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21 December, 2002

I’m off for a few

I’m off for a few days while I head over to
Amsterdam for Christmas. I will be back early in the New Year with hopefully some slightly more polished things to say about modus ponens failures, Dr. Evil and countable additivity, privileged access and narrow content, and, it being unavoidable in January and February, philosophical gossip. (Though I can’t promise that the gossip will be polished – I half think I should promise that it will not be.) Happy holidays all, and good luck to everyone going on
the job market!

Posted by Brian Weatherson at 9:23 pm

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I was updating a few

I was updating a few links when I discovered
something I didn’t really expect to find out during a regular webcrawl. If you crawl
on over to John
Hawthorne’s CV
, and scroll not too far down, you’ll see that he has a paper
forthcoming in The Monist, co-authored
with me. This is very
exciting news, especially to me!

Despite the somewhat incredulous tone of the last
paragraph, I was more or less aware that the
paper was more or less likely to appear,
so it wasn’t like I had a paper accepted at a journal with no knowledge of it
(and in fact I even have a draft
of the paper available
) but it still wasn’t exactly how I expected to get
confirmation of another publication. I wonder if news of its acceptance is official
enough to put on this year’s annual report?

In other co-authoring news, it looks likely that
the paper Andy Egan and I wrote on pranks
will be presented at the Symposium
on Theoretical and Applied Ethics
at LSU next February. I think it’s my
duty to play this up for all it’s worth – it’s only fair that adding a few
jokes to a good idea for a paper that someone else (i.e. Andy) had gets me to
count as an ethicist. I’m not sure why it’s fair, but
now that I’m an Ethicist, I can just say that it’s fair and that’s already got
some evidential weight.

Posted by Brian Weatherson at 6:43 am

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20 December, 2002

Well, here’s something you don’t

Well, here’s
something you don’t see every day. The review in Notre Dame Philosophical
Reviews of Beyond
Rigidity
takes Soames to task for not being Millian enough. That’s the kind
of thing that happens in any field when you stake out an extreme position early
on, any subsequent movement back towards the middle ground will be interpreted
as betrayal by someone ;)

Posted by Brian Weatherson at 1:55 am

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19 December, 2002

There are about a million

There are about a
million other things I should be doing right now, so it’s probably time to say
something more about Dr. Evil. I
knew that deep down one of the reasons I disliked approaches to probability
based on principles of indifference was that they threatened to collapse the
important distinction between risk and uncertainty. What I hadn’t realised,
until very recently, was Adam’s argument for his indifference principle involves
just such a collapse at one point.

First some
background. To my mind, what should have been a very important discovery in
early 20th century work on probability was that there is a
distinction between risk and uncertainty. Here’s how Keynes introduces the
concept of uncertainty in an article from 1937 (“The General Theory of Employment”
Quarterly Journal of Economics).

By ‘uncertain’
knowledge, let me explain, I do not mean merely to distinguish what is known
for certain from what is only probable. The game of roulette is not subject, in
this sense, to uncertainty; nor is the prospect of a Victory bond being drawn.
Or, again, the expectation of life is only slightly uncertain. Even the weather
is only moderately uncertain. The sense in which I am using the term is that in
which the prospect of a European war is uncertain, or the price of copper and
the rate of interest twenty years hence, or the obsolescence of a new
invention, or the position of private wealth owners in the social system in
1970. About these matters there is no scientific basis on which the for any
calculable probability whatever. We simply do not know. Nevertheless, the
necessity for action and decision compels us as practical men to do our best to
overlook this awkward fact and to behave exactly as we should if we ha behind
us a good Benthamite calculation of a series of
prospective advantages and disadvantages, each multiplied by its appropriate
probability, waiting to be summed.

I think this is
all incredibly important, and any theory that ignores the distinction between
what is probable and what is genuinely uncertain is mistaken. Decisions based
on what is probable or improbable are grounded at least in well understood
principles about risk; decisions grounded in what is genuinely uncertain are
not. And I’m inclined to think that any theory that says that an agent’s attitude
to some uncertain propositions can be expressed by a single probability function
does ignore the distinction. This is especially true for theories that say this
about ideal agents.

