From stapp@thsrv.lbl.gov Fri Jul  3 11:38:20 1998
Date: Fri, 3 Jul 1998 11:33:16 -0700 (PDT)
From: Henry Stapp <stapp@thsrv.lbl.gov>
To: stapp@online04
Subject: Re: Reply to Unruh's letter of June 26,1998

On Thu, 2 Jul 1998, Bill Unruh wrote:

> > On Fri, 26 Jun 1998, Bill Unruh wrote:
> > 
> > > Well, I guess we have finally come to the knub of the disagreement. I
> > > contend that your willingness to separate the truth of the proposition
> > > from the evidence (which once upon a time you agreed was not valid in
> > > QM) is an assumption about reality. 
> > 
> > Dear Bill,
> > 
> > It does appear that we have isolated our point of disagreement. Let me 
> > summarize the situation as I see it. 
> > 
> > You claim that I am inserting a reality assumption that is alien to 
> > quantum thinking. You have admitted that my framework does satisfy some of the
> > reality assumptions that quantum thinking normally requires:
> > 
> > 1. I have no ``hidden variable'' assumption: no assumption that outcomes of
> > unperformed measurements have definite (or predetermined) values.
> > It is completely allowed, within the framework I employ,
> > that the values of the outcomes of the actually performed experiments are not 
> > defined or specified in nature until that experiment is actually
> > performed; and no outcome is assumed to be defined in nature for an 
> > experiment that is not performed.
> 
> Sorry, I have not agreed to this. In fact I believe you have made
> assumptions about unperformed experiments-- namely R1, which is by
> assumption an unperformed experiment.

I draw a clear distinction between the one real situation, which is
supposed actually to occur, and a set of hypothetical possible worlds. The
real world is the one in which L2^c^R2^g holds: experiment L2 is performed
in L, and outcome c appears to the observers of L2, and experiment R2 is 
performed in R and outcome g appears to the observers of R2. My aim is to
examine the class of theories that allow the single real world, presumed
to enjoy the properties specified by quantum theory, to be imbedded in a
set of hypothetical worlds that are structurally similar, in the sense
that they enjoy the exact analogs of the quantum rules. In accordance with
quantum philosophy the outcomes of the real experiments are presumed to be
not predetermined: they are allowed to be undefined in nature until the
moment that some outcome appears to the observers of the experiment.

The condition LOC1 specifies that the nonpredetermined outcome
appearing to the observers of the earlier experiment in L does not depend
on which choice will later be made in region R: this condition limits
the set of allowed hypothetical worlds. You have, in your explanation of
your position (of June 24), not objected to LOC1.

My assertion that ` no outcome is assumed to be defined in nature for an 
experiment that is not performed' asserts just that: ` no outcome is
assumed to be defined *in nature* for an experiment that is not
performed'. R1 is not `in nature': it is a purely hypothetical construct.
Conditions on R1 are, therefore, not conditions on nature, or on reality:
they are, strictly speaking, conditions that are being imposed on a
*theoretical construct* that we are trying to build up AROUND reality.

Moreover, it is not ASSUMED that R1 has some outcome: on the basis of the
actual outcome c of L2 and LOC1 and a prediction of QM (IF L2 has outcome c, 
then, in the hypothetical world in which R1 is perfomed the outcome of R1 will
be f) I DEDUCE that the hypothetical R1 has some definite outcome, namely f.

> > 
> > 2. My formalism is such that no outcome appears to any observer unless
> > the associated experiment is actually performed, and no two incompatible
> > experiments can both be performed.  
> > 
> > 3. There are no presumed realities except for the performed experiments 
> > and the outcomes that appear to the observers of the actually performed 
> > experiments: e.g., There is no Einstein Reality Assumption that some other 
> > kind of reality exists if some value `could be measured' but is not actually
> > measured.
> 
> In removing the condition c but retaining the condition f you are doing
> so I would contend.

Condition f is short for `outcome f appears to the observers of
experiment R1'. But R1 is not real: it is purely hypothetical. Thus any
`outcome  appearing to the observers of experiment R1' must be hypothetical: 
it belongs to the realm of hypothetical (nonreal) things no matter what
is said about c. Thus outcome f never become real: an element of reality.
Nor is f ever claimed to be true in nature, or factual. What is claimed to
be true, or factual is the assertion L2->SR, which says that *under some
hypothetical and theoretical conditions* the hypothetical `outcome f
*would be* true. But R1 and the outcomes appearing to the observers of R1 
remain always in the realm of hypothetical/theoretical things.

