Narrow content and
I assume (at least here) that there is such
a thing as narrow mental content. And I assume that all mental representations,
not just beliefs, have narrow content. In particular, I imagine that conceivings or imaginings have narrow content, and that
often this content differs radically from the wide content of those very same conceivings or imaginings. So if I imagine the world having
atomic stuff in its rivers, lakes and oceans, the narrow content of my
imagination is that water is atomic, and the wide content of it is that there
is no water in the rivers, lakes and oceans.
So something distinguishes narrow content
from wide content. What might it be? An obvious solution is that I have
privileged access to the narrow content of my imaginings, but not to their wide
content. Some people claim I do have privileged access to the wide content of
my mental states – this position is bizarre even by philosophical standards, so
Iíll ignore that here. I think privileged access doesnít produce a distinction
between narrow and wide content because we donít have privileged access to
narrow content either. Hereís an example to prove this.
Cian, Hilary and Ted are all philosophy
professors. Today they are all, at different spots along Highway 95, teaching
about the identity of indiscernibles, and Max Blackís
objection to it. So they are all imagining a world consisting of naught but two
duplicate atoms. They arenít thinking about this right now, but they all have
quite different views about whether (1) is true in the world they are
imagining. And if asked they would tell you what they think of whether (1) or
(2) are true in the world at the drop of a hat.
(1)††††† $x$y"z (z = x ŕ z = y)
(2)††††† ~$x$y"z (z = x ŕ z = y)
Ted thinks that (1) is false in that world.
He thinks that there are three objects in the world, the two atoms and their
fusion, so (1) couldnít be true. Cian thinks that (1) is true in the world,
because atoms never fuse, so these atoms donít fuse. And Hilary thinks there is
no fact of the matter as to whether (1) is true in such a world. All of them
would, if asked, think similar things about the contents of their imaginings.
Ted thinks that (2) is part of the content of what he is imagining, Cian thinks
that (1) is part of the content of what he is imagining, and Hilary thinks that
there is no fact of the matter as to whether it is part of the content of what
he is imagining is that (1) is true or(2) is true. Note that while there are
other attitudes one could take towards the question of whether (1) and (2) are
part of the content of what is being imagined, Cian, Ted and Hilary presumably
exclude the range of attitudes one could take towards the question of whether
the two atoms in question have a fusion.
If that example is possible (and I am pretty
confident it is, being so close to actual examples) then the following
principles cannot all be true.
Privileged Access (SPA) – For all imaginings i and all propositions p,
if x imagines i, and xís introspective
faculties are properly functioning, then x can know by introspection whether
p is part of the narrow content of i.
(DEK) – If x believes that ōp, then x does not know that p.
the Logical Constants
(SLC) – Any sentence consisting entirely of logical vocabulary (quantifiers,
connectives, variables and identity) is semantically stable.
implies Common Content
(SCC) – If a sentence s is semantically stable, then s is part of
the narrow content of i iff s is part
of the wide content of i.
Necessity (MN) – If there is a world w in which there exist two atoms and nothing else
and those two atoms do not have a fusion, then in any world in which there
exists two atoms and nothing else, those two atoms do not have a fusion.
Closure of Content Under Immediate
(CCI) – If x explicitly imagines that
p, and q is an immediate consequence of p, then q is part of the wide
content of what x imagines.
Immediacy of Mereological Facts (IMF) – If it is a necessary
truth that two objects have a fusion, then the existence of that fusion is an
immediate consequence of the existence of those objects. Similarly, if it is a
necessary truth that they do not have a fusion, or that it is indeterminate
whether they have a fusion, then the non-existence, or indeterminate existence,
of that fusion is an immediate consequence of the existence of those objects.
Hereís the argument that these claims are
not compatible. First, assume that Ted is right and the atoms have a fusion, so
(1) is false. By (MN), it is either necessarily true if there are two atoms in
the world and no other distinct objects, then (2) is true. By (IMF), (2) is an
immediate consequence of the existence of those atoms. By (CCI), (2) is part of
the content of the imagining. By (SLC), (2) is semantically stable. So by
(SCC), (2) is part of the narrow content of the imagining. By (SPA), Cian knows
that (2) is part of the narrow content of what he is imagining. But Cian
believes that (2) is not part of the content of the imagining. He believes, in
fact, that he is imagining something coherent and that part of its content is
(1). So by (DEK) he does not know the content of what he is imagining. If Cian
is right and the atoms donít have a fusion, a similar argument shows that Ted
does not know the content of what he is imagining. If Hilary is right, then
both Cian and Ted do not know what they are imagining, because they believe
that one of (1) and (2) is part of the content of whatís being imagined.
The above argument assumes that Ted and Cianís introspective faculties are properly functioning.
This may or may not be true in reality, but thereís no reason to assume it is
not true in the example. One of them has a false mereological belief, but this
can hardly be sufficient to make their introspective faculties dysfunctional,
unless we think that true philosophical beliefs are required for introspection.
