[lit-ideas] Re: The Serpent's Club
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sun, 14 Mar 2004 17:36:31 EST
Continuing with our examination of Grice's Nachlass on the formalisation of
number and gender ('ey'), R. Paul writes:
>After considering two of JL's formulations, of 'When a man is tired of
London,
>he is tired of life,' I wrote:
>Maybe this is unnecessarily heavy going.
>'Tired of London' is a singular predicate (the 'of' doesn't introduce a new
>predicate: e.g.: 'Sea of Japan' doesn't mean 'is a sea and is of Japan').
I agree. But tetrapyloctomically, I would distinguish between 'introducing a
predicate' and 'introducing a _term_'. I'm not sure the 'of' of "tired of"
behaves like the 'of' of "sea of": the 'of' of 'tired of' can be replaced, I
think, by 'by' ("tired by London") whereas it does not seem to make sense to
speak
of the sea by Japan. But let that be.
>So, we
>can just write
>(x) (Tx -->Lx) 'For all x, if x is tired of London, x is tired of life.'
Again, in my view that the predicate is the _dyadic_ predicate "... to be
tired _by_ ...", that would allow us to retain the _same_ dyadic predicate --
which I think is Johnson's point in the dictum ('repetition'):
(x) (T(x, London) -> T(x, life))
Alternatively, one can try the word 'tire', and invert the order of the terms:
(x)(T(London, x) -> T(life, x))
read: "When London tires x, life tires x". R. Paul's own paraphrase goes:
>(If anything is tired of London it is tired of life.)
>Of course, Johnson wrote 'man,' so we might write, for clarity
>(x) [Mx-->(Tx -->Lx)]
>where Mx means 'x is a man'
>thus leaving it open that women and children although tired of London may not
>yet be tired of life.
Exactly, and I think this rephrases quite well Johnson's intention. -- in a
way the 'anythingarian' view ("if anything is tired of London, it is tired of
life") does not?
>The x in 'for all x,' and 'for some x' is a variable that unless bound ranges
>over any conceivable object or state of affairs, and is only given a 'gender'
>when it falls under an appropriate predicate, such as 'stallion' or 'mare.'
This reminds me of Hungerford's concern, as aired recently:
"Why do we feel so anxious? Even quite small children
ask if our dog is a boy or a girl."
with boys being statistically more interested? Hungerford's case is
especially tricky, for we have _bitch_ for 'female dog' (or female 'hound',
strictly,
for 'dog' is _masculine_ dog). (Incidentally, I think people feel particularly
anxious about _certain_ animals, dogs rather than flies -- or amoebae? Why
would that be?
Paul continues:
>So
>there's no need to try to express in logical notation a grammatical
infelicity
>which that notation does not commit us to.
I agree with R. Paul that _gender_ is, as he puts it, a 'grammatical
infelicity'. I'm less sure I want to agree about _number_ being _ditto_.
Warnock said
(in 'Metaphysics in Logic') that the following is valid:
Nietzsche (and Nietzsche alone) was a Nietzschean philosopher
___________________________________________________________
Therefore, some philosophers are Nietzschean.
and (this become relevant below)
Therefore: someone (some_body_) is a Nietzschean
philosopher.
Therefore: some_thing_ is a Nietzschean
philosopher
In Warnock's view (and mine), 'some' does not _entail_ plurarity ("Some party
we had yesterday!" does not entail we had just _one_), etc. On the other
hand, adding '-one' ("Someone is watching you") _does_ entail singularity --
but
that's because of the '-one', not the 'some-'. R. Paul notes:
>I did not know that in writing this I was rehearsing something that Stephen
>Pinker seems to be trying to say in The Language Instinct (Chapter 12, 'The
>Language Mavens')
http://www.crossmyt.com/hc/linghebr/s-pinker.html>
Thanks for the link.
>namely:
Pinker's Quote:
>'everyone' and 'they' are not an "antecedent" and a "pronoun" referring to
the
>same person in the world, which would force them to agree in number. They
are a
>"quantifier" and a "bound variable," a different logical relationship."
(1) Everyone returned to their seats
>means
(2) For all x, x returned to x's seat.
>The "X" does
>not refer to any particular person or group of people; it is simply a
>placeholder that keeps track of the roles that players play across different
>relationships. In this case, the X that comes back to a seat is the same X
that
>owns the seat that X comes back to.'
--- end of Pinker's quote.
Paul comments:
>The first part of this may seem right.
>'Everyone,' (and 'anyone') might appear
>to [be] treated in propositional logic as 'for all...,'
>just as 'any,' 'all,' and 'every,' are; but is this
>really so? Logic doesn't provide uncontroversial
>translation rules for putting ordinary language into
>formal notation, and Pinker's confidence in his
>reading of 'everyone,' is unjustified. Surely
>'everyone' might equally well be 'translated' as
>'for all...where...is a
>person.'
Or equally _wrong_, you mean? If someone likes a treat, it does not mean a
_person_ -- it can be a _dog_. Or would you use 'some_body_' in that case? (cf.
Spanish 'alguien', 'algo', 'algUNO' -- and the equivalent French expressions
J. Evans should be familiar with). R. Paul continues:
>For example, 'anyone,' if translated as (x) [i.e.,'for all x'] would
>make it impossible to distinguish between
(x) (Tx implies Lx)
>where 'Tx' is 'x is a table', and Lx = x has legs, and
(x) Fx implies Nx
>where Fx = speaks French and
>Nx = speaks a natural language
>so that we could write
>'If anyone is a table, then...,' which verges on nonsense
>(unless it is said by way of organizing the
>actors in a school play, for instance).
Well, I'm not sure about that point. It certainly does not hold in Tamil. As
far as English is concerned, it seems that 'anyone' did not _mean_,
etymologically, 'any one _person_': for one, 'person' is a Latinism. It
couldn't mean,
either, 'any one _body_' -- and what's a 'body'? -- for 'body' is Low Dutch.
And the Anglo-Saxons were using 'anyone' BEFORE the items 'person' or 'body'
were introduced in their lexicon. So I take it that, literally, there is no
connotation or entailment to the effect that 'anyone' implies something
_spiritual_, if that's Paul's point (although, what's _spiritual_ about 'body'
in 'Has
anybody here seen Kelly?').
R. Paul concludes his interesting post:
>What I'm trying to say is that if you treat 'everyone' ('anyone')
>merely as a quantifier (all) and a bound variable (x), you'll still
>be faced with the awkwardness of distinguishing (in notation)
>between 'anyone' and 'anything,'
>which, although not easy to do there may still have a point outside logic.
Mmm. Will think about it. One small problem here -- with distinguishing
between 'anything' and 'anyone' -- is something of a Hornian (after L. Horn)
scalar
implicature:
<anyone, anything>
<someone, something>
i.e. there is an _implicature_ (thus cancellable and defeasible) that if x is
someone, x is not something. Surely the class of something includes as a
proper subset the class of someone's?
Back to the logical niceties of plural, it should be pointed out that while
we say 'something', we don't say 'allthingS', but 'everything' -- suggesting
that 'every' is not really 'all', but 'each'? (Cf. "When everyman is tired of
London, _he_ is tired of life").
Cheers,
JL
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