Alex Byrne and Ned Hall

Department of Linguistics and Philosophy, MIT

0 Introduction

The textbook presentation of quantum mechanics, in a nutshell,
is this. The physical state of any isolated system evolves deterministically
in accordance with Schrödinger's equation until a "measurement"
of some physical magnitude M (e.g. position, energy, spin) is made.
Restricting attention to the case where the values of M are discrete,
the system's pre-measurement state-vector f is a linear combination,
or "superposition", of vectors f_{1}, f_{2},...
that individually represent states that have particular values m_{1},
m_{2},... of M; these vectors are eigenvectors of the (Hermitian)
operator corresponding to M. Thus f = a_{1}f_{1}+a_{2}f_{2}+...,
where a_{1}, a_{2},... are (complex) scalars. Typically,
more than one of the a_{i} are non-zero, which means that
the pre-measurement system does not have a "definite"
value of M. If f and f_{1}, f_{2},... are normalized
(i.e. have unit length) then, by the usual statistical algorithm,
the probability that the measurement results in value m_{i}
is |a_{i}|^{2}. On measurement, the state instantaneously
changes, or "collapses", taking on the measured value
of the magnitude; its state-vector thus becomes one of the corresponding
eigenvectors.[1]

For familiar reasons, this understanding of quantum mechanics is highly problematic. But for equally familiar reasons some sort of "collapse" postulate would appear necessary, or at least highly desirable. Without it, quantum mechanics will describe some systems (for example, voltmeters) without saying whether they have or lack some properties (for example, the property of pointing to `10'). And plainly voltmeter needles have particular positions. Thus, without a collapse postulate, it seems that quantum mechanics fails (radically) to describe the world completely and correctly.

However, perhaps that is too hasty. Maybe all we can be sure of
is that voltmeter needles *look to be* in particular positions,
not that they actually are in them. If we could somehow explain
how needles, despite not pointing in any one particular direction,
nonetheless *look that way*, then a simple "no collapse"
interpretation of quantum mechanics might be viable. Such an interpretation
is suggested by a famous, and famously obscure, paper by Hugh Everett
III (1957).

In a recent and deservedly much-discussed book, *The Conscious
Mind* (1996), David Chalmers argues that an "*independently
motivated* theory of consciousness" (349), namely his own,
can "lend support" (xv) to the Everett interpretation.[2]
Chalmers aims to settle crucial questions left open by Everett's
own account, thereby producing an interpretation of quantum mechanics
which, he claims, outranks all others in "theoretical virtue"
(356).

Chalmers' theory of consciousness "lends support" to
the Everett interpretation because, he thinks, it predicts "that
a superposed brain state should be associated with a number of distinct
subjects of discrete experience" (349)--for example that a
brain in a "superposition" of the states *perceiving
the needle at `10'*, and *perceiving the needle at `5'*,
supports two distinct experiencing subjects, one of whom perceives
the pointer as being at the 10 volt mark, while the other perceives
it as being at the 5 volt mark.[3] Thus, even though needles almost
never point anywhere, our perceptions invariably tell us otherwise.

Chalmers' argument is, then, of considerable interest. Although
it fails, it does so instructively, for two reasons. First, Chalmers
is one of the few proponents of an Everett-style interpretation
who attempts to provide it with a sustained positive argument, derived
from an explicit philosophical account of the mind-body relation.[4]
Seeing why his ingenious argument doesn't work will lessen the temptation
to appeal to the philosophy of mind in interpreting quantum mechanics.
Second, examining Chalmers' argument will show the deep and underappreciated
flaw in *any* Everett-style interpretation (to be distinguished
from the well-known objection that such interpretations cannot accomodate
the quantum mechanical probabilities). And some antidote is certainly
desirable, because Everett-style interpretations appear to be getting
increasingly popular (see, e.g., Lockwood 1996 and the accompanying
commentaries).

Section 1 sketches Chalmers' account of the relationship between consciousness, cognition, and the physical. Then, in section 2, we explain Chalmers' argument that, given his theory of consciousness, the simple no-collapse interpretation can explain why we perceive the world as containing needles at particular positions, etc. We divide this argument into three phases. The first phase is an argument for one major premise. The second phase is an argument for another major premise. And the third phase puts the two major premises together in an attempt to draw the desired conclusion. In sections 3, 4, and 5, we critically discuss, respectively, these three phases. Although Chalmers has failed to establish his Everett-inspired interpretation, there remains the question whether anything resembling it should be taken seriously. The answer is "no": section 6 exposes the deep flaw in such interpretations. Section 7 sums up.

1 Conciousness, cognition, and the physical

By `consciousness', Chalmers means what Ned Block (1995) has called `phenomenal consciousness': a phenomenally conscious state is a mental state there is something it is like for the subject to be in. Normal cases of pain and visual experience are uncontroversial examples of phenomenally conscious states; a controversial example is conscious belief.

Cognitive states are intentional mental states; that is, mental states with propositional content. Beliefs and other propositional attitudes are uncontroversial examples of cognitive states, and visual experience is relatively uncontroversial. Pain, however, is a controversial example of a cognitive state.

Physical properties are "the fundamental properties that are invoked by a completed theory of physics" (33). Physical facts are "the facts concerning the instantiation and distribution of [physical properties]" (33).

Physicalism is the view that any metaphysically possible world
exactly the same as the actual world with respect to the physical
facts is exactly the same *simpliciter*. (Here we ignore some
irrelevant complications.[5]) In other words, according to physicalism,
everything actual supervenes with metaphysical necessity on the
physical.

