' he is working with the slogan, as per
a graffito:
meaning = use
-- where we can go on to symbolise 'meaning' with "M" and 'use' with "U"
and contradict a relation (of identity).
The fact that these hold:
"A thing is identical with itself" -- FIRST otiosity
"Everything bears some relationship with anything else" -- SECOND otiosity
would be, for Russell, and Whitehead, a proof that "Principia Mathematica"
holds and that it's principles (in their presentation as conceptual axioms
of the structure of our thought, rather than otiosities) that the
philosopher (or The Philosopher) is interested in (*pace* Paul).
Cheers,
Speranza
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