Most of the other assumptions here apart
from (SPA) should be fairly self-explanatory, but I want to make brief notes
about my notion of Ďimmediate consequenceí and about how Iíve phrased
Sometimes the content of what we imagine
goes beyond a simple description of the state of imagining. If I imagine
holding three apples in my left hand, and two apples in my right hand, then I
imagine that I am holding five apples. On the other hand, imagination is not
closed under entailment generally. If I imagine holding three apples then I do
not imagine holding a number of apples n
such that xn + yn = zn has
no solutions in integers x, y, z.
More generally, we do not want every mathematical truth to be part of the
content of every imagining. There is obviously quite a bit of work to be done
to specify just which entailments Ďget iní to the content of the imagining. I
assume that one of the crucial factors that determines whether q is part of the content of an imagining
that is explicitly an imagining that p,
is how many steps it takes to infer q
from p in a properly designed proof
theory. Assuming (as might be contested) that the true theory of mereology
licences particular rules of proof, (IMF) will be more or less a
It seems clear that it will often be
indeterminate whether q is an
immediate consequence, in this sense, of p.
But that is no challenge to (CCI). For all it shows is that it will often be
indeterminate whether q is part of
the content of what is being imagined. And we know full well that the content
of a particular act of imagination is often indeterminate.
It is not entirely common to provide a
quantified version of privileged access. It is more common to write things like
the following (from McLaughlin and Tyeís Phil Review paper)
When our faculty
of introspection is working properly, we can know what we are thinking by
Of course, Iíve extended this to imaginings,
if that wasnít meant to be included already in Ďthinkingí. But I donít think
the use of quantifiers does more than spell out what is involved in McLaughlin
and Tyeís definition. In general (as Lewis says in
ďWhether ReportĒ) know wh- claims are quantified
claims. If I know whoís coming to the party, I know for each person whether
they are coming to the party. If I know which teams are in the playoffs, I know
for each team whether they are in the playoffs. And if I know what the governor
is doing, I know for each action whether the governor is performing that
action. So by analogy I think that if I know what Iím imagining, I should know
for every proposition whether I am imagining that proposition.
There is a weaker interpretation of know wh- claims that might be more appropriate here. Imagine
that the playoff teams are the Cats, the Dogs, the Rabbits and the Kangaroos,
and for each of those teams I know that they are in the playoffs. But there are
other teams, not in the playoffs, such that I donít know whether they are in.
Perhaps I donít know how many teams make the playoffs, or perhaps Iíve
forgotten which teams there are, so I donít have propositional attitudes
towards them. Then thereís still a sense in which I know which teams make the
playoffs, for it is true for each team making the playoffs that I know it makes
the playoffs. A similar account can be given of privileged access. I know what
Iím imagining iff for every proposition that I am imagining, I know that I am
If we adopt this account of privileged
access, and we adopt Hilaryís account of the two-atom world, then possibly we
can avoid the argument above. Even if, for example, Ted thinks that (2) is part
of the content of what he is imagining, but it is not, that is no threat to
privileged access under its current interpretation, for privileged access only
has implications for the content of his imagination.
It might be worried that even if we adopt
all this, there will still be propositions that are part of the content of what
is being imagined that Ted believes are not part of its content. For instance,
it will be part of the content of the imagining that it is indeterminate
whether (1) is true. But there are a few moves that will block that position.
First, it might be denied that we can genuinely form propositions using an
Ďdeterminatelyí operator. Secondly, Hilaryís position might be altered so that
it is indeterminate Ďall the way upí, whether (1) is true in the world in
question. That is, no proposition formed by prefixing strings of determinately
operators and negations to (1) is determinately true in that world. It is not
so hard to build formal models such that this is the case as long as we put few
formal constraints on the determinately operator, although it is sometimes hard
to see the philosophical motivation for the position.
The real objection to this way of saving
privileged access, I think, is that Hilaryís position is incoherent. (1) and
(2) recall, are constructed entirely out of logical vocabulary. As Ted Sider
has stressed in a few places, it is implausible that such claims are
indeterminate. Indeterminacy arises in normal language because there are too
many competitors to be the meaning of a particular term, and considerations of Lewisian naturalness do not settle the issue. But this is
not the case when a sentence is constructed entirely from logical vocabulary,
for there are very natural candidate meanings for the logical terms. If the
only way out for the defender of privileged access with respect to narrow
content is to claim that (1) is indeterminate, then things look very bad indeed
for privileged access.
Posted by Brian Weatherson at 6:26 pm
The results of the vagueness experiment were
quite encouraging. Hereís 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 itís a small sample, but itís 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 donít have the references with me, but Iíll
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.
Posted by Brian Weatherson at 4:58 pm
Say your preferred account of the a
priori is that ďS is a priori iff it knowable just on the basis of
oneís understanding of SĒ, 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
Iím 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 ģ are
given by the equivalence of the following two sequents.
A ģ 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 ģ q) ģ p) ģ 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 ģ.
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 isnít an unintelligible
position, but it might be grounds for rejecting his account of what it is to be
Posted by Brian Weatherson at 2:19 pm
Thereís 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 donít know, but it is progress.
On principle Iíd rather not link to sites as
conservative as Instapundit, but itís 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 Iím Ďmatureí enough to disobey them.
Not the best state to be in perhaps, but not the worst either.)
Posted by Brian Weatherson at 3:23 pm