This is hardly an
original thought. It was the basis of Keynes’s theory of probability outlined
in his dissertation of 1909, which eventually became the Treatise on Probability of 1921. Keynes had the probability, which
for him was just rational credence, of an uncertain proposition be a
non-numerical value. Ramsey criticised this on the grounds that probability
values are meant to enter into computations, according to the theory we can add
and multiply them, for example, and we don’t know how to add and multiply
non-numerical values. In my dissertation, I proposed that the theory that holds
that the credal states of a rational agent can be
represented by a set of probability functions rather than just a single
probability function could capture all of Keynes’s insights without being
vulnerable to Ramsey’s objection. This is not a new theory, it has been
discussed by Isaac Levi (“Ignorance, Probability and Rational Choice” 1982) Richard
Jeffrey (“Bayesianism with a Human Face” 1983), Bas
van Fraassen (“Figures in a Probability Landscape”
1990) and extensively by Peter Walley (Statistical Reasoning With Imprecise
Probabilities
1991), and in Walley’s case there’s
some connection drawn to Keynes’s work, so I still don’t want to make any dramatic claims to originality.

We draw a
connection between Keynes’s theory and these new theories by identifying the
probability of a proposition p as a
function from members of S, the set
of probability functions that represents the credal
states of an ideal agent, to [0, 1], where the value of the function is
the value of P(p) according to each P in
S. For most purposes we can simplify
this by saying the probability of p
is the range of that function. Then p
has a numerical probability in Keynes’s sense iff its probability is a singleton,
it is uncertain otherwise. Arguably the range of the function should always be
an interval (well, I argue for this at any rate) and if so we can say p is more uncertain the larger that
interval is. This gives us a concept of comparative uncertainty, and with that
we can say that everything Keynes
says in the above quote is true.

Now one of the
surprising things about interpreting Keynes’s term ‘uncertainty’ this way is
that a proposition can become more uncertain as we acquire more evidence about
it. Keynes seemed to think this was impossible, but here I think he was just
mistaken about the behaviour of some of his own concepts. (We all make
mistakes.) Here’s a case where just that happens. (As it turns out, it’s a case
I’ve written about. See my “Keynes,
Uncertainty and Interest Rates
Cambridge
Journal of Economics
2000).

I’m watching a
roulette game going on, and in particular paying close attention to one player,
called Kim. It’s a crowded room, so I can’t see the roulette wheel, or the
board where bets are placed, but I can see the croupier, and I can see Kim. I see
Kim place a bet on either red or black (I can see that from where she’s leaning
over the table) but I can’t tell which. And I have no evidence that tells me
one way or the other. I know from prior observation that this is a fair
roulette wheel. And I can see that the croupier is about to spin the wheel. Now
consider the following propositions. (For simplicity we’ll assume it’s a
roulette wheel with no green slots – this makes the example rather unrealistic,
but simplifies the computations no end without having any major philosophical
costs.)

kr = Kim bet on red
kb = Kim bet on black
br = The
ball lands on red
bb = The ball lands on black
 h
= Kim is happy in a few seconds

At this stage, I
think I can assign numerical probabilities in the following cases:

1. P(hkr Ù br) = 1
2. P(hkr Ù bb)
= 0
3. P(hkb Ù bb)
= 1
4. P(hkb Ù br) = 0
5. P(br | kr) = ½  
6. P(bbkr)
= ½
7. P(br | kb) = ½
8. P(bbkb) = ½

Also note {kr, kb} and {br, bb} are partitions, and my credences reflect that (e.g. P(kr Ú kb) = 1.)

What I can’t do is
assign a numerical probability to kr or to kb, they
are just uncertain. Perhaps they’re not so uncertain that their probability is
[0, 1] – that’s what happens when a proposition is completely uncertain,
but they are uncertain to a degree.

Now I wait a few
seconds, and see that when the wheel stops, Kim is happy. So I update my
credences accordingly. What should my new credences be? Some may suggest that
my credences in br,
bb and bg should be unchanged, because I
have no new evidence that is relevant to their assessment. But this must be
false. For if it were true, I could do the following computations (11 and 12
are background, the new assumptions come in at 13 and 14).