Chalmers is almost a physicalist. He thinks that *nearly*
everything--including the cognitive--supervenes with metaphysical
necessity on the physical. It is impossible, he thinks, for a world
physically the same as the actual world to differ from it with respect
to who believes what: in particular, such a world contains a physical
duplicate of Chalmers himself, who believes that he has written
a book on consciousness, and so forth. But consciousness is the
residue that does not supervene with metaphysical necessity on the
physical[6]: there are (non-nomologically) possible worlds exactly
the same as the actual world with respect to physical facts, and
so with respect to facts about cognitive states--but from which
consciousness is entirely absent. Such "zombie worlds"
contain, of course, zombies (in the philosophers' sense): creatures
cognitively just like you and us, some of whom are publishing weighty
tomes on the problem of consciousness, but who are never in any
phenomenally conscious states.[7]

2 The argument

Some terminology: the causal structure, or "functional
organization", of a system may be described more or less finely;
we shall call whatever is described at the level that is just fine
enough for the purposes of functionalist psychology the system's
*fine-grained* functional organization (sometimes the qualifier
`fine-grained' will be omitted).[8] Chalmers first argues "for
a *principle of organizational invariance*...given any system
that has conscious experiences, then any system that has the same
fine-grained functional organization will have qualititatively identical
experiences" (248-9). And: "The invariance principle holds
that functional organization determines conscious experience by
some lawful link in the actual world" (250). Thus the principle
of organizational invariance is the following supervenience thesis:

POI

For all nomologically possible worlds w_{1}, w_{2},
times t_{1} and t_{2}, and possible systems s_{1}
and s_{2}, if s_{1} in w_{1} at t_{1}
and s_{2} in w_{2} at t_{2} share the same
fine-grained functional organization, then they have qualitatively
identical experiences at t_{1}, t_{2}, respectively.

Following Chalmers, let "a *maximal physical state* be
a physical state that fully characterizes the intrinsic physical
state of a system at a given time" (349). Chalmers then argues
that if a system in maximal physical state * P* has functional
organization *F*, then any system "in a superposition
of *P* with orthogonal physical states" (350) also has
functional organization *F*. The new system might have other
functional organizations, but that is not relevant: the claim is
simply that it still has *F*. So functional organization is
preserved by superposition (with "orthogonal states").
Let us call this thesis *organizational preservation under superposition*
(OPUS).

Chalmers defines a *maximal phenomenal state* as "a phenomenal
state that characterizes the entire experience of a subject at a
given time" (349), and then draws the following conclusion
from POI and OPUS:

If...a system in maximal physical state *P* gives rise to
an associated maximal phenomenal state *E*, then...a system
in a superposition of *P* with some orthogonal physical states
will also give rise to *E* (349).

And he continues:

If [the above is right], then a superposition of orthogonal physical
states will give rise to at least the maximal phenomenal states
that the physical states would have given rise to separately. This
is precisely what the Everett interpretation requires. If a brain
is in a superposition of a "perceiving up" state and a
"perceiving down" state, then it will give rise to at
least two subjects of experience, where one is having an experience
of a pointer pointing upward, and the other is experiencing a pointer
pointing downward. (Of course, these will be two *distinct*
subjects of experience, as the phenomenal states are each maximal
phenomenal states of a subject.) (349).

We now assess this argument, starting with the first phase, where Chalmers tries to establish POI.

3 The first phase: the principle of organizational invariance

Oscar is looking at a ripe tomato in good light. Suppose that
his fine-grained functional organization is *F*, and that POI
is false. Then one of the following cases, involving Twoscar, who
also has functional organization *F*, is *nomologically*
possible:

(AQ) Twoscar has no conscious experience at all (so-called "absent qualia").

(IQ) Twoscar has conscious experience, but it differs qualitatively from the experience of Oscar (perhaps, to take the usual example, this is a case of "spectrum inversion" or "inverted qualia" [Shoemaker 1982]).

Chalmers argues (chapter 7) that if either AQ or IQ were nomologically possible, then the world would be extremely bizarre--implausibly bizarre, in fact. He concludes by reductio that POI is true.

Now we are quite unpersuaded by Chalmers' argument here, but it
is not necessary to go into the details. For Chalmers' main opponents--orthodox
physicalists--hold a *stronger version* of POI, obtained by
replacing `nomologically possible' with `physically possible'. In
other words, orthodox physicalists hold that once functional organization
and the physical laws are fixed, all facts about consciousness are
fixed. Chalmers, on the other hand, only holds that once functional
organization and the physical *and psychophysical* laws are
fixed, all facts about consciousness are fixed. So orthodox (i.e.
functionalist) theories of consciousness entail POI, and since this
is the only premise concerning consciousness in the overall argument
this means that Chalmers has both overstated (at least in our opinion)
and understated its significance. It is not his *own* theory
of consciousness that supports the Everett-style interpretation,
if his argument goes through, but rather *almost everyone else's*
theory of consciousness.[9]

4 The second phase: organizational preservation under superposition

4.1 OPUS explained

We now need to be a bit more precise about what exactly is
supposed to be preserved under superposition. In chapter 9, Chalmers
gives an account of how a physical system may implement a certain
kind of abstract computing device, a * combinatorial-state automaton*
(CSA). A CSA is simply a set of "state-vectors" {[S^{1},
..., S^{n}],...} "input-vectors" {[I^{1},
..., I^{k}],...} and "output-vectors" {[O^{1},
..., O^{m}],...}, together with state transition rules that
map each pair of input- and state-vectors to a pair of output- and
state-vectors. The transition rules determine (informally speaking)
how the CSA produces an output, and changes its state, given its
current state and input. Chalmers' proposal is "that a physical
system implements a computation when the causal structure of the
system mirrors the formal structure of the computation" (317-8).
More exactly:

A physical system *P* implements a CSA *M* iff there
is a decomposition of internal states of *P* into components
[*s*^{1},..., *s*^{n}], and a mapping
*f* from the substates *s*^{j} into corresponding
substates S^{j} of *M*, along with similar decompositions
and mappings for inputs and outputs, such that for every state transition
rule ([I^{1}, ..., I^{k}], [S^{1}, ...,
S^{n}]) -> ([S´^{1}, ..., S´^{n}], [O^{1},
..., O^{m}]) of *M*: if *P* is in internal state
[*s*^{1},..., *s*^{n}] and receives input
[*i*^{1},..., *i*^{n}], which map to formal
state and input [S^{1}, ..., S^{n}] and [I^{1},
..., I^{k}] respectively, this reliably causes it to enter
an internal state and produce an output that map to [S´^{1},
..., S´^{n}] and [O^{1}, ..., O^{m}] respectively
(318).

