[lit-ideas] Re: TLP1: Elements and their relations in giving the sense of 'p'
- From: Eric Dean <ecdean99@xxxxxxxxxxx>
- To: lit-ideas <lit-ideas@xxxxxxxxxxxxx>
- Date: Mon, 16 Feb 2009 23:49:46 +0000
I too want to thank Donal for an interesting post, and like John McCreary I
don't think I've got much to add about whether the Wittgenstein who wrote the
Tractatus did or did not hold the views Donal ascribes to him.
That said, I do think the question of whether a proposition depends for its
sense solely on the relation between the elements of the proposition is
interesting.
I think one can read at least one strand of the history of work in the
foundations of mathematics as an effort to develop a mathematics wherein the
sense of every proposition ultimately depends entirely on the relations between
elements of the propositions and not on the character or content of its
elements.
That effort has arguably been all but entirely successful with the
formalization of all (or almost all) mathematics in terms of set theory and the
formalization of set theory in terms of basic first order logic with a single
constant, the empty set, and a single operator, membership -- so that all sets
are either the empty set or sets that contain sets that contain sets that...
contain the empty set. The only definition of the empty set is this: any
assertion is false which says that some object is a member of it.
Out of such spare resources all of number theory can be constructed and with
number theory come the rational numbers and with them, by way of the technique
of "Dedekind cuts" come the real numbers and voila the continuous line, the
foundation of geometry, etc.
While practicing mathematicians, except perhaps some who do foundational work,
don't really work with such structures, thinking instead, presumably, about
things like obscurely complex foldings of geometric surfaces or intricate
articulations of algebraic formulas rather than endlessly elaborated nestings
of containers of emptiness, it does seem to me that the theoretically possible
expression of all of modern mathematics in terms solely of modern set theory
constitutes an example of the possibility of substantive propositions whose
sense is to be found entirely in the relations of their elements rather then in
the character or content of the elements.
Which simply says that *if* in fact Wittgenstein was reaching for such an
understanding of propositions there has turned out to be at least one fully
reputable discipline which has explicitly and deliberately instantiated that
very model of propositional meaning.
I think, though, that Wittgenstein had larger fish he sought to fry than the
foundations of mathematics, so I'm not sure that that one illustration of the
potential viability of the view Phil Enns appears to have attributed to
Wittgenstein actually provides much support but it's what struck me when I read
Donal's post today.
Regards to one and all,
Eric Dean
Washington DC
Date: Mon, 16 Feb 2009 20:28:49 +0900
Subject: [lit-ideas] Re: TLP1: Elements and their relations in giving the
sense of 'p'
From: john.mccreery@xxxxxxxxx
To: lit-ideas@xxxxxxxxxxxxx
On Mon, Feb 16, 2009 at 7:38 PM, Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx> wrote:
7. Let us assume that distinction between "elements" and their relations is one
that can only be shown and that cannot be said. It is nevertheless a separate
issue to the one at 5. whether we adopt the traditional view and take the TLP
as offering propositions about unsayable matters that, though they are strictly
nonsense, are trying to say what is true – or whether we take the
Conant-Diamond view that the TLP itself is on the same level as the kind of
nonsense it condemns philosophers for traditionally offering because they are
trying to say what cannot be said. On the first view the distinction between
"elements" and their relations, though unsayable, would nevertheless be true
(and perhaps even "unassailable and definitive"). On the second view the
distinction, while not true and indeed nonsense, is still needed as a ladder
from which to gain a perspicuous view of the character of 'p's and their sense.
First, a warm thank-you to Donal for taking the time to so cogently articulate
an interesting argument. The following remarks should be taken as tangential,
since they involve no claims whatsoever about what W was intending to say in
TLP, a topic on which I am totally ignorant.
Serendipitously, I am hard at work on a bit of research involving social
network analysis (SNA), in which social relationships are idealized and
formalized in terms of graph theory, with actors represented by vertices and
relationships between them represented by (undirected) edges or (directed)
arcs. One interesting thing about this form of analysis is that, while it
requires two discrete sets of primitives, the vertices and the links (the set L
comprising the union of E, the edges, and A, the arcs), the specific content of
these sets is irrelevant to the mathematics of the software I am using.
Getting down, then, to specifics, I am looking at (1) a set of prize-winning
ads published in the Tokyo Copywriters Club Annual and (2) a set of creators
who were members of the the teams that created the ads. The software is
entirely unconcerned with whether I designate the creators as the vertices,
with the ads forming the links between them, or, conversely, treat the ads as
the vertices connected by the creators.
Because this project is much on my mind, I read 7. above and find myself
wondering if something similar couldn't be said about the elements and
relations to which Donal refers. To be sure, when we compare "The cat on the
mat" with "The dog on the mat," we "naturally" assume that the elements in
question are the cat, the dog and the mat and the relation in question is that
implied by "on." But is the "naturalness" with which we draw the distinction
tell us something about the real world or the way that human brains and nervous
systems process information, or is it an artifact of the languages we speak?
Could "on" be the element, while "cat," "dog," and "mat" are relationships
between different instances of "on"?
Anyway, thanks again to Donal. The little grey cells are stirring, and that
feels good.
John
--
John McCreery
The Word Works, Ltd., Yokohama, JAPAN
Tel. +81-45-314-9324
jlm@xxxxxxxxxxxx
http://www.wordworks.jp/
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