On 1/26/2012 08:19, Pierz wrote:
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

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.

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

Why would any structure give rise to qualia? We think some structure (for example our brain, or the abstract computation or arithmetical truth/structure representing it) does and we communicate it to others in a "3p" way. The options here are to either say qualia exists and our internal beliefs (which also have 'physical' correlates) are correct, or that it doesn't and we're all delusional, although in the second case, the belief is self-defeating because the 3p world is inferred through the 1p view. It makes logical sense that a structure which has such beliefs as ourselves could have the same qualia (or a digital substitution of our brain), but this is *unprovable*.

If you don't eliminate qualia away, do you think the principle described here makes sense? http://consc.net/papers/qualia.html If we don't attribute consciousness to some structures or just 'how a computation feels from the inside' then we're forced to believe that consciousness is a very fickle thing.

As for arithmetic/numbers - Peano Arithmetic is strong enough to describe computation which is enough to describe just about any finite structure/process (although potentially unbounded in time) and our own thought processes are such processes if neuroscience is to be believed. Arithmetic itself can admit many interpretation and axioms tell you what 'arithmetic' isn't and what theorems must follow, not what it is - can you explain to me what a number is without appealing to a model or interpretation? Arithmetical realism merely states that arithmetical propositions have a truth value, or that the standard model of arithmetic exists.

If you think that isn't enough, I don't see what else could be enough without positing some form of magic in the physics, but that forces us to believe consciousness is very fickle. Attributing consciousness to (undefinable) arithmetical truth appears to me like a better theory than attributing it to some uncomputable God-of-the-gaps physical magic , if one has to believe in consciousness (as a side note, the set of arithmetical truths is also uncomputable and undefinable within arithmetic itself). If you must use Occam, the only thing that you can shave would be your own consciousness, which I think is overreaching, although some philosophers do just that (like Dennett), if you use Occam and accept consciousness and that you admit a digital substitution, an arithmetical ontology is one of the simplest solutions.

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