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REVIEW
The
Structure
and
ESSAY*
R. I. G.
Mechanics,
and
1989
Hughes,
Cambridge:
Philosophical
on BelVs Theorem,
Consequences
Theory: Reflections
of Quantum
James T. Cushing
and Ernan McMullin.
Notre Dame: University
of
Notre Dame Press, 1989.
Interpretation
of Quantum
Harvard University
Press,
on the philosophy
else had been published
of quantum
in 1989, these two books would have made
it a good year.
to the foun
has written
the best self-contained
introduction
Hughes
to
dations of quantum mechanics
and
the
volume
appear,
yet
by Cush
an
and
is
McMullin
accessible
but
ing
sophisticated
snapshot of philo
on
a classic.
Bell's
that
to
theorem
is
become
sophical thinking
likely
For the reviewer,
the two books make an appealing pair. Hughes
has
an essay in the Cushing and McMullin
volume (henceforth C&M) that
If nothing
mechanics
sketches his own position,
but also amounts in some ways to a reply to
a
various of the papers
in the collection.
I will begin by discussing
selection of the essays from C&M,
all of which seem to me to raise
issues that bear interestingly on Hughes's
position. At that point, I will
take up Hughes's
view, weaving
together his essay in C&M with the
more developed
in
his
book.
position
Philosophical
Consequences
of Quantum
Theory consists of thirteen
a
with
papers on Bell's theorem,
essay by James
together
background
a
a
at
historical
discussion
of
action
distance
Cushing,
by Ernan McMul
lin and an extensive
Some
of
the
have appeared
papers
bibliography.
elsewhere
are new
and part of Mermin's)
but most
contribution,
(van Fraassen's
to this collection.
I will single out three papers for special
attention: Bas van Fraassen's, Arthur Fine's, and Paul Teller's.
In the
I will refer to several of the other essays. I will not mention
process,
I will not be discussing
the contribu
every essay in C&M. In particular,
tions by Abner
Michael
Linda
Don Ho
Redhead,
Wessels,
Shimony,
ward and Henry Folse, nor the introductory
and concluding
essays by
Cushing
Synthese
and McMullin
86: 99-122,
1991.
respectively.
However,
I don't
think
there are
100
REVIEW
ESSAY
a
I have made
is mostly
any bad essays in the book, and the selection
reflection of my idiosyncrasies.
Van Fraassen's
contribution
is a somewhat
version of his
expanded
of Realism: Epistemological
of Bell's
1982 'The Charybdis
Implications
an
on
with
based
'EPR:
his
1985
When
together
appendix
Inequality',1
Not a Mystery?'.
is a Correlation
The thesis of "Charybdis"
is that
a
violations
of
Bell's
confirmed
strong
inequality provide
experimentally
calls epistemic realism. This is the
argument against what van Fraassen
view that we can have reasonable
about future regularities,
expectations
in particular,
of correlations,
about the persistence
only if we have
some
is
that under
reasonable
that
there
causal
mechanism
certainty
In the case of the Bell-type
the
writes
the regularities.
experiments,
are
of
correlations
between
separated
regularities
pairs
space-like
causal account would
events, and van Fraassen urges that a reasonable
sense - an event
have to appeal to a common cause in Reichenbach's
in the past that renders the correlated
He gives an elegant demonstration
events
that
stochastically
there are no
independent.
such common
causes.
Let us concede
that there can be no
(as virtually everyone
does)
common
cause explanation
for failures
of Bell's
Van
inequality.
so long as our
moral:
Fraassen
thinks this carries an epistemological
are based on well-supported
theories, we are justified in
expectations
or
not a causal account
to
is
whether
regularities
expecting
persist
or even possible.
In the end, this might
be right, but not
available
in a way that conflicts with the deep intuitions of epistemic
necessarily
van Fraassen
In "Charybdis",
realism.
realists as
depicts
epistemic
but surely that is too strong.
insisting on causal accounts of correlations,
The strongest reasonable position would be that in order to have reason
we need reason
about the persistence
of correlations,
able expectations
that there is some account of the correlations,
able certainty
whether
turn out to be a
it be causal or of some other form. And
it might
constraint on the confirmation
of theories that they either embody or
are consistent with some account of the correlations
they predict.2
I think there is an interesting
the point
issue here, but let us waive
a
amounts
to
for now. Van Fraassen's
in
C&M
concession
appendix
that not all accounts of correlations
need be causal. He lists five ways
than common cause in which correlations
have traditionally been
us
are
two
most
to
and logical
The
of
interest
coordination
explained.
link - to
Van
takes
coordination
direct
causal
Fraassen
i.e.,
identity.
other
REVIEW
101
ESSAY
and
require matter or energy to travel from one location to another,
are space-like
if the two locations
he thinks that this is incoherent
events
he adds, "Correlations
between
distant
Further,
separated.
same
are
to
not
of
the
extended
less
facto
parts
entity
happening
ipso
are
What
that
remains,
then,
mysterious"
explanations
appeal
(p. 112).
to "logical
of this matter
is in the 1985
identity". The full discussion
is based. I would
like to turn to that
paper on which the "Appendix"
account, which I find quite curious.
identity explanations
proceed by showing that the correlated
are aspects of a single variable. Here's
how van Fraassen
seem to work for quantum
suggests that this might
systems. Suppose
that A and B commute,
have a set {</>,-}of common
such
eigenstates
Logical
variables
that
A(f)i
=
a?(t>i,
B(?>?
=
/>/</>,,
and
the
that 4> = 2/c?
suppose
measured
jointly, we can be certain
for some k, the joint outcome will be
is that there is a maximal
quantity C
distinct.
Now
a's,
as well
as
the
6's,
are
all
</>,-.In that case, if A and B are
that the results will be correlated:
(ak, bk). The apparent explanation
such that A = /(C) and B = g(C),
and the measurements
of A and B are just partial measurements
of C.
us
on
sort
not
Van Fraassen
to
this
that
of
"is
tell
goes
explanation
This
is
because
embarrassed
(1985, p. 118).
by spatial separation"
AI and IB for systems X and Y (I have deleted
observables
the tensor
are
are
and
both
of
AB. An
functions
product sign)
always compatible,
choice of state will produce
correlations
of the sort dis
appropriate
cussed above, and once again, it will apparently be no mystery
that the
are correlated:
results of AI and IB measurement
in measuring
AI and
of C = AB.
IB, we are really just making partial measurements
Van Fraassen
to the
thinks that this account breaks down. Return
value z, then we could claim
general case. If C had a pre-existing
that the correlated
and y = g(z) simply reveal partial
values x = f(z)
information
about z. But suppose C has no such pre-existing
value.