Importantly, the substates and inputs and outputs of *P *have
to be the sorts of properties that can enter into causal relations--"causally
efficacious properties", for short. For dropping this restriction
trivializes the notion of a physical system implementing a CSA:
any system would implement any CSA, because, by various "grue-like"
devices, we can always find properties of the system that map in
the right way to the elements of the CSA. Indeed, one of Chalmers'
main purposes in proposing this account is to rebut Searle's charge
(1990) that to say that a system implements a computation places
no interesting physical constraints on it.

With the account of implementation in hand, OPUS can be expressed more exactly as follows:

OPUS

"If a computation [i.e. a CSA] is implemented by a system in
maximal physical state *P*, it is also implemented by a system
in a superposition of *P* with orthogonal physical states"
(350).

Recall that Chalmers' argument for POI was an argument only for
the supervenience of phenomenology on "fine-grained functional
organization", in other words on causal structure (at the appropriate
fineness of grain).[10] Nothing in that argument appealed to the
idea that mental processes are computations. So talk of "computation"
in the statement of OPUS is a minor distraction. For the purposes
of Chalmers' overall argument we do not have to regard an implementation
of a CSA as actually *computing* anything: the crucial point
is that Chalmers has provided a way of taking a CSA to be a description
of the *causal structure* of a physical system.

Before we turn to the argument for OPUS, three observations are in order.

First, Chalmers follows common practice in speaking of a physical state as being a "superposition" of other physical states, and of two physical states as being "orthogonal". But although widespread, this way of talking can encourage serious confusion. In quantum mechanics, remember, vectors represent physical states; more precisely, to each physical system there corresponds a Hilbert space (a particular kind of vector space), and certain of the vectors in that Hilbert space represent different possible physical states of the system. The terms `orthogonal' and `superposition' refer in the first instance to relationships among vectors, not physical states. When a state is said to be a "superposition" of other states, this means, or should mean, that the vector representing the state is a superposition of the vectors representing the other states. Similarly when two states are said to be "orthogonal": this means that the vectors representing the states are orthogonal.

Unfortunately, talk of "superposed" or "orthogonal"
states encourages the view that these terms are *physically *significant.
In particular, it can suggest that "superposed" states
are somehow *physically composite*. But without further argument,
this is a mistake. It is the same kind of mistake as thinking that
the property of being a *monosyllabic primate* (Ned is a monosyllabic
primate because his name has one syllable, but Alex isn't) or the
property of having *prime mass* (for some unit of mass, a mass
of prime-numbered units), are physically or biologically significant
properties. In fact, the latter is a better analogy: *everything*
with mass has prime mass, and *every *state is "superposed"--for
every state-vector can be expressed as a superposition of other
state-vectors (indeed, in countlessly many ways). The importance
of these cautionary remarks will become clear shortly.

The second observation is that OPUS can be more perspicuously rewritten as follows:

OPUS*

If a CSA is implemented by a system in maximal physical state *P*
(represented by f), it is also implemented by a system whose state-vector
is not orthogonal to f.

Since the state-vectors not orthogonal to f are exactly the state-vectors that are non-trivial superpositions of f with orthogonal vectors, OPUS* and OPUS are equivalent.

The third observation is that OPUS has the following remarkable
consequence: any two systems simultaneously implement *exactly
the same *CSA's, provided only that their state-vectors belong
to the same Hilbert space. For suppose a system in state *P *implements
a certain CSA, and that its state-vector f is not orthogonal to
the state-vector y of a system in *P**. Then OPUS (in the guise
of OPUS*) immediately delivers the result that the *P**-system
also implements that CSA. Suppose, alternatively, that f is orthogonal
to y. Consider the superposition f + y. It is not orthogonal to
f, so by OPUS* the system whose state it represents implements the
CSA.[11] But f + y is not orthogonal to y either, and so applying
OPUS* once more yields that a system in state *P* *also implements
that CSA.

For short: all systems of the same type (i.e., whose states are representable on the same Hilbert space) implement the same CSA's.

4.2 The argument for OPUS

We now turn to Chalmers' argument for OPUS, expressed concisely as follows:

Assume that the original system (in maximal physical state *P*)
implements a computation [i.e. a CSA] *C*. That is, there is
a mapping between physical substates of the system and formal substates
of *C* such that causal relations between the physical substates
correspond to formal relations between the formal substates. Then
a version of the same mapping will also support an implementation
of *C* in the superposed system. For a given substate *S*
of the original system, we can find a corresponding substate *S*´
of the superposed system by the obvious projection relation: the
superposed system is in *S*´ if the system obtained by projecting
it onto the hyperplane of *P* is in *S*. Because the superposed
system is a superposition of *P* with orthogonal states, it
follows that if the original system is in *S*, the superposed
system is in *S*´. Because the Schrödinger equation is linear,
it also follows that the state-transition relations between the
substates *S*´ precisely mirror the relations between the original
substates *S*. We know that these relations in turn precisely
mirror the formal relations between the substates of *C*. It
follows that the superposed system also implements *C*, establishing
the required result (350).

Drawing on the third observation in the previous section, if this
argument is right then any system *A* simultaneously has the
causal structure of *any* other system *B* whose states
are representable on the same Hilbert space. But all *that *requires
is for *A *and *B *to comprise the same number of each
type of fundamental particle (same number of electrons, protons,
etc.). Thus, if the universe has causal structure at all, this structure
exhibits an astonishing amount of duplication. And this conclusion
is apparently supposed to follow *without assuming any controversial
interpretation of quantum mechanics* (let alone controversial
theories of consciousness): we just observe that quantum mechanics
applies to physically possible systems with causal structure, and
then appeal to the "projection relation" and the linearity
of the Schrödinger equation. There's got to be a catch in that!