Einstein's criterion asserted that one element of reality, P, exists if
the experimenter actually performs one `nondisturbing' measurement, but
another element of reality, Q, would exist if the experimenter were to
perform the other `nondisturbing' measurement. EPR then draw their
`incompleteness' conclusion by asserting, in the penultimate paragraph,
"This makes the reality of P and Q depend on the process of measurement
carried out on the first system, which does not disturb the second system
in any way. No reasonable definition of reality could be expected to
permit this."

That argument embraces the notion that *the real* consist of something
besides that actually performed experiment and the outcomes appearing to
to the observers of these actually performed experiments. I strictly
exclude from consideration any notion of any realities except for
the actual ones just mentioned: L2^c^R2^g.

> > 
> > 4. I define the issue that I am considering as a theoretical one of whether
> > the actual world can be considered to be imbedded in a set of hypothetical
> > worlds that satisfy certain conditions. This is intended to be useful as a 
> > condition that limits the ways that we may consistently and coherently
> > think about (e.g., model) nature.
> > 
> > 5. These conditions are closely connected to the microcausality conditions
> > that are basic conditions on local relativistic quantum field theory. 
> > There one can imagine the quantum world to be imbedded in a classically
> > describable world that allows certain `external parameters' to be manipulated.
> > These changes can alter, relative to the actual world, which experiments
> > are performed. In relativistic local quantum field theory one can, and does,
> > impose the demand that the changes in expectation values induced by a
> > hypothetical change in which experiment is performed in a spacetime region
> > be confined to the forward light cone of that region. 
> > 
> > 6. In quantum field theory the dynamical laws of quantum theory are
> > exactly the same in the actual and hypothetical worlds, apart from the
> > small localized perturbation in the hypothetical world that alters the 
> > choice of which experiment is performed. 
> > 
> > 7, This restriction is something we want to retain. Indeed, the whole idea of 
> > `what would happen' in a hypothetical world becomes ill-defined if one allows
> > the laws of nature to fail in the hypothetical world: the notion that the laws
> > of nature apply equally to the actual and hypothetical worlds is the 
> > *sine qua non*  of scientific discussions of such matters. 
> > 
> > 8. I explicitly specify the pertinent QM law/prediction that holds in case
> > L2 and R1 are performed in the actual world: L2^c^R1-> L2^R1^f. And
> > I explicitly specify that THIS is the law/prediction that is assumed to
> > holds also in the hypothetical world.
> > 

> This is not a "law of nature" This is a statement about the inferences
> which one is permited to draw about actually performed experiments (not
> about hypothetical experiments). If L2 and R1 are actually performed
> then one is allowed to assert this statement. If they are not actually
> performed, then one is not. 

I make the ASSUMPTION that the direct analogs of the "laws of nature"
hold in the allowed hypothetical worlds. It is this assumption that
makes the whole idea of `what would happen' well defined. It is an
assumption that characterizes my enterprise.

> I, as I stated, would allow the weaker
> L2^c^r1->L2^c^R1^f to be asserted.
> Ie, quantum mechaincs certainly does place limits on what one can say
> about "hypothetical" situations, and in particular about the outcomes of
> hypothetical experiments.

> I assert again that if the only evidence for f is c (L2 and R1 being
> assumed) then c^f-/-> f. To do so gives f an independence and reality
> which quantum mechanics does not give one leave to do.

You are saying that although you will allow me to deduce that
L5c: L2->[R2^g->[(R1/R2)-->(L2^c^R1^f)]],
you will not allow me to deduce that
L5: L2->[R2^g->[(R1/R2)-->)(R1^f)]].

But L5c says that it follows from certain conditions that the
defining conditions for L2^c are satisfied *and* the defining conditions
for R1^f are satisfied; whereas L5 says that it follows from these same
the conditions that the defining conditions for R1^f are satisfied. But
just the meanings of the words entail that if L5c is true then L5 is true.

So you are claiming that in order to conform to quantum limitation
on the conception of reality I must abandon the normal meaning of the
logical word "and" in my hypothetical worlds, even though this normal
meaning holds in the real world. But that is upside-down: reality
condition should be about what is real!

I answer that I am considering theories in which the laws of both nature
and logic are the same in the hypothetical and real worlds.
Moreover, any breaking *only in the hypothetical worlds* of the
normal rules of logic or physics that hold in the real world is not a
condition on reality---on the real world---: it is manifestly a condition
on the hypothetical worlds.  

Whatever you are trying to get at is not adequately represented by this
difference between L5 and L5c. That is because L5c, by virtue of
its form alone, claims MORE than L5, not less. You should express your
objection without redefining such a basic feature of rational discourse as
the meaning of the word "and".