Then we can't account for the x-result of the A-measurement
by saying
that if we had measured
z, and x is just
C, we would have observed
nor
can
we
can
we
assume that
B.
such
about
Worse,
say
any
/(z),
thing
have ready-made
values if we adopt a contextual
quantum observables
hidden variable theory, but to accept such a theory is
...
to admit
a radical
and unverifiable
difference
between
observables
and
the
of
Hermi
among
algebra
. . .
tian operators
(1985, p 121)
the relations
102
REVIEW
ESSAY
I find much about this discussion
the initial, gen
puzzling. Consider
eral case of A, B, and C. At one point, van Fraassen
suggests that there
is something
to
that
mechanics
quantum
gives the putative
peculiar
we
its
Whereas
might expect in general that co
explanation
purchase.
a
not
would
among observables,
measurablilty
logical connection
imply
the world ismuch more
"sub specie the quantum mechanical
formalism,
intuition
and internally connected
than our general
tightly organized
is
there
Nonetheless,
might suggest" (1985, p. 118).
nothing peculiarly
to make
the present
about the intuitions needed
quantum mechanical
no
reason
and
is
also
values
should
there
run,
why pre-existing
example
a thoroughly
be required. Consider
classical device: a tetrahedral die,
with faces with one, two, three or four spots on them. Now consider
two experiments.
The first, A, consists of tossing the die and recording
the number of spots mod 3 on the base of the die. The second, B,
consists of tossing the die and recording
the number of spots mod 2 on
can be performed
in
these experiments
jointly. Now
nor
us
not
A
will
B
the
result
tell
the
result
of
of
general,
knowing
as the reader can easily check. But suppose we have so
vice-versa,
of the roll
contrived
the state of things that even though the outcome
is not completely
the side that ends up as the base will
determined,
have either one or two spots on it. In that case, the results of A and
B will be correlated: A will have result 1 iff B has result 1; A will have
result 2 iff B has result 0. This is no mystery. When we perform A, we
the base.
Clearly,
about
the result of the experiment
information
C, i.e.,
get partial
the number of spots on the base.
tossing the die and simply noting
about the result of
Similarly, performing B gives us partial information
C. If the state of things restricts the possible outcomes
appropriately,
no
A and B will be strictly correlated.
But notice:
there is absolutely
need to assume that there is a pre-existing
fact about what the result
of C was to be before the die was actually tossed, or that in tossing the
die,
we
are discovering
facts
about
the pre-existing
value
of
some
variable.
to
has said points
My point thus far is that nothing van Fraassen
at
at
and
least
the
mechanical,
further,
anything peculiarly
quantum
of pre-existing
values is a red herring. We
general level, the question
can describe a classical case that is like the quantum one in relevant
but for which a
and includes the feature of indeterminism,
respects,
is
of
correlations
identity" explanation
"logical
perfectly
acceptable.
REVIEW
ESSAY
103
in the same way in the quantum case? Why
isn't
Why can't we proceed
this a perfectly good way to account for the correlations?
An objection
that won't work is that in the quantum
case, we are
and
this
measurements,
presupposes
pre-existing
supposedly performing
that quantum measurements
values. We needn't
presuppose
merely
For all we have said - for all we know
reveal pre-existing
information.
- a
information
is like a roll of a die, with
quantum measurement
like a roll of
created in the process. Suppose a quantum measurement,
a die, is a process in which a system comes to be in a certain condition,
events
and hence in which an event from a certain range of possible
will occur, though precisely which event is not, in general, fixed. The
state places restrictions on the range of possibilities
open to
quantum
the system, but quantum
like
other
rich
any
theory, provides
theory,
resources for individuating
events. In the case van Fraassen describes,
the theory tells us that the event of the system coming to display A =
=
a? is the same event as the event of the system coming to display B
to the third observable
C is not
b?. In fact, we see that the reference
crucial; what is crucial is the identity of certain possible events.
It seems that we really can explain some correlations
among chance
to
the
hidden variables,
without
outcomes,
by appealing
identity of
events. Without
there is no reason
further argument,
certain possible
case. However,
I want to look
why we can't do this in the quantum
more closely at van Fraassen's discussion of contextual hidden variables.
We will find that he is straining at a gnat while
standing ready to
swallow
a camel.
Let us grant that the "radical and unverifiable
difference"
between
and the algebra of hidden variables is a serious
the algebra of operators
But suppose we could somehow know that
objection.
epistemological
structure really is correct. That leaves the real problem:
the contextual
in a very peculiar way. There
the hidden variables will be non-local
a
will be pairs AB, AD such that AB has
value associated with the pair
to
and a+a'.
of numbers
Now
(a,b), AD is associated with (a',d),
measure
"here" and you use a B-apparatus
AB, I use an A-apparatus
and you use your D
"there". To measure
AD, I use my A-apparatus,
I am partially measuring
observable
apparatus. Thus, which maximal
depends on which apparatus you set up. And for the hidden state under
this translates
into a constraint on results: what result
consideration,
my apparatus will display depends on what apparatus you set up. But
104
REVIEW
how
does my
apparatus
"know"
ESSAY
what
quantity
is undergoing
partial
measurement?
already
underlying
point here is actually one that van Fraassen
AB and AD are non-local
This suggests
that the
quantities.
sort of extended
system is a particular
entity,
(and peculiar)
underlying
and the displays of results in the two wings of the experiment
are, in
to parts of the same extended
effect, "distant events happening
entity"
as
van
in such
But
Fraassen
(C&M p. 112).
pointed out, correlations
The
made.
a case
are
not
automatically
unmysterious.
The
local entities. They are connected
presumably,
contact" with some aspect of a single entity,
to tell the apparatus which
local information
should be looking at. So the real problem
it is that
variables
is not their unverifiability;
measuring
devices
are,
by virtue of being "in
but there is no obvious
feature of the entity it
with contextual
hidden
seem
they
incapable of
their explanatory
task.3
performing
hidden variables
We will return to contextual
later. I would
like to
move on to a discussion of Arthur Fine's paper,
'Do Correlations
Need
to Be Explained?'.
Fine's target is explanatory
which holds
essentialism,
that correlations
require explanation
regardless of the scientific context
essentialists
talk of "new and quasi
they arise. Explanatory
or odd 'pas
'influences'
processes
(maybe funny
mysterious
physical
to
in
of
Bell
Fine
the
failure
the
response
inequalities.
sions')" (p. 180)
believes
there is no need to invoke such oddities.
violates
The kernel of the argument
is simple: quantum mechanics
even
no
term
when
is
in the
there
interaction
the Bell
inequalities
of the two particles. Fine thinks that philosophers
should
Hamiltonian
take their lead from the theory and stop positing
influences, but he also
- a
offers a scheme for thinking about the experiments
scheme accord
in which
there are no cross-wing
influences of any sort, and thus,
ing to which
one that satisfies what Fine calls strong locality (SLOC).
out
The model
is simple enough. Think of individual measurement
comes as coming about "m a perfectly
random way" (p. 184). Suppose
in the A-wing,
with
Ai is measured
the B-wing. Fine assumes,
sensibly,
ences the other.