We will split Chalmers' argument into two parts. The first part
sets up a mapping between substates of the original system and substates
of the new system. The second part argues from the linearity of
the Schrödinger equation to the conclusion that "the state-transition
relations between the substates *S´ *precisely mirror the relations
between the original substates *S*," and thence to the
conclusion that, if the original system implements *C*, so
does the new system.

4.21 The first part of the OPUS argument

Unpacking the shorthand that allows Chalmers to speak loosely
of *systems* being projected onto hyperplanes, and so forth,
his suggested mapping is this:

the superposed system is in *S'* if the state represented
by the vector that results from projecting the state-vector of the
superposed system onto the hyperplane of the state-vector representing
*P*, represents a system in * S*

Now some jargon needs to be explained. The "hyperplane" of a vector is the one-dimensional space of vectors that are parallel to it. For any vector f, there is a unique vector y lying in this space such that f is a superposition of y with some orthogonal vector; the "projection" of f onto the space is simply y.

Since parallel vectors represent the same state, the *only*
state that a vector lying in the hyperplane of the state-vector
of the original system could represent is *P* itself. Of course,
such a vector might not represent * any* state: the zero vector,
for example, does not. Might Chalmers intend that only *normalized*
vectors represent states? No: For it would immediately follow that
the superposed system is *not* guaranteed to be in a "corresponding
substate *S'*"--since the projection of its state-vector
onto the hyperplane of *P* will necessarily have length less
than one. So we must interpret Chalmers as supposing that non-zero
vectors of length less than or equal to 1 represent states.

Putting all this together, the suggested mapping simplifies rather dramatically:

the superposed system is in *S'* if its state-vector is not
orthogonal to the state-vector that represents *P*

(For if the state-vector of the superposed system is not orthogonal,
then its projection onto the hyperplane of *P* will yield a
non-zero vector, which represents *P*, which is a state which
places the original system in *S*.)

Is this adequate for Chalmers' purposes? No. He needs to show that
there is a mapping from the relevant substates of a CSA-implementing
system to substates of a "superposed" system which preserves
causal organization. And to do *that*, he must--*minimally*--show
(i) that the mapping takes a given substate *S* of the original
system to a causally efficacious property, and (ii) that the mapping
is one-one.

Chalmers offers no argument whatsoever that the "corresponding
substates" of the superposed system are causally efficacious.
And since he gives only a * sufficient* condition--and not
necessary and sufficient conditions--for the superposed system to
be in such a substate, it is clear he has failed to define a one-one
mapping.

In fact, matters are considerably worse, for any mapping meeting
Chalmers' sufficient condition actually makes (i) and (ii) *false*.
Suppose f represents a system in (inter alia) substate *S*.
Then every state-vector not orthogonal to f (and perhaps others)
represents a system in corresponding substate *S*´. Consider
an arbitrary such state-vector y. By a second application of the
sufficient condition, every state-vector not orthogonal to y represents
a system in a substate *S´´ *corresponding to *S´*. In
other words, every state-vector not orthogonal to some state-vector
that is not orthogonal to f represents a system in substate *S´´*.

But that is *every* state-vector, period. And it is hardly
believable that the property represented--a property the system
*must* have, no matter what its state--is causally efficacious.

Furthermore, suppose our original system is in both substates *S*_{1}
and *S*_{2}. Then any system whose state-vector is
not orthogonal to that of the original system will be in corresponding
substates *S*_{1}´ and *S*_{2}´. But the
substates that, by a second application of Chalmers' sufficient
condition, correspond to *these* will be exactly the same:
the trivial substate just introduced. Thus no mapping meeting Chalmers'
condition is one-one.

4.22 The second part of the OPUS argument

Suppose these difficulties can somehow be fixed, and a mapping produced that meets conditions (i) and (ii) above. Does it follow from the linearity of the Schrödinger equation that the causal relations between successive substates of the superposed system exactly mirror the causal relations between successive substates of the original system?

Take a simple example. Suppose *S*_{1} is a substate
of the *P*-system (represented by f), mapped onto substate
*S*_{1}´ of the superposed system (represented by a
vector that we can write as `af + by'). And suppose that (the instantiation
of) *S*_{1} causes, t seconds later, the * P*-system
to be in a new substate *S*_{2}. Let Schrödinger evolution
over this time period take f to f* and y to y*. Then the *P*-system
state-vector at time t is f*, and by the linearity of the Schrödinger
equation the state-vector of the superposed system at t is af* +
by*. Then the mapping guarantees that the superposed system is in
a substate *S*_{2}´ corresponding to *S*_{2}.[12]

Does it follow that *S*_{1}´ causes, t seconds later,
the superposed system to instantiate *S*_{2}´? Well,
either the original mapping guarantees that *S*_{1}´
causes *S*_{2}´, or it doesn't. If it does (and so
goes beyond the minimal desiderata of (i) and (ii)), then the linearity
of the Schrödinger equation is irrelevant. So suppose it doesn't.
By linearity, the superposed system at the later time has state-vector
af* + by*, a component of which is af*, which (since parallel vectors
represent the same state), represents the *P*-system at the
later time. But, if we heed the cautionary remarks about "superpositions"
made earlier in section 4.1, there should be no temptation to think
that this fact about the *representation* of states implies
anything interesting at all about the * states represented*.
From the two premises (a) that af* + by* has af* as a component,
and (b) that the system represented by f* has a substate caused
in such-and-such ways, *nothing follows at all* about the causal
history of any substates of the system represented by af* + by*.
Analogously, from the two premises (a´) that `Alex' has `Al' as
a component, and (b´) that the person named `Al' has tenure, nothing
follows at all (regrettably) about the tenured status of the person
named `Alex'.