11. P(br) = ½ from 5 and 7
12. P(bb) = ½ from 6 and 8
13. P(br | h) = ½ by assumption
14. P(bb | h) = ½
by assumption
15. P(kr | h) = P(kr Ù br | h)
by 2
16. P(kr Ù br | h) = P(br | h) by 4
17. P(kr | h) = ½ by 13, 15 and 16
18. P(kb | h) = ½
by identical reasoning to the last three lines
19. P(br | Øh) =
½ (since by 11 and 13 br
and h are independent)
20. P(bb | Øh) = ½ (since
by 12 and 14 bb and h are independent)
21. P(kr | Øh) =
½ (by equivalent reasoning to 15-17, with just the relevant appeals changed)
22. P(kr) = ½ by 17 and 21

And 22 is just
what we said we couldn’t conclude, because we weren’t in a position to assign
numerical probabilities to kr and kb. So the
simple assumption that we shouldn’t change our credences in br and bb when we learn h must
have been mistaken. What should happen is that after learning h, br and bb should go from being not at all uncertain to being rather
uncertain, in fact exactly as uncertain as kr and kb were (and I guess still are).

This is contentious,
but I think that the same thing is going on in Adam’s main argument. (I.e. it’s
contentious that it’s the same thing.) Here are the main examples again.

TOSS&DUPLICATION After Al goes
to sleep, researchers toss a coin that has a 10% chance of landing heads. Then
(regardless of the toss outcome) they duplicate Al. The next morning, Al and the duplicate
awaken in subjectively indistinguishable states.

Adam wants to
argue that in this case when Al wakes up his credence in HEADS should be 1/10.
A crucial premise in the argument for this is that P(HEADS/HeadsAl
or TailsDup) (TailsDup is
the proposition that he’s the duplicate and the coin landed tails – you can
figure out the rest of the code from that) is also 1/10. And he argues for that
as follows.

COMA As in TOSS&DUPLICATE, the
experimenters toss a coin and duplicate Al. But the following morning, the
experimenters ensure that only one person wakes up: If the coin lands heads, they allow Al to wake up (and put the
duplicate into a coma); if the coin lands tails, they allow the duplicate to
wake up (and put Al into a coma)

Suppose that in the COMA case, Al
gets lucky: the coin lands heads, and so the experimenters allow him to awaken.
Upon awakening, Al is immediately in a position to assert “Either I am Al and
the coin landed heads, or else I am the duplicate and the coin landed tails”.
So when Al wakes up in the COMA case, he has just the evidence about the coin
toss as he would have if he had been awakened in TOSS&DUPLICATE and then been told [HeadsAl
or TailsDup]. So to defend (3)—to show that in the
latter case Al’s credence in HEADS ought to be 10%—it is enough to show that when
Al wakes up in the COMA case, his credence in HEADS ought to be 10%.9 Let me
argue for that claim now.

Before Al was put to sleep, he was
sure that the chance of the coin landing heads was 10%,
and his credence in HEADS should have accorded with this chance: it too should
have been 10%. When he wakes up, his epistemic situation with respect to the
coin is just the same as it was before he went to sleep. He has neither gained
nor lost information relevant to the toss outcome. So his degree of belief in
HEADS should continue to accord with the chance of HEADS at the time of the
toss. In other words, his degree of belief in HEADS should continue to be 10%.

Adam considers an
objection that Al’s memories should give him evidence that he’s Al, and hence given
HeadsAl or TailsDup, he
should have a very high credence in HEADS. He responds as follows:

That’s all
wrong. TRUST YOUR MEMORIES, AL makes the same mistake that TRUST YOUR MEMORIES,
O’LEARY does. While it is true that in the absence of defeating auxiliary
beliefs, one ought to trust one’s memories, when Al wakes up he does have defeating auxiliary beliefs. He is sure that—whatever
the  outcome of the coin toss—someone was to wake up in just the
subjective state he is currently in. As far the outcome of the coin toss goes,
the total evidence Al has when he wakes up warrants exactly the same opinions
as the total evidence he had when he went to sleep.