The
have
and B{ is measured
in
choice of setting influ
the Bx measurement
itself and the
left over would
be between
dependency
. . randomness
that
the outcome
the Ax measurement.
However,.
implies
. . .Thus
. . .we . . .
on which measurement
not depend
is performed
in the B wing
a framework
in which
is
satisfied,
184-5)
[SLOC]
(pp.
possible
outcome
of
does
result plus,
that neither
REVIEW
105
ESSAY
it is easy to describe random sequences of outcomes
that link
we
a
to
Bell's
So
have
violate
together
inequality.
apparently
purely
local model
for the correlation
experiments.
there
is the key here. In an indeterministic
world,
Indeterminacy
can
events
undetermined
that
exhibit
be
of
sequences
individually
surely
an overall statistical pattern. But, Fine adds,
Further,
. . .
are just probabilistic
two sequences
of events
between
patterns
Why,
from an indeterminist
random
should the fact that there is a pattern between
perspective,
to
than the fact that there is a pattern
internal
sequences
any more
require
explaining
Correlations
the sequences
themselves?
(pp.
191-2)
forms part of the "ideal of natural order" (a phrase that
in terms of which quantum
from Toulmin)
borrows
theory is
the correlations
of quantum
framed. Thus conceived,
Fine maintains,
than do uniform motions
in New
theory no more call for explanation
tonian and post-Newtonian
physics.
In 'Antinomies
This may puzzle readers of Fine's earlier work.
of
and
and
'Correlations
Physical Locality'
Entanglement'
(1981),
(1982)
Fine claimed that responsible
indeterminism
(see especially Fine 1981,
of Bell's
violations
pp. 544-8) does not encompass
inequality. What's
different now?
Fine, call two runs of a Bell-type
Following
adjacent if
experiment
one
in
in
be
differ
the
Let
the
Ai,
A2
wing.
they
setting
settings on the
an A^
run
the
of
and
for
Bi,
Thus,
B2.
A-wing
similarly
experiment,
is adjacent to an AXB2 run. And call two adjacent runs entangled
if the
Indeterminism
Fine
for the shared observable
differ. Even ifA{, A2,
sequence of outcomes
to satisfy Bell's
it would be very
Bi and B2 were chosen
inequality,
that the four runs of the experiment would be untangled,
but
unlikely
so long as Bell's
in
inequality stands, the statistics could be exhibited
runs. However,
if the inequality is violated,
is
untangled
entanglement
In 'Antinomies
of Entanglement',
Fine found this genuinely
required.
seem to have
p. 743). Two considerations
(see especially
puzzling
change his mind.
first is the fact, noted above,
that, Bell's
inequality aside, the
are minute. Violations
odds for finding untangled
of the
experiments
at in
these tiny odds vanish (p. 189). Looked
inequality simply make
this way, failures of Bell's inequality seem less impressive. The second
consideration
has to do with hypothetical
about a single run.
questions
helped
The
Suppose
I performed
a sequence
of A^
measurements.
Would
the
106
REVIEW
ESSAY
instead? It
Ai sequence have been the same if I had measured
AiB2
is tempting to think that locality says yes. One might
think that if the
this would amount to an influ
Ai sequence could have been different,
ence of the distant setting on the local outcomes.
Fine disagrees.
If the
are undetermined,
outcomes
there is no fact about what would have
in any respect, local or remote. To
had things been different
happened
seems to Fine to require determinism,
or something
insist otherwise
like it; indeterminism
blocks the derivation
of a Bell inequality.
This suggests weakening
the premise:
say simply that the same A!
result might have occurred
if the B-setting
had been different.
Fine
that this won't do. True, the "might" statement doesn't presup
and is a plausible
of locality. But it is
consequence
pose determinism
argues
too
weak.
might
not
probability
"wrong".
In
any
actual
run
of
an
experiment,
quantum
mechanics
for any finite experiment
there is a
indeed,
come
out
that
the
the
will
numbers
given by
theory
to
So counterfactual
derive
Bell's
strong enough
reasoning
be
verified;
counterfactual
strong premises;
requires overly
inequality
reasoning
from appropriately
weak premises doesn't
imply the inequality.
I'm puzzled. Call the principle
that the result here would have been
was in the setting there the "would"
the same if the only difference
Call the similar principle with "would" replaced by "might"
principle.
to a statistical
the "would" principle
the "might" principle. Appending
not
does
entail
that
the
statistics
of
any
theory
particular
experiment
will come out right. The interesting question
is whether
the "would"
is compatible with the statistics coming out right. For quantum
principle
see David Mermin's
it isn't. (For a very nice demonstration,
mechanics,
'Can You Help Your Team Tonight
essay,
TV?') Now
by Watching
the "might" principle
if we allow a
doesn't
imply a Bell
inequality
violation of the quantum
statistics. But neither does the "would" prin
to its
ciple. If we offer the "might" principle the same courtesy extended
brasher brother, perhaps we will get the same result. In fact, Mermin's
section
that this is so. (See pp. 47-9,
suggests
concluding
strongly
('Quantum Non
47.) Further, Henry Stapp argues explicitly
we
and
the
of
that
if
Nature')
locality
require the quantum
Description
statistics to be verified, we can extract a contradiction
from locality and
especially
the "might" principle.
I am not sure whether
he would
compare
have
every
is correct. To convince me,
Stapp's argument
an explicit
and
semantics
for counterfactuals
move
even
to
it
But
argumentative
explicitly.
though
invoke
REVIEW
107
ESSAY
I'm not certain that Stapp is right, I'm not certain that he's wrong. The
counterfactual
here are profoundly
questions
tricky, and I don't think
treatment of them is sufficiently
Fine's
to settle the matter.
detailed
But rather than agonize over counterfactuals,
I would
like to approach
the question of "influences"
in another way.
Jon Jarrett has pointed out that the usual locality condition
is the
of a condition he calls locality, and another that he calls
conjunction
A Guide
to the Implications'
completeness.
(See his 'Bell's Theorem:
for a nice summary.)
I will use Shimony's
(1986) terms, parameter
independence
independence
(PI) and outcome
(OI). PI requires that the
local outcome
be stochastically
of
the distant setting. In
independent
the elegant notation
that Mermin
the
for
volume,
proposed
(PI)
=
p(x/i, j, A) p(x/i, A)p(ylu j, A) p(ylj, A)
and B-wing outcomes,
/ and ; are
(x and y are, respectively,
A-wing
on
A
is
the
and
and
Fine
focuses
whether
B-wing settings,
state).
A-wing
in
the
distant
influence
local
results.