4.23 Another argument for (a version of) OPUS

Recapitulate the cautionary remarks about "superpositions"
made in section 4.1 with the example of the spin states of spin-1/2
particles. Spin is not spin *simpliciter*, of course, but spin
*in some direction*: spin in the x-direction, spin in the y-direction,
etc. Spin "up" (equally, "down") in any one
direction is always represented by a non-trivial superposition of
the "up"- and "down"-vectors for any other direction.
So unless we pick out some direction--hence, by implication, some
pair of "up" and "down" eigenstates--as being
somehow physically privileged, there is just no physically interesting
sense in which some spin states are "superposed" and some
are not.[13] Of course, this observation applies not just to spin
states, but to any kind of quantum mechanical state.

If, however, some basis *is* physically privileged, in that
its elements represent states that are somehow of a physically distinctive
kind, then there is a physical distinction between non-superposed
and superposed states: the former are precisely the states represented
by some element of the privileged basis.

So assume that there is a privileged basis, and in addition that any (physically possible) CSA is implemented by some system whose state-vector is in the privileged basis.

Second, assume that when a system is in the state represented by
a superposition of some privileged basis vectors f_{A},
f_{B},..., it has *physically distinct parts* that
are in states represented by f_{A}, f_{B},... Thus
any system in a state represented by the superposition will contain
a physical duplicate of a system whose state-vector is f_{A},
etc.[14]

A version of OPUS can be derived from these two assumptions, as follows.

Suppose a system in state *P* implements a certain CSA. By
the first assumption, *P* is represented by a vector f in the
privileged basis. Let y be a superposition of f with some privileged
basis vectors: y = af + .... By the second assumption, one physically
distinct part of a system in the state represented by y will implement
the same CSA as the *P*-system, for it is a physical duplicate
of that system.

Therefore, given this understanding of the formalism, causal organization
is indeed preserved under superposition. Unfortunately, this is
hardly an argument that *Chalmers* can endorse, because *he
explicitly rejects the appeal to a privileged basis*. That Everett's
original interpretation seems to require one is his main complaint
against it (348).

5 The third phase: putting POI and OPUS together

Let us temporarily waive these problems with Chalmers' premises, and ask if we can get anything out of putting them together.

Return to the conclusion Chalmers draws from POI and OPUS, mentioned earlier in section 2:

If...a system in maximal physical state *P* gives rise to
an associated maximal phenomenal state *E*, then...a system
in a superposition of *P* with some orthogonal physical states
will also give rise to *E* (349).

This is not yet the desired result--that even if "the Schrödinger
equation is all" (346), there will still be minds who experience
the world as discrete. To get that, Chalmers must discharge the
antecedent, by showing that on his picture of what the world is
like, there *are* maximal physical states that give rise to
subjects who experience the world as discrete.

But now there is an obvious difficulty. For Chalmers' interpretation
implies that perceptual experience is (more or less) *entirely
illusory*.[15] When you seem to see a voltmeter needle pointing
to `10', your perceptual experience is probably not veridical: the
needle (if, indeed, we can sensibly speak of such a thing) is not
pointing to `10' or anywhere else. Likewise for any other sort of
perceptual experience, whether of voltmeter needles, string, sealing
wax, cabbages or kings. Russell's remarks could have been written
with Chalmers in mind: "Naive realism leads to physics, and
physics, if true, shows that naive realism is false. Therefore naive
realism, if true, is false; therefore it is false." (1950,
15).

Although a whiff of paradox surrounds the suggestion that empirical
enquiry might terminate in a theory that implies that almost all
the observational "data" with which it began are false,
we are not making this complaint. Rather, we are complaining that
Chalmers has not told us what the world is like if "the Schrödinger
equation is all"; in particular, he has given us no reason
to suppose that there could be systems with the appropriate fine-grained
functional organizations. Of course, assuming that our experience
is by and large veridical, there is no problem: in that case, we
have an abundance of information about the causal organization of
various systems, including human brains. But on *Chalmers'*
view, our experience is no such guide.

This complaint can be strengthened. Chalmers can't answer the question of what the world is like if "the Schrödinger equation is all" because no one can. The constraints on an acceptable answer are too few for the question to be an occasion for genuine inquiry, rather than mere stipulation. We shall argue for this in the following section.

6 The emptiness of the "bare theory"

The "bare theory" is simply the result of subtracting the "collapse" postulate from orthodox quantum mechanics. The idea that there is something significant to be learned from studying this theory has a great deal of currency: Deutsch (1996) claims, in effect, that the bare theory straightforwardly entails that there are many worlds; Lockwood (1989, 1996) holds a view similar to Chalmers'; Albert and Loewer, who propose to augment the bare theory with certain psychophysical postulates, still turn to it for a non-arbitrary specification of the "eigenstates of mentality" (Albert 1992, 129, fn. 16); both Albert (1992, ch. 6) and Barrett (1994) find merit in pursuing the more modest aim of uncovering the "suggestive properties" of the bare theory.

These discussions apparently assume that the bare theory, while
perhaps obviously false, at least possesses powers of representation
and conditions of application that are approximately as rich as
those of orthodox quantum mechanics. And sometimes a stronger assumption
is made: if orthodox quantum mechanics can represent that a system
has a certain property, so can the bare theory. That is, if there
is a state vector f_{1} (interpreted as part of orthodox
quantum mechanics) such that necessarily any system represented
by f_{1} has property *P*, then there is a state vector
f_{2} (interpreted as part of the bare theory) such that
necessarily any system represented by f_{2} has *P*
(typically f_{1} and f_{2} are taken to be identical).
If the stronger assumption is right, then the problem raised for
Chalmers in the previous section is straightforwardly solved: the
bare theory * can* represent that systems have such-and-such
functional organizations after all--at least if orthodox quantum
mechanics can.

Both these assumptions are unfounded. There is an instructive way to dispose of the stronger assumption while granting the weaker; that is what we will do first.

