[Wittrs] Re: [quickphilosophy] Re: 1.12; 1.13; 1.2 & 1.21
- From: wittrsl@xxxxxxxxxxxxx
- To: quickphilosophy@xxxxxxxxxxxxxxx
- Date: Wed, 21 Jul 2010 23:40:03 -0700 (PDT)
Hi Neil:
Thanks for your comments. I'm not sure that I understand what you're getting
at, and if I do, then I think we're disagreeing on what W is saying here.
OK, so if "X is red" is not atomic, then how are we going to analyze it? I
don't see a good way to analyze "red". It just is or it isn't. Now, maybe you
might want to say that my car can be analyzed into doors, seats, engine, hood,
tires, and so forth. It's true that it's a thing that is composed of other
things, but, then, what isn't? Quarks? Was Wittgenstein saying that our atomic
facts are about quarks? You can't really be suggesting this, can you?
So, what is an example of an atomic fact? Russell can give them and
Wittgenstein didn't. Does that mean Wittgenstein can't?
Later, W. is going to explicitly refer to predicate logic notations for facts.
And the atomic statements are just like in first-order predicate logic: r(x)
for unary predicates ("x is red") and R(x, y) for binary predicates ("x is a
blood relative of y") and so on. So, the constants have to name something and
the relation has mean something about the named objects. So, again, let's have
the analysis.
You say there are multiple properties in my example. This is not true. There is
one property: red. There is one object: my car. Now, you could argue that "my
car" is compound, but we could give my car a name: Betsy. Now, we have "Betsy
is red".
You seem to egregiously misquote me, as follows, and then make a logical
mistake:
Your example, not mine, is "X is red or green", and that's a disjunction. Not
simple. Also, you write that "if X is red or green, then X is red", but this
does not follow. A maple leaf could be red or green, depending on the season.
From that, though, it does not follow that the leaf is red.
On trees and logic: some comments I'd be inclined to make:
I would not say that logic is the traversal of a binary tree, as you seem to
assert. Logic consists of a syntax for forming statements in a formal language,
a semantics for interpreting these statements, and a set of rules of derivation
for deducing statements from others in the language. There might be a method
for deciding whether a sentence is a tautology by constructing a binary tree
according to some algorithm, but that's not really what logic is all about. Or
perhaps I'm just missing your point.
A non-binary tree has a node N with more than two children. There is no way to
construct a binary tree from it, that replicates the parent-child relationship
of the nodes, because there is no way to know where to put the third child of
node N. I'm not sure how this bears on whether W's statement that something can
be the case or not be the case and all else remains the same is defensible or
not.
The best I can say in W's defense, though, is that he either overstates his
case, and "all else remains the same" refers only to propositions about other
named objects, or, it's really not about the propositions but about the facts
in the world. That is, Betsy can be red, and that does not affect whether the
Batcar is black or not. So, W. could be saying that the properties of one
object are independent of those of another object, unless those objects form a
compound of some sort. So, he's making a metaphysical statement about the
world, and not making a statement about our ways of describing the world
through language.
Thanks again; this is a difficult area of the text for me & it's good to argue
these things out.--Ron
--- On Tue, 7/20/10, iro3isdx <xznwrjnk-evca@xxxxxxxxx> wrote:
From: iro3isdx <xznwrjnk-evca@xxxxxxxxx>
Subject: [quickphilosophy] Re: 1.12; 1.13; 1.2 & 1.21
To: quickphilosophy@xxxxxxxxxxxxxxx
Date: Tuesday, July 20, 2010, 8:42 PM
--- In quickphilosophy@xxxxxxxxxxxxxxx, Ron Allen <wavelets@...> wrote:
> responding to http://groups.yahoo.com/group/quickphilosophy/message/43
> Ron:
> My car can be red. But it can't be anything else that would conflict
> with red as a property, because then the fact or not of it being red
> would affect the truth of the possible fact that it's green. This
> is ridiculous.
I don't think that's a killer argument. It just means that "X is red"
is not atomic, so would have to be decomposed into atomic components.
You could, for example, have:
X is red or green;
if X is red or green, then X is red;
From a mathematics/graph theory perspective, logic is just traversal of
a binary tree. When you have multiple properties, as in your example,
then you have a non-binary tree. But you can always construct a binary
tree to represent the same facts. And then the atomic facts are just
the leaf nodes of that binary tree.
There is still a possible problem. The construction of a binary tree
from a non-binary tree is not canonical. That is, there are multiple
ways of doing it, and there isn't any preferred way. I'm not sure to
what extent that would have been a problem for Wittgenstein's
methodology.
Regards,
Neil
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