However,
changes
setting
quantum
mechanics
satisfies PI, and that may explain why Fine doesn't detect
violations
of locality. On the other hand, quantum states violate OI:
(OI)
=
p(x, y/i,j, A) p(x/i,j, X)p(y/i,j, A).4
Thus a more fruitful question
is whether violations of OI embody some
sort of influence of events in one wing on events in the other. I think
reasons for answering yes. An important one goes
there are plausible
cause. In 'A Space
back to Reichenbach's
principle of the common
to the Bell Inequalities',
Time Approach
Jeremy Butterfield
gives the
following,
slightly weaker
statement
of Reichenbach's
principle:
... if x and y are correlated without
direct causation,
there is in their common past an event z that screens
off. (p. 115)
then
them
Butterfield
is not willing simply to embrace this principle, he
Although
that it can be made plausible
the
argues convincingly
by associating
screeners-off with large regions of space-time.5 But from Reichenbach's
principle, we have a corollary:
If x and y are correlated,
common past that screens
by a direct causal link.
and
there
them off,
is no event z in their
then they are connected
108
REVIEW
ESSAY
In one sense, to avert to this principle
is to beg the question
against
the burden of proof lies.
Fine. But there is a serious issue of where
The principle of the common cause is a highly general one that serves
us well
we apply it to Fine's
in a wide variety of contexts. When
we
that
violated.
conclude
SLOC
is
True, quantum
model,
proposed
term in the Hamiltonian,
but
mechanics
does not posit an interaction
are
causal connections
that may just be to say that certain fundamental
a
structure
in
of
of
the
itself.
the
Further,
theory
forthcoming
part
deep
shows that on David Lewis's analysis of causation,
article, Butterfield
a causal link between
events
in the two
failures of OI do constitute
is not prepared
Butterfield
Again,
simply to embrace Lewis's
is
and highly general.
that
but
analysis
analysis,
plausible,
sophisticated
that Fine has not made his case. Even
So I maintain
though the jury
influences.
may still be out, a prima facie case can be made for non-local
There are, of course, reasons to doubt that the quantum correlations
are causal connections.
A bad one is that faster-than-light
causation
is a bad reason because
This
violates
(I claim) no such
relativity.
conclusion
follows from relativity. What
relativity requires is that real
Lorentz
be
invariant
under
transformations.
For causes,
facts
physical
to reverse or transform away a
that it must be impossible
this means
If it were part of the
causal connection
transformation.
by a Lorentz
that the cause must unambiguously
of a causal connection
concept
wings.
the effect in time, then relativity would rule out superluminal
precede
connec
causes. But I am deeply suspicious of this supposed conceptual
to be causal, there
tion. What
ismore plausible
is that for a connection
cause and
must be an unambiguous
of some sort between
distinction
on
than
other
effect. If the distinction
could be made
temporal grounds,
causation. The more plausible
this would
leave room for superluminal
is that failures of OI are symmetric and causation
relativistic difficulty
as usually understood
this is open to challenge,
however.
isn't. Even
as
For example, Richard Healey
conceives of the quantum correlations
to
causal processes"
1989) and is attempting
(Healey
"non-separable
work out the issues in detail.
are
So what's
the point? The point is that the quantum correlations
- so much so that on some accounts
very much like causal connections
talk of "passion at a
they are causal. This suggests that when people
distance" or the like, they are not being obscurantist;
they are trying to
on the one hand, acknowledging
the important
walk the line between,
and more
familiar causal
between
similarities
correlations
quantum
REVIEW
109
ESSAY
to the differences
and on the other, giving due weight
connections,
and the ones on which traditional analyses
these phenomena
between
of causation were based. Fine admits in a footnote
(p. 190) that the
matter of "influences"
needs investigation,
but he doesn't give the point
in his discussion.
nearly enough weight
A related point about causation
and indeterminism.
Surely there is
as an ideal of
on
stress
about
Fine's
indeterminism
something
right
to terms with quantum mechanics
will require
natural order. Coming
an
to
terms
But
there
is
unresolved
with
indeterminism.
ques
coming
a
to
chalk
tion of how to tell when it is appropriate
up
surprising
simply
to the manifestations
of the natural order. Suppose
class of phenomena
we discovered
states
that
grounded
"sub-quantum"
superficial viola
tions of OI in deep probabilistic
violations
of PI. This would
strongly
suggest that there is an influence exerted by settings in one wing on
in the other. But someone might
try to insist that we need
not talk of influences; that there ismerely a complicated
pattern among
measurement
not
unlike
the pattern
and
outcomes,
"setting-events"
outcome
in the two wings of a Bell
that Fine sees between
sequences
I don't think we would be content with this. Whether
type experiment.
we are Humeans
about causation or whether we adopt a thicker view,
our overall notions of influence and causation would not cohere with
of PI. My
this story. My point is not to propose
looking for violations
even
we
not
of
Bell's
is
that
the
violations
by
inequality
point
explain
of OI as causal. It is that in trying to decide
coming to see violations
events are connected
whether
by a relation of influence, we need to
look to our more general concepts of causation and influence. We may
end up modifying
these in the light of the theory. Or we may simply
outcomes
be able to use
them
to make
clear what
the theory has been
saying all
along.
Teller
as an ideal of
of indeterminism
Part of Fine's aim in his presentation
was
was
intended to put us
natural order
it
undoubtedly
therapeutic;
at ease conceptually
correlations
with the quantum
by helping us to
overcome
aims are also
habits of thought. Teller's
old deterministic
a
different
in part, but his diagnosis
suggests
conceptual
therapeutic
ailment.
Teller's
Inequalities',
and the Bell
Holism,
paper is called 'Relativity, Relational
aim is to explain the nagging feeling
and his immediate
110
that somehow,
tum mechanics.
REVIEW
ESSAY
of Bell's
violations
inequality are in conflict with quan
He notes that there is an extremely
simple argument
the assumption
such a conflict. If we combine
of determi
that suggests
nate values for quantum observables
with the requirement
that local
not depend on distant settings, we get a Bell inequality. But
outcomes
on the face of it, relativity requires both the determinateness
of values
and the locality condition. Here's why.
for determinate
values
is essentially
the EPR argu
The argument
ment. By the correlations
of the singlet state, we know that a measure
ment here allows us to predict an outcome
at a space-like
there. But
to
is
taken
forbid
the
transmission
of
relativity
normally
superluminal
information.
here could not have created the value
So my measurement
the value must already have existed. Further,
and again
measure
must
of
this
value
be
of
choice
my
by relativity,
independent
ment
and locality, and hence,
setting. So we have determinateness
Bell's inequality,
from the correlations
and relativity.