This is what I
think is wrong. Adam is concerned to reject the line of reasoning that memories
provide evidence, because he thinks that they’re really only q-memories and
they don’t count for very much. But this ignores a crucial point I think. Al
doesn’t know whether his memories are real memories or mere q-memories. But
Adam thinks that he can assign a very precise credence to their being real: in
this case exactly 1/10. I don’t think this is true, and I think the only way
you’d come to infer it is by more or less presupposing an indifference
principle.

I’d put the
dialectic as follows. Al has some memories. These are actually conclusive
evidence that HEADS, though of course Al doesn’t know this. In fact he has no
idea whatsoever what the evidential force of those memories is. But that doesn’t
mean he should act as if they have no evidential value at all – if he does he’s
drawing a substantive conclusion, that q-memories have no evidential value from
premises that are essentially worthless, that he has no idea how much
evidential worth they have. (Substantive and, we might as well note, false.) He
should act like he has no idea how valuable the evidence is, just like in the
casino case I should act like I have no idea what the evidential force of h is. In that case I go from regarding br as risky to
regarding it as uncertain. I think Al’s attitude towards HEADS should be the
same in COMA. And if it is, the argument for the indifference principle in the Dr. Evil
paper fails.

Posted by Brian Weatherson at 4:18 pm

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18 December, 2002

I’ve had a few complaints

I’ve had a few complaints about the way
pictures work on the blog, so I’ve deleted the posts
involving graphics. So from now on it’ll just have to be me talking. That might
not be a good thing, but we’ll see.

Posted by Brian Weatherson at 1:12 pm

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16 December, 2002

In both my recent notes

In
both my recent notes on indifference principles, the comments on Nick Bostrom’s
computer simulation paper and Adam Elga’s Dr Evil paper, I’ve mentioned that
the proponents of these theories assume a theory of evidence that is
intuitively quite plausible, and may have been the mainstream view not long
ago, and may even be ultimately true, but which is not very popular among
philosophers of perception these days. I didn’t think much followed from this,
save perhaps that those presupposing a theory that is widely viewed as being
hopelessly befuddled owe us an explanation as to why they are sticking with it.
And in this little endeavour I have been utterly unsuccessful. This could be
because my heart hasn’t really been in it due to underlying internalist sympathies,
or because I’m wrong that the indifferentists need to address this, or because
I’m no good at convincing people of things, or because of any number of other
reasons. Suffice to say that in some circles, the idea that when we look at a
hand we have evidence of an epistemically different kind to a brain-in-a-vat
that is stimulated in the way our brains are when we look at a hand is not
viewed as being particular plausible.

When
in trouble in a case like this, call in the heavy hitters. Alex Byrne has a paper
forthcoming in Noûs in which he
argues that the sceptical
paradoxes are not really deep paradoxes
. By this he means, in part, that
there isn’t anything like a compelling argument for scepticism. And this is because
he thinks that the canonical arguments for scepticism turn out to rest on very
implausible premises on close inspection. One of those premises is that
perceptual evidence underdetermines what the external world is like: we could
have just this evidence and be dreaming (or a brain-in-a-vat, etc.). This,
Byrne thinks, can be shown to be false simply by carefully reflecting on the nature
of evidence. The whole paper is worth reading, but let me just extract a few
choice quotes.

          The
known (evidence) proposition e has yet to be identified. [Byrne has just
argued that evidence should be propositional. The challenge is to determine
whether there is any candidate to be e that is compatible with
thorough-going external world scepticism.]The candidates may be divided into
two classes. The first—class I— consists of propositions about S’s sense-data,
ideas, impressions, phantasms or other queer entities allegedly “given” in
experience. The second—class II—consists of propositions about how things look
or (visually) appear to S (cf. the first paragraph of this section [not
excerpted here.]).

