[lit-ideas] How elementary, elementary?
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sun, 18 Apr 2004 10:39:21 EDT
"The cat is on the mat" -- elementary
Donal McEvoy writes in reply to R. Henninge:
Are you claiming that that a name like "cat" that can be analysed in terms of
other names (eg. leg, head, tooth) can be an EP? That any name that be so
broken down can at the same time be "elementary"?
--- This reminds me of the sentence used by Stephen Toulmin -- complete with
accompanying drawing -- in _The uses of argument_ -- viz.:
"The cat is on the mat."
--- I always took a liking for this sentence. I thought it was _logical_.
Apparently, though, it is a sentence from a manual anglophones use to learn the
language, and 'mat' is used not because it's something cats usually are on --
but because it rhymes with 'cat' -- "the mat is on the rug" would not do. It's
more of a phonetic or phonographic exercise.
Now, I believe the fact that 'cat' can be analysed in terms of 'leg, head,
tooth', as Donal suggests, is pretty irrelevant. First, the total conjunction
of
such _elements_ is not there to easily be nominated. Note the ridiculousness
of the expansion
The cat's leg, the cat's head, the cat's tooth, [are] on the mat.
Surely this is dependent on having a notion of 'cat' -- for you to be able to
use it in the possessive case ('cat's'). Surely one can invent a lingo, where
the possessive is not used, and an index is introduced to mark the _origin_
of the body part: "The leg(-cat), the head(-cat), the tooth(-cat), [are] on the
mat."
I would agree that would be correct, provided we add a ceteris paribus 'ad
infinitum' clause: "The cat's leg, head, tooth, etc [and so on completing the
thing] are on the mat." Donal will say that a similar treatment awaits 'the
mat'
(threads of wool, etc.).
Now, it would seem that for Russell and Wittgenstein and Henninge and Paul
and me, 'The cat is on the mat' is indeed atomic and elementary. A closer
inspection into the logical form shows it's not, though.
'Felix is on the mat'
may be atomic/elementary, but hardly 'the cat'. 'The' involves the
iota-operator, in logic, which involves the universal quantifier, and the
particle 'if':
"There is at least a cat on the mat, there is not more than one cat on the
mat, and nothing which is the cat is not on the mat." Henninge suggests, "the
dot -- in http://www.andreas.com -- just after 'andreas' -- is blue"
"The dot is blue".
One minor problem with this is that dot are supposed to have no extension,
but colours only applied to extended surfaces. So it's not really a dot that
is blue -- but something that _represents_ or looks like a dot. I'm not sure
phenomenalist language like that would prima facie count as 'atomic' or
'elementary'. (Cf. Austin's discussion of 'That spot over there is the village
church'). Henninge says that for Wittgenstein, 'elementary' or 'atomic
propositions' were _o-kay_. But recall the very first quote for 'atomic
proposition' in
the OED: 1912 L. WITTGENSTEIN Let. (to Russell) in Notebks. 1914-16 (1961) 120,
"I believe that our problems can be traced down to the atomic propositions."
-- Perhaps having the wider context would help.
Dear Bertrand,
How's the weather in Cambridge?
Having some awful weather here -- in the trench.
Anyway, hope life's well. I'm writing something
I may end up calling "Tractatus" -- but I guess
you'll think that's pretentious? Other suggestions
welcome. ...
Sorry for the interruption here. The sargeant
has just told me, "Heil mit wir schribben schuet!"
and I wonder if that's elementary -- or atomic.
I have a copy of your the American Journal
of Mathematics (XXX) with me, and on p. 238
you define an elementary proposition. But
I cannot make myself agree with that
definition.
Anyway, nothing too serious, I hope. But I am
led [to] believe that our problems _can_ be
traced down to the atomic [propositions].
My regards to all in Cambridge
that I know,
Will be seeing ya soon,
X X O O
Lud
-----
Cheers,
JL
1908 B. RUSSELL in Amer. Jrnl. Math. XXX. 238 A proposition containing no
apparent variable we will call an elementary proposition... Elementary
propositions together with such as contain only individuals as apparent
variables we
will call first-order propositions... We can thus form new propositions in
which
first-order propositions occur as apparent variables. These we will call
second-order propositions... Thus, e.g., if Epimenides asserts â??all
first-order
propositions affirmed by me are falseâ??, he asserts a second-order
proposition.
Ibid., Propositions of order n..will be such as contain propositions of order n
- 1, but of no higher order, as apparent variables.
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