Aaargh, I see from looking at my last message to Jack Mallah at
hotmail completely ignored the paragraph breaks I put in between the
numbered items on the list of propositions, making the lists extremely hard
to read. I'll try resending from my gmail account and hopefully it'll work

> Date: Mon, 22 Feb 2010 11:41:38 -0800
> From:
> Subject: RE: problem of size '10
> To:
> Jesse, how do you access the everything list? I ask because I have not
recieved my own posts in my inbox, nor have others such as Bruno replied. I
use yahoo email. I may need to use a different method to prevent my posts
from getting lost. They do seem to show up on Google groups though. There
was never a problem until recently, so I'll see if this one works.

I just get the messages in my email--if you want to give a link to one of
the emails that didn't show up in your inbox, either from google groups or
from ,
then I can check if that email showed up in my own inbox, since I haven't
deleted any of the everything-list emails for a few days.

> --- On Mon, 2/22/10, Jesse Mazer <> wrote:
> > Hi Jack, to me the idea that counterfactuals would be essential to
defining what counts as an "implementation" has always seemed
counterintuitive for reasons separate from the Olympia or movie-graph
argument. The thought-experiment I'd like to consider is one where some
device is implanted in my brain that passively monitors the activity of a
large group of neurons, and only if it finds them firing in some precise
prespecified sequence does it activate and stimulate my brain in some way,
causing a change in brain activity; otherwise it remains causally inert
> > According to the counterfactual definition of implementations, would the
mere presence of this device change my qualia from what they'd be if it
wasn't present, even if the neurons required to activate it never actually
fire in the correct sequence and the device remains completely inert? That
would seem to divorce qualia from behavior in a pretty significant way...
> The link between qualia and computations is, of course, hard to know
anything about. But it seems to me quite likely that qualia would be
insensitive to the sort of changes in computations that you are talking
about. Such modified computations could give rise to the same (or nearly the
same) set of qualia for the 'inert device' runs as unmodified ones would
have. I am not saying that this must always be the case, since if you take
it too far you could run into Maudlin-type problems, but in many cases it
would make sense.

OK, so you're suggesting there may not be a one-to-one relationship between
distinct observer-moments in the sense of distinct qualia, and distinct
computations defined in terms of counterfactuals? Distinct computations
might be associated with identical qualia, in other words? What about the
reverse--might a single computation be associated with multiple distinct
observer-moments with different qualia?

> > If you have time, perhaps you could take a look at my post
> >
> > where I discussed a vague idea for how one might define isomorphic
"causal structures" that could be used to address the implementation
problem, in a way that wouldn't depend on counterfactuals at all
> You do need counterfactuals to define implementations.
> Consider the computation c(t+1) = a(t) AND b(t), where a,b,c, are bits.
Suppose that a(t),b(t),and c(t) are all true. Without counterfactuals, how
would you distinguish the above from another computation such as c(t+1) =
> Even worse, suppose that c(t+1) is true no matter what. a(t) and b(t)
happen to be true. Is the above computation implemented?

You say "Suppose that a(t),b(t),and c(t) are all true", but that's not
enough information--the notion of causal structure I was describing involved
not just the truth or falsity of propositions, but also the logical
relationships between these propositions given the axioms of the system. For
example, if we are looking at three propositions A, B, and C in the context
of an axiomatic system, we can ask whether or not the axioms (which might
represent the laws of physics, or the internal rules of a turing machine)
along with propositions A and B (which could represent specific physical
facts such as initial conditions, or facts about particular cells on the
turing machine's tape at a particular time) can together be used to prove C,
or whether they are insufficient to prove C. The causal structure for a
given set of propositions could then be defined in terms of all possible
combinations of logical implications for those propositions, like this:

1. Axioms + A imply B: true or false?
2. Axioms + A imply C: true or false?
3. Axioms + B imply A: true or false?
4. Axioms + B imply C: true or false?
5. Axioms + C imply A: true or false?
6. Axioms + C imply B: true or false?
7. Axioms + A + B imply C: true or false?
8. Axioms + A + C imply B: true or false?
9. Axioms + B + C imply A: true or false?

For example, one possible causal structure for three propositions would be:

1. Axioms + A imply B: false
2. Axioms + A imply C: true
3. Axioms + B imply A: false
4. Axioms + B imply C: false
5. Axioms + C imply A: false
6. Axioms + C imply B: false
7. Axioms + A + B imply C: true
8. Axioms + A + C imply B: true
9. Axioms + B + C imply A: false

Then if you had three other propositions D, E, F, they would have an
isomorphic causal structure to A, B, C if you could map the two sets of
propositions to one another such that all the logical implications would be
the same. For example, suppose the following logical relations hold for D,
E, F:

1. Axioms + E imply D: false
2. Axioms + E imply F: true
3. Axioms + D imply E: false
4. Axioms + D imply F: false
5. Axioms + F imply E: false
6. Axioms + F imply D: false
7. Axioms + E + D imply F: true
8. Axioms + E + F imply D: true
9. Axioms + D + F imply E: false

Then if you map D to B, E to A, and F to C, you can see that their causal
structures are isomorphic. On the other hand, suppose the logical relations

1. Axioms + D imply E: true
2. Axioms + D imply F: true
3. Axioms + E imply D: false
4. Axioms + E imply F: false
5. Axioms + F imply D: false
6. Axioms + F imply E: false
7. Axioms + D + E imply F: true
8. Axioms + D + F imply E: true
9. Axioms + E + F imply D: false

In this case their could be no isomorphism with A, B, and C, since D can be
used to prove either E or F, but neither A nor B nor C can be used to prove
both the other two propositions in that group. So in this case A, B, C would
not have the same causal structure as D, E, F.

So, it seems to me that identifying observer-moments with particular causal
structures avoids the implication that any possible system can be
"interpreted" in such a way as to instantiate any possible observer-moment,
but it also avoids the need to consider counterfactuals, since we can
restrict ourselves to propositions about events which actually occurred.

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