The point is an abstract one that applies not just to quantum mechanics.
Suppose T_{1} is a physical theory formalized as a family
of state spaces together with a set of trajectories through these
state spaces--the "dynamics" of T_{1}. And suppose
T_{2} is obtained from T_{1} merely by changing
the dynamics. Unless this change implies otherwise, the interpretation
of the formal apparatus of T_{2} is taken to be the same
as that of T_{1}. The two pertinent theories related in
this way are of course orthodox quantum mechanics and the bare theory:
the state spaces are the same, but only the dynamics of the latter
is deterministic. Another example is the elementary textbook theory
of the pendulum and a theory that adds to it a correction for air
resistance.

Suppose that state-space element f, taken as part of T_{1},
represents that a system has property *P*. And suppose--as
might well be the case--that this is not semantically stipulated
(as, for example, it is stipulated that `*l*' will represent
the length of the pendulum). It would be a "fallacy of subtraction"
to think it follows that f, *taken as part of T _{2}*,
also represents that the system has

This point seems to have been overlooked in discussions of the
bare theory. For authors who claim to be exploring its consequences
routinely assume that, according to the bare theory, there are possible
states of an observer's brain that constitute her having a certain
belief (e.g., that the measurement outcome was "up").
And, while no one is very explicit about this, it seems also to
be assumed that the vectors representing these "eigenstates
of belief" *are the very same* as the vectors which, according
to orthodox quantum mechanics, assign to the observer the given
belief. Thus, a typical discussion might begin by assuming that,
according to orthodoxy, there is some state-vector f for a given
observer (or her brain) such that, when she is in the state represented
by f, she has the belief that the measurement outcome was "up".[16]
This assumption is simply carried over to the discussion of the
bare theory, at which point the standard problematic takes over:
according to the bare theory observers typically won't be in states
represented by "belief eigenvectors" like f.

But this is quite wrong, because the property of having such-and-such
a belief is exactly the sort of property one would expect to be
sensitive to the prevailing dynamics (this is especially clear on
the common view that belief-properties are kinds of *functional*--therefore,
broadly construed, *dispositional*--properties). Hence, if
f is, according to orthodox quantum mechanics, a belief eigenvector,
it does not follow that f is a belief eigenvector according to the
bare theory. In fact, it's not at all obvious that the bare theory
*has* any belief eigenvectors.

We now turn to the other assumption, that the bare theory has substantive content, comparable to that of orthodox quantum mechanics. Let us begin by briefly reviewing how the representation of a system's state works in the orthodox case.

First, the physical properties that the system retains over time--being composed of such-and-such particles, and so forth--can be thought of as either straightforwardly encoded in the state-vector or else specified separately.

Second, the physical properties of the system that it can gain
or lose over time are encoded by the eigenstate-eigenvalue link:
a system possesses the value m_{i} for physical magnitude
M, represented by Hermitian operator **M**, iff the state-vector
f for the system is an m_{i}-eigenstate of **M ** (i.e.
iff **M**f = m_{i}f).

Third, the state-vector encodes a certain kind of information about
the system's *dispositions* or *propensities*: it tells
us, via the usual statistical algorithm, the probability that "measurement"
of M on the system will produce result m_{i}.

The point just made against the first assumption shows that it
cannot be taken for granted that the orthodox eigenstate-eigenvalue
link is completely preserved in the bare theory. Suppose magnitude
M is represented in orthodox quantum mechanics by operator **M**,
and suppose that this is not semantically stipulated. It doesn't
follow that the bare theory represents M by **M** (or, indeed,
that the bare theory represents M at all). But let us waive this
problem. In fact, let us suppose that if orthodox quantum mechanics
represents M by **M** (for a certain system), so does the bare
theory.

Now the bare theory rejects the *last* way of encoding a system's
properties: according to it, these propensities to produce various
outcomes do not exist. That is because, for well-known reasons,
the bare theory does not give outcomes *probabilities*.[17]
*But there is nothing else left* in orthodox quantum mechanics
that might be used to assign some information about M to a state-vector
that is not an eigenvector of **M**. Therefore the bare theory
has no resources to interpret such state-vectors as containing information
about M.

This has an important consequence. Not every operator can be intelligibly
taken to represent a property independently of the statistical algorithm.
For example, consider the operators **E** and **B**, whose
eigenvectors are those that are non-trivial superpositions of, respectively,
energy and belief eigenvectors. What properties do these operators
represent? The standard explanation appeals to the statistical algorithm
and to operators that *can* be understood independently of
it. Thus, the properties represented by **E** and **B** are
certain propensities to produce, respectively, energy and belief
"measurement" outcomes. Disallowing appeal to the statistical
algorithm, there seems to be no way of understanding which properties
are represented by ** E** and **B**. And since there can hardly
be a hidden fact of the matter, this means that operators like **E**
and **B** will not represent properties at all.

Therefore, if we say that an "ordinary" operator is one
that can be interpreted *in*dependently of the statistical
algorithm, the important consequence can be put thus: the bare theory
will be unable to interpret any state-vector which is not the eigenvector
of any ordinary operator.

The fact that the bare theory cannot interpret vectors that are
not eigenvectors of any ordinary operator seriously degrades its
representational capacity for reasons that are entirely familiar,
although their significance is perhaps not widely appreciated. Because
of the way (almost any) system--macroscopic or microscopic--interacts
with its environment, its state will typically not be represented
by an eigenvector of *any* ordinary operator.[18] Taking energy
as an illustration, we can think of the energy states of almost
any system **s** as "measuring" the momentum of some
system **s´** in its environment. That is, there will be different
initial momentum states of **s´**, represented by f_{+}
and f_{-}, and an initial state of the "apparatus"
(i.e. **s**), represented by y, such that Schrödinger evolution
takes f_{+} **x** y (i.e. the state vector representing
the initial state of the composite system **s**-plus-**s´**[19])
to f_{1 }**x** y_{+}, and f_{-} **x**
y to f_{2} **x** y_{-}, where f_{1} and
f_{2} represent different post-measurement states of **s´**
and y_{+} and y_{-} represent different post-measurement
energy states of **s**. Now, **s** at almost any time will
have just acted as this sort of measuring device for the momentum
of *something* in its environment, which moreover we can safely
presume was initially in a non-trivial superposition of vectors
representing momentum states that the system can measure. So, if
we represent the initial state of **s´** by the non-trivial superposition
af_{+} + bf_{-}, then the current state of **s**-plus-**s´
**will be represented by af_{1} **x** y_{+}
+ bf_{2} **x** y_{-}. This state is one in which
**s** is *not* in an energy eigenstate.[20] The example
can be generalized to all ordinary operators. Almost every system
at almost any time will not be in an eigenstate of any ordinary
operator, and so when interrogated on what the world is like, the
bare theory will fall almost entirely silent.[21]