          It
is quite doubtful that (trivial exceptions aside) any propositions in class I
are true, a fortiori known; they may accordingly be dismissed. This
would have sounded dogmatic as recently as the first half of the twentieth
century: it is only in the last fifty years or so that the deep flaws in what
used to be called the “representative theory of perception” have become
gradually visible. Admittedly, not everyone agrees that the theory rests on a
soggy bog of error: in one form or another, it still has its defenders. However,
it is unnecessary here to rehash the argument: because we are playing the first
sceptical game, the sceptic must steer clear of philosophical controversy.

          That
leaves the members of class II: propositions about how things look or appear to
S—in other words, certain propositions about S’s mental states.
But because the representative theory of perception is off-limits, there is
very little motivation for thinking that one’s knowledge of the external world
rests on a foundation of knowledge about one’s own psychology…

          Propositions
about how things look or appear to S can be divided into two types. The
first—type IIE—comprises external world propositions,
because they entail the existence of o: that o looks square to S,
that it appears to S that o is square, etc. Hence, propositions
of type IIE, despite not entailing p, and perhaps being
known by S, are quite unsuitable candidates to be e. For e is
not supposed to be an external world proposition.

          The
second—type III—comprises those propositions about how
things look or appear to S that are not external world propositions (or
so we may suppose): that it appears to S that (some x) x is
square, that it appears to S that the F is square (for various fillings
for ‘F’, e.g. ‘tile’, ‘pink thing’), etc. If e is to be found in
class II, it must be of type III.

          [I]t
is not plausible that e is a type III proposition.
First, these propositions have to be true; clearly we need not suppose
that it appears to S that the tile, or the pink thing, is
square. But is it even clear that it must appears to S that (some x)
x is square? If not, then since there are no better candidates, e is
not a type III proposition. Second, S believes e, and it is
quite unobvious why S, if he is to know p via his senses, must
have any beliefs about how things appear, let alone believe one of the
specific propositions under consideration. Suppose S is a conceptually
challenged animal who cannot entertain these comparatively sophisticated
thoughts about appearances; does this fact alone imply that S cannot use
his eyes to come to know that o is square?

Posted by Brian Weatherson at 11:40 pm

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Kieran Healy writes on the

Kieran
Healy
writes on the (slow-)growing controversy over the role of intuitions
in philosophy. For background, see the papers by Jonathan Weinburg et
al
here,
here
and here. (If you haven’t seen the survey results about intuitions on Gettier cases across cultural and social groups in these papers yet, you should. And prepare to be a little suprised.)
Kieran has a rather funny caricature of the way philosophers (or at least
metaphysicians) generally argue, but then goes off on a riff about why we
should care more about where intuitions come from.

In the meantime, you might be interested in looking at other writers, who
have explored the
idea
that our intuitions might have institutional
roots
; that culture might mold conceptions
of rationality
and thus deeply affect
how you think
; that classification
is a social process
which might have its origins in
material life
; and that although individual and social cognition interact in
complex ways
, getting socialized into a culture often implies subscribing
to its point of view
.

I’m
not sure how any of this undercuts the use philosophers make of intuitions. It
seems to me that even if we acknowledge all of this, there are still epistemological
and metaphysical reasons to use intuitions in philosophy. (You
mean you’ll be defending philosophy by using more philosophy?
Yeah,
well what did you expect me to use, chemistry or something?)

The
epistemological reason is that for each of these facts about intuition, we
could (I think) find an equally
disturbing fact about perception. How we see the world around us is affected by
the kind of culture we’re in, what we expect to find and so forth. But none of
that implies that we should stop trusting perceptions as a source of evidence,
provided we’re suitably careful about how we employ them. Of course, practically
nothing should stop us trusting perception as a source of
evidence; that way lies madness, if not philosophical
immortality
.

The
metaphysical reason is that intuitions are sometimes constitutive of the
concepts we’re aiming to analyse. Want to know what’s a house? Well, presumably
houses are things that satisfy the predicate “house”, or fall under the concept
HOUSE. And presumably the facts about what makes an object satisfy the
predicate “house” include facts about how the term “house” gets the meaning it
gets in the language we speak. And presumably those facts include facts about
the intuitions people have about houses. A similar story is probably true for
the concept HOUSE, though here there are some more prominent
dissenters
. Now it’s rather controversial whether a similar story could be
true if we replaced “house” with “item of knowledge”, or “rational belief”, or “mind”,
or “person”, or “just act”, or (I guess most controversially) “object”, but at
least for terms towards the left of that list, it seems plausible enough.

