On 26.01.2012 07:19 Pierz said the following:
As I continue to ponder the UDA, I keep coming back to a niggling
doubt that an arithmetical ontology can ever really give a
satisfactory explanation of qualia. It seems to me that imputing
qualia to calculations (indeed consciousness at all, thought that
may be the same thing) adds something that is not given by, or
derivable from, any mathematical axiom. Surely this is illegitimate
from a mathematical point of view. Every mathematical statement can
only be made in terms of numbers and operators, so to talk about
*qualities* arising out of numbers is not mathematics so much as
numerology or qabbala.
Here of course is where people start to invoke the wonderfully
protean notion of ‘emergent properties’. Perhaps qualia emerge when
a calculation becomes deep enough.Perhaps consciousness emerges from
a complicated enough arrangement of neurons. But I’ll venture an
axiom of my own here: no properties can emerge from a complex system
that are not present in primitive form in the parts of that system.
There is nothing mystical about emergent properties. When the
emergent property of ‘pumping blood’ arises out of collections of
heart cells, that property is a logical extension of the properties
of the parts - physical properties such as elasticity, electrical
conductivity, volume and so on that belong to the individual cells.
But nobody invoking ‘emergent properties’ to explain consciousness in
the brain has yet explained how consciousness arises as a natural
extension of the known properties of brain cells - or indeed of
matter at all.
Let my quote Jeffrey Gray (Consciousness: Creeping up on the Hard
Problem, p. 33) on biology and physics.
"In very general terms, biology makes use of two types of concept:
physicochemical laws and feedback mechanisms. The latter include both
the feedback operative in natural selection, in which the controlled
variables that determine survival are nowhere explicitly represented
within the system; and servomechanisms, in which there is a specific
locus of representation capable of reporting the values of the
controlled variables to other system components and to other systems.
The relationship between physicochemical laws and cybernetic mechanisms
in the biological perspective on biology poses no deep problems. It
consist in a kind of a contract: providing cybernetics respects the laws
of physics and chemistry, its principles may be used to construct any
kind of feedback system that serves a purpose. Behaviour as such does
not appear to require for its explanation any principles additional to
Roughly speaking Gray's statement is
Biology = Physics + Feedback mechanisms
Yet even at this stage (just at a level of bacteria, I guess there is no
qualia yet) it is unclear to me whether physics includes cybernetics
laws or they emerge/supervene. What is your opinion to this end?
I wanted to discuss this issue in another thread
but at the present the discussion is limited to the question of
information is basic physical property (Information is the Entropy) or not.
In the same way, I can’t see how qualia can emerge from arithmetic,
unless the rudiments of qualia are present in the natural numbers or
the operations of addition and mutiplication. And yet it seems to me
they can’t be, because the only properties that belong to arithmetic
are those leant to them by the axioms that define them. Indeed
arithmetic *is* exactly those axioms and nothing more. Matter may in
principle contain untold, undiscovered mysterious properties which I
suppose might include the rudiments of consciousness. Yet
mathematics is only what it is defined to be. Certainly it contains
many mysteries emergent properties, but all these properties arise
logically from its axioms and thus cannot include qualia.
I call the idea that it can numerology because numerology also
ascribes qualities to numbers. A ‘2’ in one’s birthdate indicates
creativity (or something), a ‘4’ material ambition and so on.
Because the emergent properties of numbers can indeed be deeply
amazing and wonderful - Mandelbrot sets and so on - there is a
natural human tendency to mystify them, to project properties of the
imagination into them. But if these qualities really do inhere in
numbers and are not put there purely by our projection, then numbers
must be more than their definitions. We must posit the numbers as
something that projects out of a supraordinate reality that is not
purely mathematical - ie, not merely composed of the axioms that
define an arithmetic. This then can no longer be described as a
mathematical ontology, but rather a kind of numerical mysticism. And
because something extrinsic to the axioms has been added, it opens
the way for all kinds of other unicorns and fairies that can never be
proved from the maths alone. This is unprovability not of the
mathematical variety, but more of the variety that cries out for Mr
Occam’s shaving apparatus.
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