7 Summary

Chalmers makes it abundantly clear that he considers it an extremely important desideratum for any interpretation that it neither modify the Schrödinger equation (by admitting exceptions to it in the case of "measurements"), nor supplement it (by introducing "hidden variables"). Apparently such a conservative approach is warranted because, as he puts it, "the heart of quantum mechanics is the Schrödinger equation. The measurement postulate, and all the other principles that have been proposed, feel like add-on extras". We thus are supposed to have excellent reason for exploring the consequences of "extend[ing] superposition all the way to the mind" (346).

However, as we have argued, this "bare theory" is no real theory at all: it is quantum mechanics eviscerated, and consists largely of dry bones of uninterpreted mathematics.

Further, although we have examined just one proposal, we hope our discussion has poured some cold water on the idea that a theory of consciousness might help rescue quantum mechanics from the difficulties with the standard interpretation. After all, Chalmers' attempt strikes us as about the best that can be offered, at least if we forego exotic psychophysical postulates, as in the "many minds" theory of Albert and Loewer (1988).

Why was consciousness thought to be relevant in the first place?
Because, supposedly, although we *can* deny that needles are
hardly ever at particular positions, and so forth, what we *cannot
possibly deny* are facts about our conscious mental states, in
particular that we *seem to see* needles at particular positions.
Of course, the claim that the mental enjoys a peculiar epistemic
security is hardly new: it has pervaded Western philosophy since
Descartes. But it is a controversial assumption, and one that much
epistemology in this century has been devoted to overturning. Any
interpretation of quantum mechanics motivated by it deserves to
be viewed with suspicion.[22]

References

Albert, D. 1992. *Quantum Mechanics and Experience*.
Harvard University Press.

Albert, D, and B. Loewer. 1988. Interpreting the many-worlds interpretation.
*Synthese* 77, 195-213.

Barrett, J. 1994. The suggestive properties of quantum mechanics
without the collapse postulate. *Erkenntnis* 42, 89-105.

Block, N. 1995. On a confusion about a function of consciousness*.** Behavioral and Brain Sciences* 18, 227-87.

Byrne, A., and N. Hall. 1988. Chalmers, Papineau, and Saunders on probability and many minds interpretations of quantum mechanics. MS.

Chalmers, D. J. 1996. *The Conscious Mind*. Oxford University
Press.

Dennett, D. C. 1991. *Conciousness Explained*. Little, Brown.

Deutsch, D. 1996. Comment on Lockwood. *British Journal for the
Philosophy of Science* 47, 222-8.

Dretske, F. 1995. *Naturalizing the Mind*. MIT Press.

Everett, H. 1957. `Relative-state' formulation of quantum mechanics.
Reprinted in J. Wheeler and W. H. Zurek, eds., *Quantum Theory
and Measurement*, Princeton University Press, 1983.

Hall, N. 1996. *Composition in the Quantum World*. Ph.D. diss.,
Princeton University.

Harman, G. 1988. Wide functionalism. In S. Schiffer and S. Steele,
eds., * Cognition and Representation*, Westview Press.

Lewis, D. K. 1980. A subjectivist's guide to objective chance.
Reprinted in his *Philosophical Papers*, vol. 2., Oxford University
Press, 1986.

Lewis, D. K. 1983. New work for a theory of universals. *Australasian
Journal of Philosophy* 61, 343-77.

Lewis, D. K. 1986. *On the Plurality of Worlds*. Basil Blackwell.

Lockwood, M. 1989. *Mind, Brain and the Quantum*. Basil Blackwell.

Lockwood, M. 1996. `Many minds' interpretations of quantum mechanics.
* British Journal for the Philosophy of Science* 47, 159-87.

Loewer, B. 1996. Comment on Lockwood. *British Journal for the
Philosophy of Science* 47, 229-32.

Lycan, W. G. 1996. *Consciousness and Experience.* MIT Press.

Russell, B. 1950. *An Inquiry into Meaning and Truth*. Allen
& Unwin.

Searle, J. 1990. Is the brain a digital computer? *Proceedings
and Addresses of the American Philosophical Association* 64,
21-37.

Shoemaker, S. 1982. The inverted spectrum. *Journal of Philosophy*
79, 357-81.

Tye, M. 1995. *Ten Problems of Consciousness*. MIT Press.

[1]For magnitudes like position and momentum, which admit of a continuum of possible values, the mathematical representation is a little more complicated, although the basic idea is the same.

[2]All references are to this book unless otherwise noted.

[3]Here `perceives' is not supposed to be factive: one may perceive
that *p* when it is false that *p*.

[4]`Proponent' is perhaps a bit too strong: "We may never be able to accept the view emotionally, but we should at least take seriously the possibility that it is true" (357).

[5]Problems arise because a physicalist might well agree that there could have been "epiphenomenal spirits" that do not interact with anything physical (Lewis 1983, 362); in which case physicalism as stated in the text is false. For discussion and different suggested repairs, see Lewis 1983, 361-4, and Chalmers 1996, 38-41.

[6]So, according to Chalmers, those facts with "a dependence on conscious experience" (72)--e.g., on some views, facts about color and other "secondary qualities"--do not supervene with metaphysical necessity on the physical either.

[7]Chalmers makes a slight qualification to the claim that our zombie twins share absolutely all our intentional states (203-9).

[8]Chalmers use of `fine-grained' is different: "at a level fine enough to determine behavioural capacities" (248). But we think our characterization is more faithful to his overall intentions.