> > 9. You admit that *if* THIS assumption is made then my proof is OK.
> > 10. So you are, in that sense, admitting that my proof of line 5 is OK:
> >  L2->SR, does follow from my explicity stated assumptions. 
> 
> 
> > 
> > 11. You are not objecting to my locality assumption, LOC1, which is the
> > only locality assumption that goes into the proof of line 5. 
> > 
> > 12. And you accept that the problem I address makes sense only if the
> > laws/prediction of QM are assumed to carry over to hypothetical world.
> > I explicitly state the pertinent law/prediction that would hold if L2 and R1
> > were actually performed, and you agree that if I assume that this
> > law holds also if that world is hypothetical then my proof goes through. 
> > 
> > So what is the problem?  
> > 

> In the hypothetical world, the experiments are not "actually performed".
> They are by explicit assumption not actually performed. Those laws are
> only valid if those experiments are "actually performed", not
> hypothetically performed.

True! But I am studying to what extent it is possible to imagine, as a
theoretical construct, the possibility of imbedding the real world in 
a set of hypothetical worlds that do obey the same general laws of nature
and logic, and that are related in ways similar to the connection that
holds in local relativistic quantum field theory: there the effects
on *expectation values* of changing from the real world  to a 
hypothetical one in which the same laws hold, apart from a localized
change that alters the choice of which experiment is performed, are
confined to the forward light-cones of the region of the localized
change.

> > You say:
> > 
> > > R1 is not, by explicit assumption,
> > > actually measured independently of L2. R1 is a counterfactual. As such
> > > it is not actaully measured, but the value of R1 is infered from the
> > > actual measurement on L2. Such inference is a form of measurement (a la
> > > von Neumann) but it is not an independent measurement. If R1 were
> > > as I discussed above
> > > actaully measured and L2 were actaully measured and found to have value
> > > c then your statement would be justified. However, by explicit
> > > hypothesis, R1 is not actually measured. R2 is actually measured by
> > > hypothesis.
> > 
> > Correct.
> > 
> > > Under that condition, the best you can say is that 
> > > L1^c^R1->L1^c^R1^f and not L1^c^R1->L1^R1^f. 
> > 
> > I assume that you have made the same misprint again, writing L1
> > in place of L2:
...
> > Yes, it is again L2.
...

> > 
> > I ALLOW *also* the prediction L2^c^R1-> L2^c^R1^f.
> > What this assertion means in logic, and normal language, is that under the 
> > condition that the conditions for L2 and for c and for R1 are all 
> > satisfied, it is true that the conditions for L2 and for c and for R1 
> > and for f are all satisfied. This meaning is a matter of how logical 
> > words/symbols are to be used. They are to be used in this way no matter 
> > whether we are speaking about abstract mathematical propositions, 
> > about properties of graphs or topological structures, about properties
> > of languages, or sociological constructs, or whatever. They are just 
> > conventions about how the words are to be used.
> 
> 
> > 
> > The fact that the sufficient conditions for L2 and for c and for R1 and
> > for f are all satisfied entails that any subset of these conditions are
> > satisfied: A^B->A. Your method of expressing your objection to my argument 
> > is not a satisfactory method because your substantive objection. whatever 
> > it might be, is obscured by your violation of the conventions of rational 
> > discourse.
> 
> That may be. However when language does not capture the nature of
> reality, then one has to try to warp the language so that it does. This
> means that under a conventional interpretation of the language, the
> phrases can look odd. 
> 
> As I have consistantly and repeatedly stated, counterfactual sitations
> cannot, by their very nature, comply with all of the rules of discourse
> and logic. If they did, then we know that, from the false counterfactual
> supposition, one could prove any proposition at all. Thus, only some
> statements which can be made of reality can apply in one's
> counterfactual arguments.
> 
> In this case, f is not a statement about reality, but rather is
> a statement about a non real, hypothetical, counterfactual world. The
> truth of such a statement is, in the case of quantum mechanics, not
> something that one can assert on its own. It can only be asserted by
> grounding it in the simultaneous assertion of a true statement about the
> real world, about real, actually performed experiments, and obtained
> valuesi (c in this case). It has no meaning when asserted on its own,
> since the experiment R1 was not performed, and the outcome therefor is
> non-existant.

But f is not asserted on its own. It is asserted only in a complex
context: L2->[R2^g->[(R1/R2)-->f]].
On its own, f it is neither true nor false: I do not assign
a truth value to any proposition unless it can be deduced from some facts
and the specified theoretical conditions.  