Posted by Brian Weatherson at 9:18 am

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Brad DeLong writes that he

Brad
DeLong
writes that he only just realised that there could be non-spectral
colours.

Until yesterday, it had never occurred to me that I could see colors that
weren’t in the spectrum—I had thought that all colors were somewhere in the
rainbow (or could be made from rainbow colors by darkening or lightening them).

But that is clearly false. Consider magenta. A magenta light plus a
green light equals a white light—all colors. But green is in the middle of the
spectrum. So where in the spectrum is magenta? Magenta is red and blue—the
complement of green. And nowhere in the spectrum is there a wavelength of light
that excites both the red-cones and the blue-cones but does not excite the
green-cones.

I was
going to write a comment saying just how magenta was possible, then I realised
I wasn’t exactly sure. Then I was going to link to a website that explained it
all clearly, until I realised I couldn’t find one. So if anyone could enlighten
me, or Brad, please write in!

Here’s
what I think happens, though I’m not entirely sure. The spectral colours are
colours produced by light of constant length. But we know there’s lots of waves
that do not have constant wave lengths. This is obvious for sound: you never
hear the sound of a trumpet, even a trumpet playing a ‘constant’ note, when you
just listen to waves of constant length. Magenta, I think, is one of the things
that happens when the light in question is not a wave of constant frequency.

But, that
doesn’t really say enough about what happens. I don’t know how the waves ‘mix’.
Is it that magenta light contains only photons of a constant frequency, but
some of them are around the typical frequency of red light and some of them
around the typical frequency of blue light? Or is it that individual photons
‘vibrate’ in some non-sinusoidal pattern, as the air does when two or more
notes are played? Or does this distinction not really make sense when we’re
dealing with light?

And
I’m not even sure this is the right story about magenta. I think it is, but for
all I’m certain of, magenta could be a contrast colour, like brown, that is
only apparent when there are other visible colours with which it contrasts.

Some
might think that it’s embarrassing how little I know about colours, but (a) if
I was going to be embarrassed by my ignorance there are many other things I’d
be embarrassed about first, and (b) since my department already has an expert on
colour
, the marginal value of my learning more is not very high.

Posted by Brian Weatherson at 7:33 am

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15 December, 2002

all the time

The most fun seminar I’ve been attending
this semester has been Jeff King’s seminar at Harvard on the
semantics/pragmatics distinction. (Hang on, isn’t that the only seminar you’ve
been attending? – ed.
Not at all, I’ve also been attending my own seminar,
and normally I’d think that would be the most fun seminar, because I get to
talk .) The main theme of the seminar has been a sustained
attack on theories that provide too small a role for semantics in a theory of
communication. (Some of the attack is presented in this
paper
co-written with Jason Stanley.) These theories usually say, in one
way or another, that the explanation for the success of certain kinds of
communication is pragmatic not semantic. (They often go on to say other things
too, but that’s the part that I’m most interested in.) So, to provide a
representative sample, consider two stories about how (1) gets the intuitive
truth conditions that it has.

(1)      If
Charlie drank ten beers and drove home, she broke the law.

Intuitively, (1) is true, because (1) is
true iff it is the case that if Charlie drank ten beers and drove home shortly
afterwards
, she broke the law, and that’s clearly true. How could (1) have those
truth conditions? Some theorists (including some time-slices of me) say that
the semantic content of (1) is just that if the conjunction (Charlie drank ten
beers Ù
Charlie drove home) is true then it is true that Charlie broke the law. The
intuition is explained by the truth of some more or less complicated pragmatic
theory, that somehow predicts that if “Charlie drank ten beers and drove home”
is normally only said if the events happened in that order, then (1) is
normally only said if Charlie’s drinking and driving in that order implies
that she broke the law. And of course there’s a story in Grice about why “Charlie
drank ten beers and drove home” is normally only uttered if the events occurred
in that order, even if the ordering is not part of the truth conditions.