Teller does not think this is a valid argument. However,
it is at least
as plausible as the (surely very plausible) EPR-style
argument on which
there. Hence,
it rests. Teller's project is to figure out is what has gone wrong. To do
about relativity. Teller accepts Einstein's
that, he has to say something
is a principle
view that relativity
theory; "a set of general constraints
must
which
detailed
any more
theory
satisfy"
(p. 212). For special
one
most
constraint
the
is
the
mentioned
earlier:
general
relativity,
invariant. But our working
"real" physical processes must be Lorentz
theories as describing
picture is more detailed. We think of relativistic
at space-time
the world
in terms of the values of physical quantities
theory. Further,
points. That is, we think of relativity as a space-time
"classic" relativistic
theories describe processes
in terms of
That is, there is no "action at a distance"
in space or time;
are always between
connections
close"
"infinitesimally
or light-like.
causal chains are always
time-like
finally,
local action.
direct
points.
Teller
causal
And
calls
theories
Causal Theories.
satisfying all of these constraints Relativistic
are
so
we
to
wed
relativistic
As
causal
theories?
Teller sees it,
Why
it is because we accept an even more basic metaphysical
doctrine, which
is the view that
Particularism
he calls particularism.
. . . the world
is composed
ties, and that all relations
of the relata,
(p. 213)
of individuals,
that the individuals
on
individuals
between
supervene
have
nonrelational
the nonrelational
proper
properties
REVIEW
111
ESSAY
that physical
Teller doesn't
think that particularism
literally entails
theories must satisfy contact action and no superluminal
propagation,
but he does believe
that both of these theses are natural adjuncts to
particularism.
next question
is a particularistic
is whether
quantum mechanics
no.
as
answer
is
Teller's
States
such
the
singlet state
theory.
superposi
to pairs
states
tions of tensor product
ascribe relational properties
on non
and larger collections,
but the relations
do not supervene
relational facts about the individuals. Now relational holism is compat
ible with Lorentz
invariance, as relativistic quantum theory makes clear.
But relational holism clashes with the idea that all respectable
theories
must be relativistic
local action
causal theories,
i.e., must incorporate
and no superluminal
This is not because relational holism
propagation.
or
action-at-a-distance
it is because
superluminal
propagation;
posits
for
that
doesn't
allow
the
there
be non
may
possibility
particularism
The
relations between
systems.
supervening
How does this help us shake off the grip of the EPR-style
argument
are
to
that
for Bell's
be
told
there
Merely
inequality?
nonsupervening
relations
is not to be told enough. Teller doesn't address this question
directly, but the answer seems to be a corollary of his treatment of the
stochastic case. The standard locality condition
for stochastic
theories
has been
Factorizability.
A metaphysically
naive
like this:
go something
a direct causal link or
and A are sufficiently
p(x,y/i,j,
A)
=
p(x/i,
A)/?(y//,
A).
argument from relativity to factorizability
a correlation between x and y presupposes
a common cause.6 But (recall Butterfield)
would
either
if /, /,
common
any possible
x
causal link between
inclusive,
they encompass
a direct
cause. And
for Bell-type
experiments,
and y is ruled out by the relativistic No Superluminal
Propagation
naivit? here resides in thinking that relativ
principle. The metaphysical
to be accounted
for by positing either a com
ity requires correlations
mon cause or a direct causal link. As Teller sees it, these are presupposi
not of relativity.
tions of particularism;
In fact, we can be more precise. We know from Jarrett that factoriz
of PI and OI. We also know that quantum
ability is the conjunction
mechanics
argues that the
respects PI and violates OI. And Teller
failure of OI can be seen as a failure of particularism.
To see this, we
need
two premises:
112
REVIEW
ESSAY
First Assumption:
When
holds, nonaccidental
particularism
correlations
arise only through
(a) The action of a common cause, or
(b) The action of a direct causal chain.
Second Assumption:
When
holds, relativistic
particularism
causal theories exclude superluminal
causal propagation,
(p.
220)
This
yields
a simple
argument:
of a common cause has been eliminated
by mak
on
conditional
the
list
of
all
A,
ing everything
possible known
common causes. The action of a direct causal
and unknown
2. Thus, there are no nonacci
link is ruled out by assumption
on A. That is, outcome
dental correlations
conditional
inde
The
action
pendence
holds,
(p. 221)
are failures
failures of outcome
Hence,
by contraposition,
independence
of particularism.
But the perfect correlations
of the EPR thought ex
are special cases of the failure of outcome
periment
independence.
out
in one wing are perfectly
correlated with appropriate
Outcomes
comes in the other not because of a direct causal link, not through a
common cause, and not by the obtaining of locally definite,
correlated
values, but because
mechanics
embody
the conditional
probabilities
a nonsupervenient
relation
provided by quantum
the two part
between
icles.
on his thinking
that when
the grip of particularism
Teller writes
became clear to him, his resistance to the "random devices in harmony"
of Fine's 1981 and 1982 melted
away.7
- as an
correlation
of the pair of
property
objective
is simply a fact about the pair. This
objects taken together
The
fact.
. . need
not
be
. . .
supervenient
upon
some
facts. There need be no mechanism
can be analysed,
the correlations
(p. 222)
nonrelational
more
basic,
into which
I find that the gestalt of Teller's
view switches uncomfortably
back
and forth between a species of realism about relations and a deflationary
view. Is the claim that there are real relations
that ground and, in a
or
account
for
is it simply that the
the
sense,
correlations,
quantum
REVIEW
113
ESSAY
patterns among events have formal features that our classical
leads us not to expect? Teller spends much time talking the
experience
he talks of ontological
of
locality of values vs.
language
metaphysics:
or
He
that
"relational holism
holism.
relational
says
nonsupervenience
relations"
takes there to be things in the world
(p.
nonsupervening
no
room.
the
claim
think
about
But
makes
which
for
223)
particularism
that failures of outcome
just are failures of particularism.
independence
statistical
One would expect Fine to reply that failures of outcome
independence
are just particular
statistical patterns among events and nothing more.
then we
If failures of OI are ipso facto instances of relational holism,
and
both Hume
have a grand name for a humble fact. A comparison:
use the term "necessity"
in talking about causation. But
his opponents
for
is simple talk of regularities, whereas
for Hume,
talk of necessity
it is a way of saying that something grounds the regulari
his opponent,
I honestly can't tell is whether
relations are
ties. What
nonsupervening
meant
to be part of the glue of the universe
or mere
oil on
troubled
waters.
about
raises other questions
The analogy with accounts of causation
the nature of relational holism. The salient contrast throughout Teller's
relativistic causal theories (RCTs) and nonsuperven
paper is between
is that (a) RCTs are particularist
ient relations. The suggestion
theories,
causal accounts of the correlations
and (b) relational holism eschews
be
But I find the connection
(though it does not forsake relativity.)
tween the principles
and particularism
obscure.
The
of RCTs
quite
standard relativistic construal of events as the instancing of properties
But
at place-times
has a reasonably clear connection with particularism.
are that
that actually figure in Teller's
the aspects of RCTs
arguments
I don't see that
causal action is (i) "local" and (ii) subluminal. And
these have any connection with the reducibility of relations.
a correlation
Begin with a simple question.