But this *whole statement* specifies a set of conditions that are
sufficient to ensure that the `defining conditions for f to be true' are
satisfied. On its own f is, indeed, neither true nor false. But the whole
statement does capture just this connection of f to real data that
you correctly claim needs to be maintained.

>  To assert f^c->f is, in my estimation, precisely to give f
> the same reality as the outcome of some actually performed experiment.

The assertion that `the outcome f appears to observers of the outcome of
R1' is purely hypothetical, whether or not `outcome c appears to the
observers of the outcome of L2': this statement about the hypothetical
world in which L2^c^R1^f hold cannot be made into a statement about
the real world, in which L2^c^R2^g hold,  by dropping out the mention of
c. To say that omitting the mention of a real condition is *precisely* to
make something that is purely hypothetical into something real is truly
mind-boggling. 

> Without c, f is in this case non-existant. It not either true of false,
> it is simply nonsense, just as is the value for any quantum attribute
> which is not actually measured.
> 

f does not stand alone: it is stated to be true only under certain
conditions.

> > 
> > I do believe that your inability to express your objections
> > within the normal linguistic framework is a reflection of some basic
> > confusion. 
> > 
> No, it is the problem of expressing a situation about the real world in
> a language designed with different assumptions about that real world.

> What I am trying to express is the statement that in quantum mechanics,
> values of attributes have no existence on their own. They have existence
> only to the extent that they are actually "measured", and if that
> measurement is via a correlation with some meaureing apparatus, then
> they have existence (statements about them can be described as
>  having attributes like true or false) only in so far as the statements
> are made about those attributes of the measuring apparatus which are
> actually measured.
> 

But the assertion is that L2->SR is true, and this means that the
conditions specified in this statement (and the theoretical assumptions)
are enough to ensure that `outcome f appears to the observers of R1'.
In the analogous von Neumann measurement situation to which you are
alluding one can have the measuring device being measured by a SECOND
measuring device, and it is enough to mention the only the outcome of this
second device. Here, analogously, it is the real outcome g of the real
measurement R2 that is mentioned: the hypothetical f is asserted to hold
under the condition that g actually occurs. 

There is no need to mention the redundant information about the outcome
c  of the FIRST measuring device. 

This idea of using a *chain* of measuring devices was central to von
Neumann's work, and it is also central to this work.

So YOUR CORE DEMAND  about the nonseparability of the truth of the
proposition about f from the actual outcome upon which it is based, via a
von Neumann chain, IS FULLY SATISFIED!!

> > This particular statement, L2^c^R1-> L2^c^R1^f-/-> L2^R1^f pertains 
> > explicitly to a hypothetical world, not to the real world. So it is certainly 
> > not a reality assumption: it is a theoretical assumption about what sort of
> > logical conditions are going to be placed on the allowed hypothetical worlds. 
> > You are saying that the laws of logic breakdown in the the allowed
> > hypothetical worlds, even though they hold in the real world. What sort of 
> > ``reality'' condition is that?
> 
> I do not understand this paragraph. The hypothetical world is not real.
> f is not real. I am arguing that you are making an assumption about
> "reality" in the hypothetical world. 
> 

I cleanly separate  the real world [L2^c^R2^g] from the others. Reality
conditions are conditions on the real world. Imposing the condition
that the quantum rules and the the rules of logic in the hypothetical
worlds should `mimic' the ones that hold in the real world does not mean
confusing or conflating the worlds that are taken to be real with the
worlds that are identified as being imaginary. It only means taking over
the general rules that hold in the real world and specifying that these
same rules (or their direct analogs) should hold also in these theoretical
possible worlds. "Reality" in a hypothetical world is an oxymoron..

> > 
> > > Just as in the vonNeumann analysis of STern Gerlach, you cannot say that
> > > the electron has spin up independent
> > > of the direction of deflection of the electron beam in the magnet. 
> > 
> > The analogy to the Stern-Gerlach experiment does not support your position.
> > Rather it  undermines it.
> > There is no breakdown of the rules of logic in that case. The
> > analog of L2^c^R1->L2^R1^f is normally taken to hold: if L2^c^R1 
> > *were to be true* then L2^R1^f *would be true*. That certainly does not 
> 
> I disagree.
> 

But, as I now point out, the claim L2^c^R1-> L2^R1^f certainly does not
entail that f holds in the real world, which is the world in which L2^R2
are performed: How can you deny this??