Jeff doesn’t want to accept any of that. He
argues that the most plausible story about the semantics of (1) has the
intuitive truth conditions fall out as being the truth conditions. The first
point to note is that every sentence in English (and every other natural
language) is tensed, and the tenses are presumably part of the semantic
content. So “Charlie drank ten beers” has as its semantic content $t (is in the
past) (Charlie drinks ten beers at t). Importantly, the quantifier here is
restricted. Whether Charlie drank ten beers at Bill Clinton’s second inaugural doesn’t
really matter to the truth of an ordinary utterance of “Charlie drank ten beers”
unless for some reason we are talking about Clinton’s second inaugural.

Arguably (and
better philosophers than I have persuasively argued for this at length) every
sentence that isn’t in the present tense literally expresses a proposition that
contains a quantifier over time. And this quantifier isn’t present because of
some mysterious pragmatic process, it’s encoded in the verbs of the sentence,
just like most semantic content is encoded somewhere in surface structure. And
what goes for whole sentences goes for constituent sentences too, so to a first
approximation, the semantic content of (1) is (2).

(2)      If $t1 (Past t1)(Charlie
drinks ten beers at t1) and $t2 (Past
t2)(Charlie drives home at t2) then
$t3 (Past
t3)(Charlie broke the law at t3).

This isn’t much
help yet, but if we also hold (a) all three quantifiers here are restricted,
and (b) the restrictions are somehow co-ordinated, then we can have the
semantic content of (1) really be something like (3).

(3)      If $t1 (Past t1)(Salient
t1)(Charlie drinks ten beers at t1) and $t2 (Past
t2)(t2 is shortly
after t1)(Charlie
drives home at t2) then
$t3 (Past
t3)(t3 = t2)(Charlie
broke the law at t3).

This is obviously
very rough, because as it stands we’ve got variables appearing outside the
scope of the quantifers that bind them, but at least this is a workable
suggestion for how (1)’s truth conditions might match its intuitive truth
conditions. And to the extent that the argument for radical pragmatic theories was
premised on the assumption that there isn’t even a workable suggestion for how (1)’s
truth conditions might match its intuitive truth conditions, well those
arguments are looking fairly weak. (That would include some arguments I’d
previously adopted. Oh well – you can’t be right all the time.)

But not all the
examples of alleged separation between truth conditions and intuitive truth
conditions are handled with quite such ease.

(4)      If Hannah insulted Joe and Joe resigned,
then Hannah is in trouble.

As Jeff and Jason
note, (4) “seems to express the proposition that if Hannah insulted Joe and Joe
resigned as a result of Hannah’s insult, then Hannah is in trouble.” The
suggestions above about using restricted quantifiers over times won’t help
here, because they won’t get the causal link between Hannah’s (possible) insult
and Joe’s (possible) resignation into the proposition. So what can our heroes
do? They start by taking a rather sensible approach: when in trouble, ask What
Would Bob Stalnaker Do?

As Robert Stalnaker has argued, indicative conditionals normally
exploit a similarity relation that counts only worlds compatible with the
mutually accepted background assumptions as the most similar worlds for
purposes of semantic evaluation. … An indicative conditional is true if and
only if the consequent is true in every one of the most relevantly similar
worlds in which the antecedent is true. (King and Stanley, 48)

Well, I’m not
sure that’s exactly what Stalnaker said, for reasons that shall become apparent
presently. Anyway, applying this theory to (4) we get the following
conclusions.

