David Nyman wrote:
> Bruno Marchal wrote:
>
> > > As usual, the truth of a mathematical existence-claim does not
> > > prove Platonism.
> >
> > By Platonism, or better "arithmetical realism" I just mean the belief
> > by many mathematician in the non constructive proof of "OR" statements.
> >
>
> Lest we go yet another round in the 'reification' debate, is it not
> possible to reconcile what is being claimed here?
>
> Bruno, I'm assuming that when you eschew 'Platonic existence' for AR,
> you are thereby saying that your project is to formalise certain
> arguments about the logical structure of possibility - and through
> this, to put actuality to the test in certain empirical aspects.
> Questions of how this may finally be reconciled with 'RITSIAR' (I hope
> you recall what this means) are in abeyance. Nevertheless, some aspect
> of this approach may ultimately be ascribed a status as 'foundational
> existent' analogous to that of 'primary matter' in materialism.
> Alternatively, such a hypothesis may be shown to be redundant or
> incoherent.
>
> Peter, as we've agreed, materialism is also metaphysics, and as a route
> to 'ultimate reality' via a physics of observables, is vulnerable to
> 'reification'. Might it not be premature to finalise precisely what it
> is that physical theory decribes that might actually be RITSIAR?
The point of the phrase RITSIAR is to leave it deliberately
unstated what that reality consists of. If Bruno is
going to come to conclusions about my reality, RITSIAR,
he must be making *some* sort of ontological assumption,
even without knowing what specific kind of ontology is involved
in RITSIAR.
Matter is a bare substrate with no properties of its own. The question
may well be asked at this point: what roles does it perform ? Why not
dispense with matter and just have bundles of properties -- what does
matter add to a merely abstract set of properties? The answer is that
not all bundles of posible properties are instantiated, that they
exist.
What does it mean to say something exists ? "..exists" is a meaningful
predicate of concepts rather than things. The thing must exist in some
sense to be talked about. But if it existed full, a statement like
"Nessie doesn't exist" would be a contradiction ...it would amount to
"the existing thing Nessie doesnt exist". However, if we take that the
"some sense" in which the subject of an "...exists" predicate exists is
only initially as a concept, we can then say whether or not the concept
has something to refer to. Thus "Bigfoot exists" would mean "the
concept 'Bigfoot' has a referent".
What matter adds to a bundle of properties is existence. A non-existent
bundle of properties is a mere concept, a mere possibility. Thus the
concept of matter is very much tied to the idea of contingency or
"somethingism" -- the idea that only certain possible things exist.
The other issue matter is able to explain as a result of having no
properties of its own is the issue of change and time. For change to be
distinguishable from mere succession, it must be change in something.
It could be a contingent natural law that certain properties never
change. However, with a propertiless substrate, it becomes a logical
necessity that the substrate endures through change; since all changes
are changes in properties, a propertiless substrate cannot itself
change and must endure through change. In more detail here
The Case Against Mathematial Monism
Mathematical monism is both too broad and too narrow.
Too broad: If I am just a mathematical structure, I should have a much
wider range of experience than I do. There is a mathemtical structure
corresponding to myself with all my experiences up to time T. There is
a vast array of mathematical structures corresponding to other versions
of me with having a huge range of experiences -- ordinary ones, like
continuing to type, extraordinary ones like seeing my computer sudenly
turn into bowl of petunias. All these versions of me share the memories
of the "me" who is writing this, so they all identify themselves as me.
Remember, that for mathematical monism it is only necessary that a
possible experience has a mathematical description. This is known as
the White Rabbit problem. If we think in terms of multiverse theories,
we would say that there is one "me" in this universe and other "me's"
in other universes,a nd they are kept out of contact with each other.
The question is whether a purely mathematical scheme has enough
resources to impose isolation or otherwise remove the White Rabbit
problem.
Too narrow: there are a number of prima-facie phenomena which a purely
mathematical approach struggles to deal with.
* space
* time
* consciousness
* causality
* necessity/contingency
Why space ? It is tempting to think that if a number of, or some other
mathematical entity, occurs in a set with other numbers, that is, as it
were, a "space" which is disconnected from other sets, so that a set
forms a natural model of an *isolated* universe withing a multiverse, a
universe which does not suffer from the White Rabbit problem. However,
maths per se does not work that way. The number "2" that appears in the
set of even numbers is exactly the same number "2" that appears in the
list of numbers less than 10. It does not acquire any further
characteristics from its context.
The time issue should be obvious. Mathematics is tradionally held to
deal with timeless, eternal truths. This is reflected in the metpahor
of mathematical truth being discovered not found (which, in line with
my criticism of Platonism, should not be taken to seriously). It could
be objected that physics can model time mathematically; it can be
objected right back that it does so by spatialising time, by turning it
into just another dimension, in which nothing really changes, and
nothing passes. Some even go so far as to insist that this model is
what time "really" is, which is surely a case of mistaking the map for
the territory.
Consciousness is a problem for all forms of materialism and
physicalism to some extent, but it is possible to discern where the
problem is particularly acute. There is no great problem with the idea
that matter considered as a bare substrate can have mental properities.
Any inability to have mental properties would itself be a property and
therefore be inconsistent with the bareness of a bare substrate. The
"subjectivity" of conscious states, often treated as "inherent" boils
down to a problem of communicating one's qualia -- how one feels, how
things seem. Thus it is not truly inherent but depends on the means of
communication being used. Feelings and seemings can be more readily
communicated in artistic, poetic language, and least readily in
scientific, technical language. Since the harder, more technical a
science is, the more mathematical it is, the communication problem is
at its most acute in a purely mathematical langauge. Thus the problem
with physicalism is not its posit of matter (as a bare substrate) but
its other posit, that all properties are physical. Since physics is
mathematical, that amounts to the claim that all properties are
mathematical (or at least mathematically describable). In making the
transition from a physicalist world-view to a mathematical one, the
concept of a material substrate is abandoned (although it was never a
problem for consciousness) and mathematical properties become the only
possible basis for qualia. Qualia have to be reducible to, or
identifiable with, mathematical properties, if they exist at all. This
means that the problem for consciousness becomes extreme, since there
is no longer the possibility of qualia existing in their own right, as
properties of a material substrate, without supervening on
mathematically describable properties.
The interesting thing is that these two problems can be used to solve
each other to some extent. if we allow extra-mathemtical properties
into our universe, we can use them to solve the White Rabbit problem.
There are two ways of doing this: We can claim either:-
* White Rabbit universes don't exist at all
* White Rabbit universes are causally separated from us (or remote in
space)
The first is basically a reversion to a single-universe theory (1).
Mathematical monists sometimes complain that they can't see what role
matter plays. One way of seeing its role is as a solution to the WR
problem. For the non-Platonist, most mathematical entitites have a
"merely abstract" existence. Only a subset truly, conceretely, exist.
There is an extra factor that the priveleged few have. What is it ?
Materiality. For the physicalist, matter is the token of existence.
Material things, exist, immaterial ones don't.
The second moves on from a Mathematical Multiverse to a physical one
(3). The interesting thing about the second variety of
non-just-mathematical monism is that as well as addressing the White
Rabbit problem, it removes some further contingency. If the matter,
physical laws, and so on, are logically possible, then the general
approach of arguing for a universe/multiverse on the grounds of
removing contingency must embrace them -- otherwise it would be a
contingent fact that the universe/multiverse consists of nothing but
mathematics.
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Received on Mon Oct 23 2006 - 11:06:23 PDT