> > entail or mean that f holds in the actual world where R2 is performed 
> > and g appears: f cannot appear in that actual world because it is a possible 
> > outcome of R1, which is not performed in the actual world. It does help always
> > to speak only of `outcome appearing to observers of anexperiment', in 
> > order to keep thinking straight.
> 
> And since f cannot appear in the actual world (where by assumption R2
> was measured), f cannot be assumed to
> behave within an argument as though it were real.

You do not seem to be on board, as regards my whole project.

My enterprise is precisely to see whether it is possible to imbed the
actual world in a set of hypothetical worlds that obey the same
(or directly analogous) quantum and logical rules that hold in the 
real/actual world, and that are connected to the actual world by the
locality conditions that I have specified. Thus although a strict
ontological distinction is maintained throughout between the one real 
world and the hypothetical ones associated with it via these stringent
requirements, nonetheless I CAN AND MUST treat the hypothetical worlds in
parallel to the way one can treat the real world: that is the enterprise! 
[In the counterfactual conditionals there is, however, an essential
dissymmetry, with the premises involving the real world and the
counterfactual claims being about the hypothetical worlds.]

> > 
> > It is the whole statement that is true in the Stern-Gerlach case, not just 
> > the free-floating conclusion.  The statement specifies some particular 
> > conditions that are sufficient to ensure *the validity of the defining 
> > conditions for the conclusion*. One does not need to squeeze the
> > meaning of the whole statement into the conclusion: i.e., to conflate these 
> > particular sufficient conditions with the defining conditions. The 
> > whole true 
> > statement is the correct way to specify specify the connection between 
> > these two logically separate conditions.  
> >  
> > Similarly, it is the whole statement L2->SR that is claimed to be true 
> > under some conditions. These include the theoretical condition that 
> > L2^c^R1->L2^c^R1^f. This condition would be a prediction of quantum theory 
> > if R1 were real, and it is assumed to hold also in the 
> > theoretical/hypothetical world. 
> > 
> > The need for c to hold is an aspect of the whole statement: it need not,
> > and cannot, be made part of the definition of what it means for SR
> > to be true. What it means for SR to be true needs to be defined before one
> > proves it: its meaning does not change once it is prove.
> 
> > 
> 
> > Everything is perfectly taken care of without disrupting the rules of 
> > rational discourse. If one pursues the rational course, then one takes 
> > careful account of the full statement of the particular sufficient 
> > conditions under which the defining  conditions for the conclusion is 
> > derived, rather that trying make these particular sufficient conditions 
> > part of a new definition of the conclusion. 
> > 
> > > Counterfactual reasoning is very tricky, again because such reasoning
> > > asserts a falsehood. The reasoning allowed in those situations is
> > > crucially dependent on the theoretical framework within which the
> > > reasoning is applied. Not all logical steps are allowable (otherwise the
> > > well known attribute of logic, namely that from a false premise, any
> > > statement can be proven true, would also apply). 
> > > 
> > 
> > I have carefully specified the logical framework that I use. As regards
> > the problem of logical coherence and self-consistency, I am
> > protected from any problem of that sort by the fact that I follow
> > the rules of a consistent modal logic. Logicians have been very concerned
> > about this question of consistency, and by staying within a consistent modal
> > logic I am protected against the kind of problem you mention. 
> > 
> 
> Of course here we disagree. Modal logic has been developed (as as far as
> I have been able to determine is still a very contentious and far from
> settled field, even in classical counterfactual reasoning) with a model
> of classical physics as the theoretical underpinning. What we are at
> least in part engaged in here is trying to determine the expent to which
> arguments can be made without change in the quantum world. This argument
> is a bit like someone saying in physics that classical physics is a well
> developed theory and by using it one will not make mistakes in quantum
> theory.
> 

We are talking about the first five lines of my argument. I do conform
to the rules of David Lewis's modal logic, which is, I believe the most
standard one. But I very strongly doubt that there would be any
disagreement at all among modal logicians about the validity, within all
viable modal logics, of these five lines. But all these logics are
constructed to conform to what intelligent people normally mean by these
statements. So in this very simple case I need appeal only to normal
liguistic conventions as understood by physicists. For you to
bring up the fact that in subtle cases not controlled rigidly by
the physical there can be disagreements over what ``would happen'' 
means is to ignore the fact that in this simple case at hand the normal
linguistic conventions do control the  logical connections.

> > I agree that the quantum physicist cannot take over a modal logic without
> > question. I do not accept it blindly. I have carefully tailored what I
> > accept in order both to retain fully the logical structure that ensures 
> > consistency, yet to restrict the real to what is essential to quantum
> > theory, as I discussed at the beginning.
> 
>  I disagree that you have  been careful enough.