Fortunately, however, there is no reason to give a non-semantic account
of the intuitive readings of (4). The relevant reading of (4) is simply
predicted by the semantics for indicative conditionals that we have endorsed.
In a context in which the speaker has in mind a causal relationship between
Hannah’s insulting of Joe and Joe’s resignation, all relevantly similar worlds
in the speaker’s context set in which Hannah insulted Joe and Joe resigned,
will ipso facto be ones in which Joe’s resignation is due to Hannah’s insult.
The speaker’s context set is what is epistemically open to her. This may include
worlds in which the conjunction holds, and there is no causal relationship between
the conjuncts. But given that she has a causal relationship saliently in mind,
such worlds will not be the most relevantly similar worlds in the context set.
So, if she has a causal relation in mind between the two events, that is just
to say that the similarity relation for indicative conditionals will select
those worlds in which there is a causal relationship between the conjuncts of
the antecedent as the most similar worlds to the world of utterance in which
the antecedent is true. So, the causal reading of (4) is predicted by the
simple semantics for the indicative conditional that we have adopted above.
(King and Stanley, 53, numbering adjusted.)

Imagine
that all the following circumstances obtain:

(5)      Jeff and Jason are right about the
semantics of indicative conditionals;
(6)      Hannah recently insulted Joe;
(7)      Shortly after that, Joe resigned
(8)      Joe’s resignation was not due to
Hannah’s insult
          (in fact it was because he just realised
he always wanted to be a lumberjack)
(9)      Hannah is not in trouble.
(10)    Someone uttered (4) knowing (6)
and (7), but not (8).

In
those circumstances, I think the utterance of (4) may well be true. All the
epistemically open scenarios in which (6) and (7) are true are ones in which
Hannah is in trouble. And according to Jeff and Jason, if the antecedent of (4)
is true iff (6) and (7) are true. So all (epistemically) nearby worlds in which
the antecedent is true are worlds in which the conclusion is true, so the
utterance of (4) is true.

But,
per hypothesis, the actual world is also a world in which (6) and (7) are true,
and hence the antecedent of (4) is true. And the actual world is a world where
the consequent of (4) is false. So the actual world is a world where the
premises of the following argument are true and the conclusion false.

If
Hannah insulted Joe and Joe resigned, then Hannah is in trouble.
Hannah insulted Joe and Joe resigned.
So, Hannah is in trouble.

So modus
ponens is not a valid argument form. Something may have
gone awry. There’s two problems here, both of them potentially serious. First, on
the formal semantics Stalnaker adopts for the indicative conditional, modus
ponens is valid, yet Jeff and Jason claim to just be implementing Stalnaker,
and they’ve ended up rejecting modus ponens. Either Stalnaker’s got his own
theory wrong, or Jeff and Jason have got him wrong.

Secondly,
THEY’RE REJECTING MODUS PONENS. Isn’t this something that should be a serious
issue? I mean, it’s at least somewhat surprising. Not as surprising as, say, the
fact that Rocky
VI is going to get made
. But surprising. Reading through Jeff and Jason’s
papers, and certainly listening to Jeff, one gets the impression that the
forces they’ve lined up against present views that are seriously flawed in some
way or other. I do hope that rejecting modus ponens is not the only
alternative to these positions.

Posted by Brian Weatherson at 1:45 am

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Sometimes I think it would

Sometimes I think it would be fun to run a critical
thinking course focussing on how to spot fallacious reasoning that only ever used examples drawn from the contemporary media.
Depending on how sensitive Brown students are, I could end up getting accused
of every sort of bias imaginable. (And the evidence is that some of them are much
too sensitive
.) But I don’t have such a course yet, so I’ll have to stick
to the blog. This is from the Washington
Post
.

"This Lott
story has continued primarily because of criticism from conservatives,"
said Whit Ayres, a Republican pollster based in Atlanta. “If the only people
raising doubts were Jesse Jackson and Al Sharpton, this story would have died
of its own weight several days ago. It’s the anguish from conservatives that
has kept the story going.”

Um, yeah. The hidden premise here that only
people who ‘raised doubts’ were Jesse Jackson, Al Sharpton and conservatives.
Given that extra premise, the conclusion that “it’s the anguish from
conservatives that has kept the story going” I guess would follow. And you
know, if you’re prepared to count Josh
Marshall
, Paul
Krugman
and Al
Gore
as conservatives, well the hidden premise still wouldn’t be true, but
at least there wouldn’t be a refutation I could find within five seconds of
scanning the NY Times.

Posted by Brian Weatherson at 12:13 am

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