Suppose we discovered
that was not mediated
i.e., that acted "at
by any intervening process,
a distance",
but was in all other respects just like a causal connection.
to a failure of particularism? Why
events are "at a distance" make
one?
should the interpolation
Why
nonsupervenient
events be a step in the direction
series of "connecting"
relations - of particularism?
The possibility
of such
rests on the continuity
But what does
of space-time.
Would
that
this amount
the correlated
the fact
the relation a
of a continuous
should
of supervenient
an interpolation
that have to do
114
REVIEW
ESSAY
fail if space-time
with particularism? Would
automatically
particularism
were discrete? Or would particularism
events were
hold if neighboring
a
or two?
but fail when the connection
connected,
space-atom
skips
I am similarly confused
about the connection
between
subluminal
and particularism.
Teller concedes
propagation
(p. 212) that tachyonic
accounts of the Bell correlations
can't be ruled out. I therefore assume
that he does not want to say that tachyonic connections
would amount
to nonsupervenient
relations. But if not, I am still puzzled about the
connection
between
the slower-than-light
signals and particularism,
which after all is a view about the reducibility
of relations.
are causal relations not
To all of this I add a related worry. Why
cases of nonsupervenient
Since Teller believes
that failures
relations?
seems especially
acute
of OI are failures of, particularism,
the question
a correlation
two
for stochastic
causal connections.
Consider
between
cause of y. (My
events x and y in which x is the complete probabilistic
in part to Andrew
discussion
here
is indebted
Elby's
forthcoming
Then x and y
the EPR Correlations
'Should We Explain
Causally?')
will be stochastically
and there will be no event z that
dependent,
screens y off from x. In other words, we will have a situation
that is
a
case
outcome
of
So
like
the
of
failure
why
formally
independence.
in
one? What
between x and y a nonsupervenient
isn't the relationship
terms of
from the supposedly
causal relations
distinguishes
enter
that
failures
of
OI? True, failures
relations
into
nonsupervenient
are not. But
of OI are symmetric, whereas,
causal
relations
perhaps,
a relation is reducible?
what does symmetry have to do with whether
is
but my diagnosis
there are answers to all these questions,
Perhaps
at too high a level of gen
that relational holism has been formulated
erality. What we need to do is look more closely at the crannies and
crotchets of quantum
theory itself. And with that, we turn to Hughes.
is a clear,
The Structure and Interpretation
of Quantum Mechanics
relations
to the foundations
of quantum me
sound introduction
pedagogically
chanics. Part one (the first six chapters) treats the basic facts of quantum
for use with under
in Hubert
mechanics
space and is well-suited
are
and there are
and
finite
The
manageable,
graduates.
examples
two
six
text.
the
Part
exercises
(the remaining
throughout
sprinkled
more
more
covers
is
material
and
advanced
self-consciously
chapters)
students.
It will probably work best with graduate
interpretive.
a
a
at
the book may
look
and
casual
is
teacher,
clearly
gifted
Hughes
a
a
In
definite
it
is
textbook.
that
fact,
suggest
interpretive
primarily
REVIEW
ESSAY
115
the book. Hughes's
is developed
essay in C&M,
throughout
perspective
a
and
'Bell's Theorem,
Structural
Ideology,
provides
Explanation',
summary of many of the most important themes, as well as a perspective
on Bell's theorem.
I will structure the discussion by weaving back and
as the
forth between
the book and the essay, with Bell's
theorem
will be to Hughes's
book unless otherwise
guiding focus. References
indicated.
Pace Fine, van Fraassen,- and Teller, Hughes
thinks that quantum
the
What
for the account is
mechanics
correlations.
is
crucial
explains
an explanation.
his conception
in providing
of what
is involved
Two
influences
his
view:
the
"Western
Ontario"
general
quantum
shape
of theories. These come
logical tradition and the semantic conception
in the way that Hughes
the idea that quantum me
together
develops
sense.
As Bub puts it, principle
chanics is &principle
in
Einstein's
theory
theories "introduce
abstract structural constraints
that events are held
to satisfy"
at p. 258). Much
in Hughes
too
1974, p. 143. Quoted
believes
that
mechanics
structural
quantum
briefly, Hughes
provides
A principle
these ground-level
explanations.
theory provides
explana
tions by "making
the structural
features of the models
the
explicit
so
In
doing
theory employs"
(p. 258).
(Bub
... it disassembles
the black box, shows the working
and puts it back together again. (C&M, p. 198)
parts,
is used here in the sense of abstract mathematical
"Model"
structures
such as those studied in model
theory. But these same structures are
also the focus of the semantic conception
of theories. So the semantic
the natural setting for expounding
the notion of a
conception
provides
In the case
structural explanations.
theory, and for providing
principle
are
of quantum mechanics,
features of the models
many
important
in the same structures that have been the focus of quantum
embodied
space, generalized
logic: the lattice of subspaces of Hilbert
probability
measures
on these subspaces and the like.
of a structural explanation
of the
What,
then, are the components
There are four, dubbed Representability,
Non
quantum correlations?
terms appear only
and Entanglement.
These
Orthodoxy,
Projectability
in the essay, but the ideas are worked out in detail in the book.
is just the fact that the observables
and probabilities
Representability
on a single Hilbert
of a quantum system can be represented
space. This
or even trivial, but chapters three and four
may sound unenlightening
116
REVIEW
ESSAY
book make
clear that this is not so. The treatment of
observables
in chapter
three is especially
nice. Here
incompatible
an
makes
but
Consider
very important point.
any
Hughes
elementary
and a single statis
family {A,-} of, e.g., two-valued physical observables
of Hughes's
to represent
tical state pi. It will always be possible
the state and the
on a single vector space. However,
observables
if we consider even a
A and B and a pair of states pi and p2,
observables
pair of two-valued
then unless px and p2 are related in a highly constrained
it will
way,
not be possible
to represent
these observables
and states on a single
vector space; representability
is a highly non-trivial
feature of quantum
systems.