I have cut reality back to the bare bones required by the Copenhagen
interpretation, and use only the simplest normal linguistic conventions.

> > 
> > > To repeat myself, in quantum mechanics the truth of a proposition cannot
> > > be separated from the evidence used to demonstrate its truth.
> > 
> > To repeat myself, this statement is ambiguous, and your argument rests on that
> > ambiguity. 
> > 
> > The statement ``the outcome appearing to observers in L in the actual
> > world where L2 and R2 are performed is d'' might be true and might be
> > false: it is true or false depending on what the facts of the matter are.
> > Thus the `defining condition for the statement to be true' IS SEPARABLE
> > from the facts that determine whether or not that condition is 
> > satisfied: otherwise there would be no way to distinguish the condition
> > for the statement to be true from the condition that it be false.
> > 
> > > The truth of a 
> > > propostion in a situation is not in attribute simply of the proposition
> > > but of the complete situation. 
> > 
> > In rational thought *the defining conditions for a proposition to be true*
> > must be specified by the words/symbols in the proposition. In a situation
> > described by a statement in which the proposition appears that statement
> > may describe conditions that are sufficient to ensure that the defining 
> > condition for the proposition to be true are met. Thus *the fact that
> > a proposition true* in a certain situation described by a statement that
> > contains that proposition certain can depend (and normally does depend)
> > on the conditions specified in the statement. But the *defining conditions 
> > for the proposition to be true* do not.
> > 
> 
> The question is whether one can say of the  counterfactual proposition 
> R1^f  that it is  true. My argument is that one cannot do so, unless one
> asserts at the same time that L2^c is also true. 

The hypothetical condition R1^f is asserted to be true WITHIN A CONTEXT,
and this context includes the condition that the ACTUALLY PERFORMED
MEASUREMENT R2 has outcome g [the outcome g is actually observed by the
observers of the actually performed measurement R2]. This is the FACTUAL
DATA that is the basis of the claim that in the hypothetical world in
which R1 is performed, instead of R2, the outcome f would appear to the
observers of the outcome of R1.

> R1^f, being a
> counterfactual proposition, can have a truth value only in conjunction
> with L2^c, and not on its own, 

R2^g will do.

> in that L2 can be considered as the
> measuring apparatus for R1 and because of the correlations in the Hardy
> state, The truth of L2^c can be used to infer the truth of f (even
> though R1, being counterfactual is false). However the truth of f cannot
> thereafter be divorced from the statement c. To assert f has no meaning
> if c is not also asserted. 

R2^g will do just as well.

> It is not that its truth value is unknown,
> but that it is meaningless, just as in the well discussed cases, the
> value of an unperfomed experiment has no meaning ( not is unkown, but is
> meaningless). R1 is an unperformed experiment, by explicit assumption.
> (R2 is by assumption performed). Given L2^c 

or R2^g

> one can make some statements
> about the counterfactual world of R1, but only some statements, and
> those statements are always totally conditional on asserting L2^c.
> 

R2^g will do.

> In your statement L2->SR, you have divorced the statemtn about R1 from
> the assertion of c. Ie, SR is not true or false depending on the
> assertion made about c, but rather SR is meaningless as a statement in
> quantum mechanics without the assertion of c.
> Ie, one cannot decide about what the truth or falsity of SR means
> without asserting c.
> 

R2^g will do.

> The statement "The value of the spin of the particle in the x direction
> is +1/2" is an assertion whose truth or falsity cannot in quantum
> mechanics be even discussed unless one also appends the assertion, " the
> spin in the x direction is actually measured". 
> 

According to von Neumann's analysis it is enough that the
appropriately causally linked outcome appears to the observers of
a SECOND device, as in our case.

> To phrase it in your language, is the statement L2^c->c a sensible
> statement? The answer is no. The statement c is a statement which does
> not even make sense unless L2 is also asserted (as you keep pointing out
> when I make the error of saying L1^c instead.) 

It is enough that L2 be performed. It is quite alright to leave out an
explicit mention of L2 in a later statement if it is entailed by what has
already been stated.

> But sureley by the rules
> of logical discourse, L2^c->c (where c here is taken to mean something
> independent of L2- if the statement c includes L2 by definition, then of
> course L2^c->c is simply a tautology.) 

Yes indeed, L2^c->c is a valid inference: one does not *need* to 
restate it.

> In exactly the same sense, 
> c^f->f is not valid, 
 
read IS VALID

> since in this counterfactual situation, f has no
> meaning without c.

