The results of the vagueness experiment were
quite encouraging. Here’s the philosophically interesting part of what
happened. The subjects were asked whether they thought n minutes after midday was late (for the relevant appointment) for
increasing n until they finally said Yes at some point, call it k. Then they were asked again about
whether k-1 minutes after midday was
late. 18 out of 19 respondents (I know it’s a small sample, but it’s something)
said No, just like they had when
asked the question the first time, and despite having just said that k minutes was late, and despite that
answer being displayed in boldface just above the question. Various contextualists (I don’t have the references with me, but I’ll
try and find them later and update this post) have claimed that saying that k minutes after midday is late creates a
context where it is no longer true that k-1
minutes after midday is not late, and so when this question is asked the common
answer should be Yes. But only 1
respondent so far has said that. Some contextualists
have been relatively cautious about what the empirical consequences of their
views should be, but some have been
relatively bold about what they think will happen in experiments with just this
design. It would be good to do this test more rigorously, with random sampling
and a larger sample, but 18-1 is a pretty big split even allowing for those design
flaws. Much thanks, of course, to everyone who has taken the experiment. I will keep it up, and keep the counters running, though now that I’ve said what the experiment was testing for the flaws in the experimental design are even more alarming.

UPDATE: It is actually 17-1 in favour of being consistent, not 18-1 as I reported above. My apologies.

I’m trying to write something up about
narrow content and privileged access, and I noticed two things while doing a
bit of web surfing as background. First, a rather long, though from what I’ve
read quite good, piece on narrow content has just been published in the Stanford Encyclopedia by Curtis
Brown. Secondly, as I remember John Hawthorne telling me years ago, it is
possible to get arthritis in the thigh. I know you shouldn’t trust everything, you read on the web, but
scroll down these definitions of types of
arthritis until you get to Fibromyalgia. If you
can’t be bothered following the link, the text is: “Usually affecting women, fibromyalgia is a condition that affects the muscles at
their attachments to bones.” I don’t know about you, but I’d say that’s
something that one could have in one’s
thigh. For more details, see these links.

Say your preferred account of the a
priori is that “S is a priori iff it knowable just on the basis of
one’s understanding of S”, as Stephen Yablo suggests in his paper in the
Gendler and Hawthorne volume. And say that you also think, not unreasonably,
that understanding the logical connectives just means finding their elimination
and introduction rules primitively compelling. And say that you also think (as
I’m not sure that I do) that the relevant rules are those for a Gentzen style
single conclusion natural deduction system. So the introduction and elimination
rules for ® are
given by the equivalence of the following two sequents.

(1)      S,
A: B

(2)      S:
A ® B

I use S as a variable over pluralities
of propositions, A and B as variables over propositions, and :
for the consequence relation. Nothing above is utterly unreasonable, and indeed
everything is close to majority opinion amongst the relevant theorists, though this
being philosophy nothing in uncontroversial. Now it is well known that these
rules do not let us prove (3)

(3)      ((p ® q) ® p) ® p

(3) can be proven using the standard rules
for the connectives, but you have to use the rules for negation, not just the
rules for ®.

If you accept all the assumptions in the
first paragraph, then you have a dilemma. Either (3) is not a logical truth,
despite being a truth-functional tautology, or some logical truths are not a
priori. Dummett accepts all of the initial assumptions (I think) and
concludes that (3) is not a logical truth. Yablo I think is committed to (3)
not being a priori, despite being a logical truth. This isn’t an unintelligible
position, but it might be grounds for rejecting his account of what it is to be
a priori.

Simon Blackburn doesn’t much like Steven
Pinker’s most recent book on nativism. The most amusing part (among many)
is where Blackburn starts using plot details from The Flintstones to
work out what the world was like in hunter-gatherer days, and hence derive some
quick’n’dirty results in evolutionary psychology. But the most alarming part
was when Blackburn said, “it is not for its cultural history that people are
buying Pinker’s book in alarming numbers, but for the promise of a new
synthesis”. Alarming?! Pinker’s book is over the top, and as Blackburn
points out the enemy under attack is a strawman even by high school debating standards,
but I don’t know that makes it alarming that his book sells well. If only more
academic books would do so.

Simon Blackburn doesn’t much like Steven
Pinker’s most recent book on nativism. The most amusing part (among many)
is where Blackburn starts using plot details from The Flintstones to
work out what the world was like in hunter-gatherer days, and hence derive some
quick’n’dirty results in evolutionary psychology. But the most alarming part
was when Blackburn said, “it is not for its cultural history that people are
buying Pinker’s book in alarming numbers, but for the promise of a new
synthesis”. Alarming?! Pinker’s book is over the top, and as Blackburn
points out the enemy under attack is a strawman even by high school debating standards,
but I don’t know that makes it alarming that his book sells well. If only more
academic books would do so.

There’s been a David Chalmers sighting on Instapundit. Traffic
to his site should crash the University of Arizona system by mid-afternoon.

On a related note, my Sims
paper, which I first started thinking about after reading something else on
Instapundit, got a positive sounding revise and resubmit today! Whether this
means a publication, I don’t know, but it is progress.

On principle I’d rather not link to sites as
conservative as Instapundit, but it’s a bit childish to not mention things that
are philosophically interesting just because they may be, to a greater or
lesser degree, politically distasteful. (Just reading that over, it seems to
imply that I have childish principles but I’m ‘mature’ enough to disobey them.
Not the best state to be in perhaps, but not the worst either.)

There’s been a David Chalmers sighting on Instapundit. Traffic
to his site should crash the University of Arizona system by mid-afternoon.

On a related note, my Sims
paper, which I first started thinking about after reading something else on
Instapundit, got a positive sounding revise and resubmit today! Whether this
means a publication, I don’t know, but it is progress.