[9]E.g. Dennett 1991, Tye 1995. There is a complication because Tye, at least, would only endorse POI if a "functional organization" were taken to be individuated in part by actual environmental causes and effects (cf. Harman 1988), and in Chalmers' own presentation the other--"narrow"--kind of functionalism is tacitly assumed. Still, if Chalmers' argument works, it can be adapted to cover Tye's position. Dretske (1995) and Lycan (1996) both claim that what phenomenal state a subject is in depends on his evolutionary history, and so would deny POI (at any rate on the usual readings of `functional organization'). But it is possible to adapt Chalmers' argument even here.

[10]Not exactly. The notion of causal structure that a CSA specifies
is highly abstract, and in fact more abstract than the functional
supervenience base delivered by the argument for POI. The latter
kind, as far as Chalmers' argument for POI goes, might be individuated
by the specific nature of the (possible) inputs and outputs (e.g.
whether the input is a red tomato before the eyes); analogously,
the functional analysis of a mousetrap will mention what it does
to *mousey* input. By contrast, the former (CSA) kind might
count a mousetrap and an elephant trap as having the same causal
structure. This is a problem with the overall argument, because
we want the latter kind of causal structure to be "preserved
under superposition", and at best all we get is the preservation
of the former. Since there are more serious objections, we can afford
to set this difficulty aside.

[11] Of course, f + y may be replaced by its normalization if desired, without affecting the argument. (On whether non-normalized vectors represent states, see section 4.21 below.)

[12]Does the linearity of the Schrödinger equation come into play
here? After all, it *does* guarantee that y* will not be orthogonal
to f*. But that is quite irrelevant: for if there is a mapping between
states with non-orthogonal state-vectors, then by the two-step maneuver
of the previous section there is a mapping between any two states
whatsoever.

[13]Although Chalmers makes precisely this point at 335, on the previous page he seems to have temporarily forgotten it, writing that spin "has only two basic values...[which] can be labeled `up' and `down'", and that "In quantum mechanics the spin of a particle is not always up or down" (334).

[14]Cf. Chalmers on a "superposed pointer state": "the theory predicts that the pointer is pointing to many different locations simultaneously!" (339-40). This is presumably a slip.

[15]Chalmers at one point writes that on his view "we are experiencing only the smallest substate of the world" (356), which suggests that he does not think that perceptual experience is illusory. But without a privileged basis (see 4.23 above) there is no avoiding it.

[16]Of course, orthodox quantum mechanics doesn't * stipulate*
that certain state-vectors represent belief states (at any rate
* as such*)--the vocabulary of the theory doesn't contain any
psychological expressions.

[17] Assuming we can make sense of the bare theory attaching numbers
to *outcomes*, they cannot be "objective chances"
(Lewis 1980), because the theory is deterministic. Neither can they
be probabilities resulting from our ignorance of relevant aspects
of the system in question: they are outcomes *that the theory
tells us will happen*, and hence there is nothing relevant of
which we are ignorant. But these are the only two options, and so
the numbers cannot be probabilities. (See, e.g., Albert and Loewer
1988, 201; Loewer 1996.) Chalmers himself holds out some hope that
this argument can be defused (355-6); for discussion of his (and
others') suggestions see Byrne and Hall 1998.

[18] Of course, irrespective of this point, its state won't be
represented by eigenvectors of (e.g.) the position and momentum
operators because they don't *have* eigenvectors.

[19] f_{+} **x** y is a vector in the tensor product
of the two Hilbert spaces representing, respectively, states of
the object and the system.

[20] Of course the illustration itself shows that it is an idealization
to suppose, as we have, that the "apparatus" and the measured
system are in pure states before the measurement. Strictly speaking,
the two systems before the measurement will be "coupled"
with *other* systems. It is also worth noticing that the sort
of coupling exhibited by **s**-plus-**s´** just after the
measurement is unlikely to go away: given realistic assumptions,
Schrödinger evolution won't take **s**-plus-**s´** to an "uncoupled"
state in which **s** is in an energy eigenstate. (Cf. Albert
1992, 88-92.)

[21] It might be objected--for two quite different but equally
misguided reasons--that the bare theory *can* say quite a lot
about what a system is like when the composite state-vector is af_{1}**x** y_{+} + bf_{2} **x** y_{-},
at any rate when y_{+} and y_{-} are eigenvectors
of an ordinary operator **A**, with eigenvalues a_{+}
and a_{-}.

First, although the system is not in an eigenstate of A, it *is*
in an eigenstate of a "coarser" magnitude A*, represented
by an operator **A*** which is just like the operator **A**,
save that it assigns to y_{+} and y_{-}** **the
very same eigenvalue a*. And isn't the fact that the system has
value a* for the magnitude A* perfectly intelligible, even by the
lights of the bare theory? It just means that it has either value
a_{+} or value a_{-} for the magnitude A. Well,
no, it doesn't: given the assumption about **A**, the "disjunctive"
property of having A-value either a_{+} or a_{-}*
cannot* be represented by an operator in accordance with the
eigenstate-eigenvalue link. (The erroneous reasoning just sketched
involves the "disjunction fallacy"--see Hall 1996, 123-35.)

Second, it might be objected that the state represented by the
superposition af_{1} **x** y_{+} + bf_{2}**x** y_{-} is indistinguishable from the corresponding
mixture (represented by weighting f_{1} **x** y_{+}
by a^{2} and f_{2} **x** y _{-} by b^{2}),
which can be given a straightforward "ignorance" interpretation
(i.e. the system is either in the state represented by f_{1}**x** y_{+}** **or by f_{2} **x** y_{-},
but we don't know which). So the states can be identified. This
is doubly wrong. The two states are *not* the same, and anyway
`indistinguishable' means:* the same statistics for all feasible
measurements*--which brings in the prohibited statistical algorithm
(cf. Albert 1992, 84-92).

[22] Many thanks to David Chalmers, Tim Maudlin, and two anonymous
referees for *Philosophy of Science*.