What it means to assert in a counterfactual world in which R1 is
performed that `outcome f appears to the observers of the experiment R1'
is well defined in the theoretical universe of discourse under
consideration here, whether or not c is true. But the *truth* of the
assertion that, in the hypothetical world specified in L2->SR,
`outcome f appears to the observers of the experiment R1' 
does require the truth of some actual fact, and that fact is the asserted
(in SR) truth of R2^g.

> > The phrase `The truth of a proposition' is ambiguous: one should always replace
> > it by either `The *fact* that a proposition is true' or `The 
> > *defining condition* for a proposition to be true."
> > 
> I use it in the first sense.
> > > In this case, the truth of the
> > > counterfactual proposition R1^c is not independent of the evidence, L2^c
> > > which is used to deduce the truth of that proposition. 
> > 
> > The fact that outcome c *would appear* to the observers of the earlier 
> > L2 if R1 were to be performed later rather than R2 follows from LOC1 and the fact
> > that outcome c appear to the observers of this same L2 in the real situation
> > in which R2 was freely chosen in the later region R.
> > 
> > > In the
> > > counterfactual case, the only evidence for the truth of R1^f is L2^c
> > > (Not L2, but L2^c), 
> > 

Under condition L2 the data R2^g is sufficient.

> > The fact that R1^f is true under the specified condition depends on the 
> > fact that
> > L2^c holds under those conditions. 
> > 
> > But the *defining conditions* for R1^f to be true *could hold* also 
> > under some other conditions. 
> 
> No. It is the fact of L2^c which allows one to discuss R1^f at all. Just
> as it is the fact of L2 which allows one to even discuss c at all. The
> truth of c cannot hold under some other condition than the truth of L2.
> Similarly, the truth of the counterfactual propostion R1^f cannot hold
> under some other condition than L2^c.

R1^f could be true under certain other condition: the quantum rules do not
work backward in this Hardy case. R1^f^L2 does not entail  c. And nothing
*prohibits* R1^f from being true if L1 is performed. Logically, c can be
true only if L2 is performed, because c is by definition just one of the
possible outcomes of L2.  But L2^c is definitionally independent of R1^f.

> >  
> > > and the truth of R1^c cannot be seperated from the
> > > truth of L2^c. 
> > 
> > The symbol c stand for the condition that `outcome c appears to the observers
> > of the outcome of L2'. The symbol c has no meaning unless L2 is performed.
> > 
> Another of my misprints. That was supposed to be R1^f.[This one is
> almost impossible to be HumptyDumpty about-- it was just a screw up] However, your
> statement that "c has no meaning unless L2 is performed" is of course a
> statement of quantum world, and would not be true of a classical world.

The experiments and there outcome are, according to Bohr et. al., to be
described in classical language. By definition, c is one of the possible
classically described outcomes  that could appear to the observers of the
classically described L2: is see no classical/quantum difference at this
level of simply describing in classical terms what we do and what we 
observe.

> In exactly the same sense, I am claiming that in this situation, R1^f
> has no meaning unless L2^c are actually perfomed.
> 
> > > To do so is to adopt an attitude of realism to R1^f
> > 
> > To do what? I never separate the truth of c from L2! It is unthinkable
> > within the severely restricted realm of allowed possibilities.
> > 
> 
> To believe that R1^f, as a counterfactual statement, can have a meaning
> independent of the truth of L2^c is the assumption of reality.

The assertion that the spin of the particle  points in the +z direction
has a *meaning*, or definition, even if we do not make any measurement: 
what is lacking is a *truth value* for that statement. We know what it
*means* to say the particle is in the state |+>: we use that concept 
all the time. It is just a definition. Similarly, we can introduce
a theoretical structure in which the concept R1^f is one of the
primitive elements, to which we assign the words `hypothetical experiment
R1 is performed and outcome f appears to the observers of R1.'

> > Moreover, R1 is very explicitly identified as being hypothetical, not real.
> > So any conditions pertaining to R1 are not condition on the nature
> > of reality: they are NOT reality conditions. They are theoretical 
> > restrictions on worlds that are explicitly proclaimed to be purely
> > theoretical.
> 
> Precisely. 

But you have been claiming that these conditions on R1 *are* reality
conditions. Now you admit that they are not.

