On 03 Mar 2014, at 11:36, Stathis Papaioannou wrote:
On 3 March 2014 17:40, Bruno Marchal <[email protected]> wrote:
What if someone says that the function of the brain is to provide
consciousness. Is that functionalism?
What if someone says that the function of the brain is to link a
"divine"
soul to a person through a body?
What is a function?
No, a function is an observable pattern of behaviour.
You do use "function" in a non standard sense.
Functionalism says that if you replicate this, you also replicate
the mind.
You need to replicate not only a special behaviour (which could be
quite
easy) but all outputs for all inputs.
At all levels. Your functionalism is just what is called
"mechanism". That
generalizes indeed "digital mechanism", that is comp.
It is not "functionalism" in the sense of philosopher of mind,
where it
means computationalism, with a fuzzy fixed level.
OK then, mechanism. But I don't see why mechanism would *necessarily*
be digital. Is it a contradiction to imagine a machine that is not
Turing emulable? I don't mean here anything necessarily to do with
consciousness, just a machine that does a particular physical task.
There is no logical contradictions. Mathematically, we can easily
defined such machines, which needs some infinite components to be non
Turing emulable, but it is hard to design an experimental test to
confirm that some observable "effects" are due to something not Turing
emulable.
To be sure, if we are digital machine, then I doubt that there are any
test for us to be able to verify this, as a small machine cannot
distinguish an infinite machine from a big machine.
But it makes theoretical sense. Some optimization of soap film might
be non Turing emulable, according to some people, but I am not
convinced by their arguments.
If we take classical GR literally, it seems we can build infinite
machine by exploiting some time dilation, around black holes, and
well, why not.
The literature is difficult on this, because they use notion of
computability on the real numbers, but nobody really agree on what
that means. Pour-El and Richard wrote a book on that subject, using
the natural correction of Turing's definition of computability on the
reals, (the most decent definition) and shows that some differential
equation can have non computable solutions, or worst, that some
computable functions (from R to R) can have non computable
derivatives, and this makes such notion mathematically consistent, but
I doubt that any such math has counterparts in nature.
But, you are right, mechanism is not necessarily digital. Note that
AUDA still functions with strong weakening of comp. I use comp mainly
because the reasoning and proofs are much simpler, and non digital
machines are quite a speculative notion, from the empirical point of
view.
Some people reject them because they disbelieve in any actual infinite
in nature, but I am agnostic on this.
Note also, that the arithmetical reality is full of "non Turing
emulable" entity/machines. Their role in comp is still not clear to me.
That would be the case if consciousness were substrate-dependent.
But you can put the substrate in the function. A brain would have
the
function to associate to that substrate the experience. How could
I say no
to the doctor who guaranties that all the function of the brain are
preserved.
The term function, like set, is too general, to much powerful.
Then I'm using it in a somewhat precise sense as above.
Unfortunately, "observable pattern of behavior" is not that much
precise.
"observable" is a complex epistemic notion for example. But I got it.
By observable I mean only what you call 3p. The contention is that if
the 3p behaviour is reproduced through whatever means, the 1p
phenomenology will also be reproduced. I think this is consistent with
the original meaning of functionalism, in particular the notion of
multiple realisability.
I agree.
Of course, a non Turing emulable machine might be hard to have
substitutable parts, as we will have to replace an infinite machinery,
with an equivalent one. There might be no notion of a level of
substitution. And if there is, the task of the doctor might be an
infinite task, unless the doctor is an infinite being too.
Then Craig argued once that something can be finite and non Turing
emulable, which is close to nonsense to me. I asked him an example,
and he gave me "the color yellow", but this means that he was alluding
to the 1p experience of "yellow", which in comp is not something
"Turing emulable" either, as it makes no sense to say that the 1p is
Turing emulable, or even is a machine or anything 3p. The predicate
"machine" does simply not apply to them, except from God's eye, in
some possible sense, if we assume comp.
But the terminology doesn't really matter, and
in fact sometimes gets in the way; it's better to be clear by saying
exactly what you mean.
That is the best custom in many part of science. We don't worry to
repeat the definitions, and very often we change them, but we make
that clear to avoid any confusion.
Bruno
http://iridia.ulb.ac.be/~marchal/
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