On 14 Aug 2012, at 00:44, Russell Standish wrote:
On Mon, Aug 13, 2012 at 03:56:35PM +0200, Bruno Marchal wrote:
On 13 Aug 2012, at 00:32, Russell Standish wrote:
OK. But the question is: would an agent lost free-will in case no
random oracle is available?
I would have thought so.
OK. This is incompatible with the usual comp. But probably compatible
with comp-relative-to-an-oracle, for which UDA should still work (I
currently think). Basicaly all recursion theory works the same with
computability relativize to oracle.
I don't see why this would entail comp is false though. Perhaps
you
could elaborate?
Because comp implies that there is no randomness at the ontological
level.
Assuming that by "ontological level", you mean what I call the
"syntactic level" in my book.
Ontology and syntax are different notion. With comp they are close,
but not equivalent. Syntax concerns mainly finite symbols and finite
sequences of symbols, finite sequences of sequences of symbols.
Ontology concerns what we assume to exist independently of us. I am
not sure symbols can be said to exist, as symbol, independently of
us. but that might be a vocabulary detail.
I do understand the difference between ontology (taken as "that which
exists") versus syntactic (the lowest implementation language).
"That which exists" is fundamentally unknowable, and probably not
sensible disucssed, hence I prefer to stick with more neutral labels
like "syntactic level".
I disagree with this. With comp we know that the fundamental reality
is given by *any* Turing complete system. What cannot be discussed is
which one, but they are all equivalent.
As for being independent of us, both syntactic and semantic levels are
independent of us in the sense that two correspondents must agree on
both in order to have a sensible conversation.
I disagree. Semantics is personal and ill defined, and we don't have
to agree on the semantics to discuss. We have only to agree with the
syntactic provability rule. The whole field of logic is based on that:
the validity of the reasoning are made independent of the semantics,
which is always subjective and personal.
I guess you are alluding to the self-indeterminacy (à-la
Turing, not to be confused with the first person indeterminacy)
which can make a decision looking random for the one who does it,
I would have thought that first person indeterminancy would fit the
bill perfectly.
It can be used as a local random oracle, although in practice it is
simpler to use a quantum algorithm. I doubt people would agree to
duplicate themselves to make the right statistical choice. Actually,
they will use coin or pseudo-random algorithm.
I'm not sure that a pseudo-random algorithm would always be good
enough, as unless it is cryptographically strong, evolution will make
short work of breaking it. If a real random oracle is available, it
would be some much easier to use that.
Technically it can be shown, indeed, that random oracle are richer as
a resource for problem solving than pseudo randomness, but the proof
of this are very non constructive, so that it is hard to conceive any
practical problem for which a random oracle is better.
I am not sure I see the relation with cryptography.
If you have a coin, then flipping a coin is a good approach. Most
brains so not have coins, so I would expect a different mechanism to
be used - eg synaptic thermal noise.
But we don't know in Nature any random process, unless you believe in
the collapse of the wave packet.
Note that NO machine can ever distinguish a truly random sequence
with some sequence which can be generated by machine more complex
than themselves.
That is true. But complex machines are expensive to run.
But with comp we don't run machine. They all exists and run in
arithmetic, and the appearances are internal selection. Below the
subst level we are all confronted with an infinity of unbounded
complexity (cf the white rabbits).
Real random
oracles, if available,
They are available by first person indeterminacy. They are not
ontologically real, but they are epistemologically real, and this
plays a big role in the emergence of the physical reality. But I doubt
it plays a role in our biological evolution. That would mean that our
substititution level is lower than the quantum one, and I don't see
any evidence for this.
are so much more convenient for evolution to
use that to try to evolve sufficient complexity to achieve
cryptographic strength in a pseudo random number generator.
With comp, the following are absolutely undecidable:
- the cardinality of the universe is aleph_zero, or aleph_one, of
2^aleph_zero, etc.
- there is a random oracle at play in our experience (although we
know already that there is a random oracle at play in the
*existence* and *stability* of our experiences).
but which is not the non-compatibilist kind of randomness that some
defender of free-will want to introduce.
I have never met anyone wanting to do this. They sound like some
sort
of long-discredited Cartesian dualist. Are you sure they're not
strawmen
you have conjured up?
John Clark seems to believe that they still exist, as he argues all
the times against them, and then it seems to me that Craig Weinberg
has defended such notion, I think.
I don't think I have conjured up :)
John Clark argues against anyone who utters the words "free will". I
don't think he particularly targets the "spirit free will theorists"
(as Brent calls them).
But he agrees and even proposes a compatibilist definition.
As for Craig, apologies for being rude, but I stopped reading his
posts a long time ago.
And as David Deutcsh is want to point out, for the price of
a Multiverse, one can have one's deterministic cake and freely eat
it
too (sorry for mangling the metaphors :). But this works because the
free will exists at a different level from that where determinism
rules.
I am OK with this, but this means that free-will does not need 3-
randomness.
No, but it does need 1-randomness
Imagine the iterated WM-duplication. Why would the resulting peoples
have more free will than the same person not doing the experience?
It seems to me that if a decision relies on a perfect coin, it is less
"free" than if it relies on my partial self-indetermination, which
itself is a deterministic process, although I cannot see it.
Bruno
http://iridia.ulb.ac.be/~marchal/
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