> > 
> > > (Realism for me is precisely the claim that the truth of a proposition
> > > is independent of the evidence for that truth- that once you have proven
> > > a proposition true, then you can accept it as true independent of that
> > > proof-- in this case that the value of R1 is f even if you deny the only
> > > evidence therefor, namely that L2 is c.)
> > > 
> > 
> > The condition R1^f is not free-floating: it is not claimed to be true.
> > In fact, it cannot be true, since R2 is actually performed. What is true, 
> > under
> > certain specified theoretical assumptions, is *the whole statement* L2->SR.
> > The condition L2^c is part of what has gone into the proof that L2->SR. 
> > But the defining condition for the statement L2->SR to be true does not 
> > involve condition any on c. Nor do the defining conditions for SR to be 
> > true.
> 
> I disagree. SR has no meaning unless c is also asserted (just as c has
> no meaning unless L2 is asserted).

c is defined to be one of the possible outcomes of L2, and hence is does
not have a meaning unless L2 is performed. Their definitions are entwined.
But the defintions of SR and c are not entwined. They refer to logically
distinct elements of the logical calculus under consideration here. The 
basic elements of the locical calculus correspond to the distinct
imaginings of which experiments might set up, and what the various
possible outcomes that could appear to us, under these various possible
imagined conditions, might be. It is the distictness of our imaginings
of these various possibilities that justifies our taking them as distinct
elements in the logical calculus.

Of course, any claim that some hypothetical statement H is true under
certain circumstances can only be *valid* if those circumstances include
tha assertion of the truth of some actual fact (the appearance of some
particular outcome of some actual experiment) that is connected by a
logical chain to H. Or in any case, that condition is certainly satisfied
in the argument under scrutiny here. 

> > 
> > In summary, your argument:
> > 
> > 1. Demands abandoning a basic principle of rational discourse, the
> >    rule that A^B->A.
> 
> Just as you pesistantly do when you state that c has no meaning
> independent of L2 (Ie, L2^c->c is also meaningless for a quantum
> system.)

No! L2^c does imply c: A^B-> A holds universally.

> > 2. Demands abandoning the basic principle of rational discourse that
> >    the defining condition for a proposition to be true should be defined 
> >    by the words/symbols in that proposition.

> Assumes that in quantum mechanics, the meaning of a proposion is not
> independent of the conditions under which it is true. Just as c has no
> meaning unless L2 is asserted to be true, SR is meaningless unless c is
> asserted to be true.
> 
In quantum theory the basic theoretical element are statements about the
possible experiments we might perform and the possible outcome that might
appear to us: these are described in classical language. The meanings of
statements about these things are based in our mental images of the
different possible experiments, and the appearing outcomes. In quantum
theory the *meaning* of each pair (E, O_E), where E specifies an
experiment and O_E a possible outcome appearing to the observers of E.
is distinct, and each such pair generally corresponds to a different
quantum state. What is meaningless in quantum theory without
data/evidence is not what (E, O_E) means, or what it means for the state
to be the one labeled by (E,O_E). What is meaningless without
data/evidence is the question of whether or not the state of the system is
the one specified by (E,O_E). It is facts not the meanings that are
ill-defined without evidence. 

> > 3. Is not supported by the example of the Stern-Gerlach experiment
that you 
> >    cite for support.
> Alternatively, you do not understand the example.

In the Stern-Gerlach experiment we agree that the *fact* of whether the
spin is pointing up or down is not well defined if spin is measured in
some other direction. On the other hand, the *meaning* of the assertion
the the particle is in the spin up state is well defined. To determine  a
*fact* we need evidence: to determine a *meaning* we don't. 

> 
> > 4. Is not about a `reality' condition. You claim that I ought to allow
> >    laws of logic to fail in the *hypothetical* worlds that are being
> >    contemplated, even though they do not fail in the real world. 
> >    [You accept that L2^R2^g-> L2^c^R2^g-> L2^c^R2, but insist that I 
> >    reject L2^c^R1->L2^c^R1^f->L2^R1^f]
> 
> > 5. Is based on an ambiguity in the meaning of the phrase
> >    `The truth of a proposition': you confound the meaning `The *fact*
> >    that a proposition is true under certain conditions' with
> >    `The *defining conditions* for the proposition to be true.'
> 
> Although you may find my phrasing ambiguous, my argument does not rely
> on that ambiguity.

You keep saying that the meanings (defining conditions) are not well
defined without data/evidence, whereas it is the facts, not the meanings,
that require data. 

You think you are forced to change meanings, in order to overturn
line 5: L2->SR. You think line 5 must be wrong because it appears to
assert a conclusion f without specifying that the pertinent data c
was factual. However, that reason is not valid: following von Neumann,
it is acceptable to use data TWICE REMOVED, so long as the logical chain
is secure. Thus R2^g suffices, and the is no problem with the absence
of the relevant data. But then there is no rationale for abandoning
the basic rule if logic, and thereby challenging line 5.

Best wishes, Henry