On principle I’d rather not link to sites as
conservative as Instapundit, but it’s a bit childish to not mention things that
are philosophically interesting just because they may be, to a greater or
lesser degree, politically distasteful. (Just reading that over, it seems to
imply that I have childish principles but I’m ‘mature’ enough to disobey them.
Not the best state to be in perhaps, but not the worst either.)

The Binding Argument

Jason Stanley claims that
the following kind of argument is generally sound.

(1)      It is possible to interpret  “In every room in John’s house, every bottle
is in the corner” as being true iff in every room in John’s house, every bottle
in that room is in the corner.

(2)      Hence the logical form of “Every bottle is
in the corner” includes a quantifier domain restrictor, as it might be the
property being in this room, which is bound by the outermost quantifier
in the longer sentence.

This is a move in a dispute between those
who say that “Every bottle is in the corner” expresses the proposition that
every bottle whatsoever is in the corner, or perhaps expresses no proposition
at all, and only conveys the proposition that every bottle in this room is
in the corner. Jason thinks that the restriction to bottles in this room is not
pronounced, but it is articulated – it is a genuine feature of the syntax of
the sentence, and of the proposition that sentence expresses.

This proposal has come in for some criticism
recently, especially in Ernest Lepore and Herman Cappelen’s paper in the most
recent Analysis.
Let me add my own little objection, mostly due to a conversation with Europa
Malynicz. (The examples are very close to ones she suggested, as I guess is the argument, but the usual disclaimer that all the faults are mine applies.) (3) is a well-formed sentence, and the quantifier here does not feel
like a null quantifier. It is just the kind of thing that could be said by a
rather cautious traveller.

(3)      Everywhere
I go, I only drink bottled water.

Jason’s argument is that the quantifier here
is not a null quantifier, so it must be binding something, so the embedded
sentence must have syntactic element that is bindable. Hence I guess (4) really
expresses the proposition (5).

(4)      I
only drink bottled water.

(5)      I
only drink bottled water at place x.

But it is quite implausible that this is
what (4) means. I don’t think this is implausible for the reason Lepore &
Cappelen think it is implausible, that it puts too many variables into (4).
Maybe they are there, maybe they aren’t. I think it is implausible because it
suggests, falsely, that one could use (4) when at place x to express the
proposition that one only drinks bottled water at that place, even though you drink
tap water anywhere else. So I could use (4) here and now to express the
proposition that in Providence I only drink bottled water.

This argument needs one qualification. In
some contexts it is possible to use (4) to express the proposition that I only
drink bottled water in Providence. If I have just been asked a question about
Providence and especially its water quality, and I respond with (4), it will be
natural to view my utterance as being elliptical for the claim that I only
drink bottled water in Providence. But what Jason needs (I think) and what he
can’t have (I also think) is a situation where I could use (4) to express that
proposition without it being simply elliptical.

David Fickling makes a few sound points here
about the quirks
of the Australian character, but there are a couple of errors that suggest
he might be new to the Australian beat. For one thing, Ned Kelly was more the
bank-robbing than the sheep-shearing kind of larrikin. (I guess nowadays he’d
be thought of as a terrorist by some.) For another it’s a wee bit more than 200
miles from Brisbane to Sydney. These kinds of errors won’t happen once you’ve
been in the country long enough.

There’s something rather nice about having
one’s national identity be based around partying, even if it is grating to see
a conservative like Howard try and adopt that for his own image. In general I
think Australians are doing rather better at the pursuit of happiness thing
than Americans, despite not having deigned to adopt it as a constitutional
policy. I hadn’t realised quite how distinctive the larrikin figure is. Maybe
that’s why no one’s been able to figure out the point of the pranks
paper.

On a different topic, everyone who has
responded has had the same result in the vagueness
experiment. I can’t say what that is without biasing the experiment even
more than I already have, which would be a bad thing. So take the
experiment yourself and I’ll let you know how it all turns out.

Probably very few readers here are
interested in the minutiae of Victorian opinion polls, but I thought this was particularly
striking. The Age’s poll taken
last weekend for the upcoming Victorian state election has some surprising
number. One surprising, and too good to be true, number is that Labor is ahead by 22 points on two-party preferred. If only
that were true. But what seemed more interesting were the numbers about the
Liberal Party’s speeding policy. Traditionally in Australia, like in most other
places, if you were within 10% of the speed limit you wouldn’t get ticketed.
The Labor government abandoned this policy, directly
police to ticket anyone who was measured to exceed the speed limit by more than
the margin of error of the radar detectors (about 3 km/h). The Liberals claimed
this was just a revenue raising policy (which was probably true, even if it has
a nice public safety side effect) and promised to abandon it.

Now I’d expect this would be a vote winner
for the Libs. And I wouldn’t have expected much of a demographic
split in the results, except maybe a slightly higher support for it in
non-metro areas. Well, that was all mistaken. Here are the relevant numbers,
with the support for the policy listed first.

Overall: 33-59
Metro: 33-59
Rural: 35-60
Men: 44-49
Women: 23-69

Good thing I’m not a political advisor, huh?!
The last two lines were a complete shock though. I don’t recall seeing that big
a gender gap on any polling question in Australia for a long time. Even on
issues where one traditionally expects a gender gap, like child care or
abortion rights, there’s usually nothing this big. In fact it’s very rare for an
Australian poll to get numbers this lopsided on any partisan question. Speed
limits are obviously a very minor issue, but maybe it signals a wider gulf in
attitudes towards the proper balance between safety and liberty. If I was a
political scientist looking at Australians’ attitudes about the role of
government in setting this balance, I’d start polling on a few other related
issues to find out.