This theme is further developed
in chapter four, 'Spin and its Repre
a
sentations'. Here Hughes
account of how very
clear
gives
elementary
and
determine
the Hilbert
symmetry
general
continuity
assumptions
on
of
electron
The
is,
space representation
symmetry
spin.
emphasis
of course, old hat to physicists,
but it has been neglected
by philoso
to
goes on, both there and in C&M,
phers for too long.8 Hughes
make
the point that a system can possess many of these very general
in Hilbert
space. Mielnik
being
representable
an
a
of
system that exhibits
provided
example
possible
most
of
the
that
behaviour
symmetry conditions
probabilistic
satisfying
lists
for
the
of
electron
measurements,
Hughes
(essen
probabilities
spin
tially continuity,
invariance) but the
isotropy of space, and rotational
are not quantum mechanical.
transition probabilities
On the one hand,
this emphasizes
the point that Representability
is a non-trivial matter.
symmetries
(1968) has
without
to force
On the other hand, the additional
constraint
that is needed
It
the quantum mechanical
is
"natural".
is that
very
representation
a
vector
like
be
momentum,
spin,
angular
quantity.
and their representations
in terms of
By looking at the observables
can
see
we
as
the
considerations,
symmetry
representation
intelligible
I think this is part of the answer to a
and, we might
say, "natural".
that we raised in connection
with Fine, namely, when
it is
a
some
to
declare
that
is
manifestation
just
appropriate
phenomenon
of "nature". Begin by recalling an example
that Fine mentions,
but
that Teller also appeals to (pp. 222-3). This is the switch from requiring
to seeing it as "natural". Galileo
be explained
th^t uniform motion
question
didn't
to be natural;
in effect he offered
just declare uniform motion
to
Now
of
the
course,
symmetry arguments
symmetry
support
posit.
can
nature
fail.
could
be
consistent
Indeed,
any
way at all;
principles
REVIEW
ESSAY
117
to. But the guiding
could have made the world any way He wanted
nature
is
is
of
that
or, as Einstein
theorizing
intelligible;
assumption
not
to
be
that
but
malicious.
the
Old
One
subtle,
it,
may
put
Appeals
are
one
nature
also
into
of
call
way
symmetry
making
intelligible. They
To explain is sometimes
the dichotomy
question
"explainable/natural".
or unpuzzling. We may explain something
to render intelligible
pre
cisely by showing how it can be regarded as "natural".
we come to Entan
order of presentation,
from Hughes's
Departing
means
to
is
This
related
what
Fine
glement.
ultimately
by the same
God
sense is different.
has to do
term, but the immediate
Entanglement
each
with the fact that if we have two quantum
systems,
represented
natural way of combining
the
space, then the algebraically
by a Hilbert
- also
a
tensor
Hilbert
the
spaces
representa
product
taking
provides
tion of the observables
for the two systems. Among
the vectors in this
of which
is
ones, the existence
space, we have the "non-factorizable"
some
states
All
facts:
the
for
of
deter
pure
striking
(i)
responsible
pair
states for the subsystems,
mine "reduced"
but (ii) there are pure states
states for the
of a pair of systems
that determine
mixed
"reduced"
to the subsys
On
the
other
mixtures
hand,
subsystems.
(iii) assigning
tems does not suffice to fix the state of the joint system. Finally,
(iv) the peculiar pure states of (ii) do not render the two subsystems
are the features that
(C&M, p. 201). These
statistically
independent
are
Features
and
(iv)
(ii)
strikingly non-classi
comprise Entanglement.
cal. That is, pure states on a classical probability
space never exhibit
features (ii) and (iv). In one sense, this is a mere rehearsal of a formal
it isn't. The fact that single systems are Representable
fact, in another,
is not just a brute fact; as noted above, considerations
of symmetry can
- into
us
what
makes
the
tick
into
how the
give
insight
representation
of the black box fit together. But these same considerations
components
can be extended
to pairs and larger collections
to make some sense of
Entanglement.
is a species of holism. But the way in which Hughes,
Entanglement
or I in my (1984), appeal to it seems to me to have advantages
over
the general doctrine of relational holism. The emphasis here is on a
very specific structure, and what does the work is not just the fact that
on the states of the subsystems;
the singlet state doesn't
it
supervene
is the way in which this state is related to the eigenstates
of the observ
ables to be measured,
and the way in which, via Gleason's
theorem,
the overall structure fixes the probabilities.
We don't need to decide
118
REVIEW
ESSAY
whether
of OI per se, or, for that matter,
causal relations
violations
are cases of relational holism. Rather, we get a very fine-grained
picture
structures lead to Bell's inequality,
of how it is that classical probability
structures allow it to be violated.
but quantum
are an indication of a more general feature of quan
states
Entangled
tum mechanics:
is the fact, exhibited
Non-Orthodoxy
Non-Orthodoxy.
as
in
results
such
Bell's
theorem
and Kochen
and
especially
clearly
are
not
functions
classical.
that
theorem,
quantum probability
Specker's
- in
The underlying probability
effect, the lattice of subspaces of
space
a
structure.
assessment
of
Hilbert
has
different
very
space
Hughes's
more
in
is
his
view
from
stand
distinguishing
Non-Orthodoxy
important
ard quantum-logical
views. Putnam and, especially,
the Western
Onta
as
saw
us
rio quantum
the
lattice
of
how
the
telling
logicians
subspaces
a
are
talk
structured.
But
of
quantum system
rejects
Hughes
properties
of properties
for quantum
Instead he sees the real
systems altogether.
in its emphasis
logical program as lying precisely
insight of the quantum
- on Non-Ortho
on the non-standard
character of quantum probability
is a generalization
of classical
doxy. But associated with Non-Orthodoxy
to what has come to be known as the "L?ders Rule".
conditionalization
In the book, Hughes
spells this out in some detail. For any probability
measure
?xon the subspaces of Hilbert
space, and any subspace S, there
?
R is a subspace
is exactly one measure
such that whenever
?jls ppUS)
new measure
This
of S, /ms(R) = p(R/S)
is given by jjl(R)/p(S)
(p. 224).
on the non-standard
comes as close to conditionalization
probability
sees the application
to come. Hughes
of L?ders's
space as it is possible
he uses
rule as telling us how the state changes on measurement.
Hence,
to refer to the applicability
of L?ders's
rule.
the term Projectability
I will both follow and
Let us now tie these strands together. Here
account. Representability,
(marginally)
expand upon Hughes's
supple
mented
insight
by the account of spin in terms of symmetry, provides
for a single spin-1/2 system are related.
into how the spin observables
the tensor product representation
The story is continued by introducing
for the pair, and noting that the singlet state exhibits Entanglement.
is tied to a particular manifestation
of Non-Orthodoxy;
Entanglement
leads naturally,
the way in which the individual systems are represented
to states that exhibit the peculiar statistics character
if not inevitably,
in
istic of the singlet state. Finally,
given the result of a measurement
one wing, Projectability,
rule for the non-ortho
the conditionalization
dox probability
space, provides a revised state that predicts the perfect
REVIEW
ESSAY
119
and the more general statistical correlations
correlations
that are
the subject of Bell's
inequality.
to van
Note that this account (if it is successful) provides a response
Fraassen's
attack on epistemic
realism. It is not a causal account. But
it is a realist account. Further,
it bears on the matter of contextual
EPR
variables. Van Fraassen's
that "sub specie
throwaway comment
the quantum
the world is much more tightly organized
and
formalism,
our
connected
than
intuition
well
internally
suggests" might
general
serve as a motto
for Hughes
and for the more general quantum
logical
tradition into which his view fits. On the quantum
logical view, what
is wrong with contextual
hidden variables
is precisely
that they ignore
the tightly organized
structure of the quantum observables.
Further,
in no way presupposes
that observables
have values prior to
Hughes
hidden
measurement.
Measurement
elicits certain events; it localizes the values
so to speak,
is guided,
But the pattern of localization
are
the
in
which
the
observables
knit
in
the Hilbert
way
by
together
to - excludes - cases in which
space. The singlet state is orthogonal
have the same value. And given the way
parallel
spin measurements
in which
the singlet state is related to the eigenstates
of the other
the
Gleason's
theorem
determines
observables,
product
completely
measurement
outcomes.
for
the
probabilities
It should be clear that I am broadly sympathetic
to Hughes's
account
of the correlations.
This is not surprising, since (as Hughes
points out)
it is similar to views that I have offered
in print already.
I also think
there is genuine and important novelty here. To mention
just one thing,
I think that Hughes
has done more than anyone else to provide content
to the important but elusive notion of a principle
theory. Nonetheless,
I have some complaints
and some worries.
account of the correlations,
and the account I would favor,
Hughes's
is in the spirit of the discussion
of the tosses of the die several pages
as creating
as realizing
back. It portrays measurements
information;
a
But this presupposes
possibilities.
particular view of the measurement
of observables.
I
it presupposes
is not a linear process.
that measurement
problem:
think that something
like this must be right, but saying more
is notori
is well aware of all the problems,
and says some
ously difficult. Hughes
as a theory formulated
interesting
things about quantum mechanics
against a "classical horizon"
pp. 312 ff.) but the dis
(see especially
cussion
peculiar
leaves one thirsty for more. To be sure, this is not a problem
or the quantum
to Hughes
logician, but it takes on a particular
120
REVIEW
needs
aspect there. More
"event", and I find Hughes
to be
much
this
ESSAY
said about the underlying
notion of
less informative
than I would
like on
score.
I want to raise is not crucial in the context of Bell's
objection
a full-scale evaluation
but
in
of Hughes's
it would
inequality,
position
be important.
we
I am quite unconvinced
his
claim
that
should
by
eschew talk of properties
in dealing with quantum
The
argu
systems.
ment for the view seems to be that any attempt to ascribe properties
to quantum
little ac
systems will result in a change of logic with
and
in
the
will be
case,
any
companying
gain,
resulting properties
variants
of
these
creatures"
"pallid, scarcely recognizable
(p. 217). But
it is hard to see how Hughes
himself can avoid talk of properties.
His
is an event interpretation,
and the most natural way to think of events
is in terms of the instancing of properties.
Further, part of the pallidity
of quantum-logical
is
that
"properties"
they are frequently disjunctive.
are
But disjunctive
worse
not
than disjunctive
properties
obviously
The
cannot avoid disjunctive
and Hughes
events. This comes out
in
his
of
discussion
the
two-slit
In order to
very clearly
experiment.
are
must
L?ders's
he
that
both
when
slits
the
rule,
say
apply
open,
event A v B occurs, which is "the event that the electron passes through
either [slit] A or [slit] B" (p. 232). But Hughes
also tells us that "we
... as
will no longer be able to describe
the electron
passing either
or
A
B"
In
other words,
through aperture
through aperture
(p. 237).
a disjunctive
a fact characterizable
event has occurred,
by means of a
events,
statement. But neither of the disjoined events has occurred,
disjunctive
and so neither of the disjoined
statements
is true.
I have no intrinsic objection
to this story. But, to repeat, I don't see
events are less objectionable
than disjunctive
why disjunctive
proper
ties. Indeed, if it turns out that the best analysis of events analyzes them
in terms of properties,
then we are likely to be stuck with disjunctive
anyway. So why not just leave them in from the start?
properties
a substitute
offers
for properties,
in the form of what he
Hughes
are probabilistic
calls latencies (pp. 301-6). Latencies
of
generalizations
sees
as
Whereas
deterministic
properties.
Hughes
properties
grounding
the disposition
of a green thing to appear green
dispositions
(e.g.,
"under normal conditions")
latencies ground the probabilistic
disposi
tions of systems. Hughes writes
... we
can never
find a probability
function
p such that, for
REVIEW
121
ESSAY
=
=
every event [E], either [p(E)
1] or [p(E)
0]. That
can
never
to
be
reduced
these
latencies
say,
properties,
is to
(p.
304)
this begs the question
However,
logician, who
against the quantum
denies that properties must have any such feature. Indeed, as near as
I can tell, quantum logicians get everything
that Hughes
from properties
we can say
that
from
with
the
added
bonus
latencies,
gets
interpretive
- when
true
like
is
it
it
what
is
what
of
about
the
system
something
is not being measured.
at best a selective
In spite of the length of this essay, it has presented
contain. A virtue that I haven't
these two volumes
sample of what
to
stressed enough
is the service that these two books will provide
of quantum mechanics.
instructors teaching courses in the foundations
course,
Either, or both, could serve as the basis for an undergraduate
suitable
for use with graduate
but both contain plenty of material
students. Pedagogical
virtue aside, I hope to have conveyed my own
sense of just how stimulating
and McMullin's
in Cushing
the papers
to become
book are. Both volumes deserve
collection
and Hughes's
standard works in the foundations
of quantum mechanics.
NOTES
*
SES #8720600.
Research
for this essay was partially
by NSF Grant
supported
1
on this paper before
I have commented
(see my 1984), but I hope the reader will find
remarks to justify returning
what I have to say here sufficiently
different
from my previous
to this paper.
2
This
that confirmable
theories must be
is not completely
far-fetched.
It is plausible
framed
in terms of "natural
ness
kinds
of
figure
3
This
or genuineness
in explanations.
to me
occurred
Arthur
the APA.
4
Jarrett
Fine
as a result
in a lecture
offered
states
kinds",
"genuine
properties"
of properties
might well
these
conditions
the differences
won't
However,
as Butterfield
In particular,
of
about
thinking
holism
in a somewhat
matter
about
or some
have
such. And
to do with
a related
delivered
at the
different
(and
the natural
their
ability
of holism
critique
1990 Pacific Division
technically
superior)
to
that
of
way.
here.
to it offered
out,
apparent
by van
exceptions
points
to
fail because
take the potential
screeners-off
they don't
a
common
chunk
of
the
encompass
past (pp. 121-31).
large enough
6
This is, in effect, Reichenbach's
again. Teller notes (p. 220) that the statistician
principle
to it.
also subscribes
Lincoln Moses
7
were
"Random
in Harmony"
conceived
of as ways of thinking about conser
Devices
Fraassen,
Salmon
and Bell
122
REVIEW
ESSAY
world.
laws in an indeterministic
whose
They were
pairs of particles
were
but somehow
at the source
determined
random,
responses
completely
one another
(Fine 1981, p. 547).
8
to this rule.
is an exception
Van Fraassen
vation
individual
to mirror
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