In an excellent and clear post Peter Jones writes:

> 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 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.

So on this basis alone are you opposed to a *physical* multiverse, in which 
every possibility is physically instantiated somewhere, but some possibilities 
are more common/ have greater measure than others?
> 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

Why must "change... be change in something"? It sort of sounds reasonable 
but it is our duty to question every assumption and weed out the superfluous 
ones. If there is an object with (space, time, colour) coordinates (x1, t1, 
and another object (x1, t2, orange), then we say that the object has changed 
from red to orange. This could describe a poker left in a fire, for example. We 
only need to talk about properties (and we can add as many as we like to be 
sufficiently specific); we don't need the propertiless substrate.

> 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.

I don't see how a physical multiverse would be distinguishable from a virtual 
reality or a mathematical reality (assuming the latter is possible, for the 
of this part of the argument). The successive moments of your conscious 
experience do not need to be explicitly linked together to "flow" and they do 
not need to be explicitly separated, either in separate universes or in 
rooms, to be separate. If you died today and just by accident a possible next 
moment of consciousness was generated by a computer a trillion years in the 
future, then ipso facto you would find yourself a trillion years in the future.
> 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.

But if you had the successive moments of your consciousness implemented 
in parallel, perhaps as a simulation on a powerful computer, it would be 
to tell that this was the case. For all you are aware, there may not *be* any 
moments: your present experience may include false memories of your past, and 
whole world may have been created a second ago.
>  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.

Physical existence is only an improvement on the WR problem as compared 
to mathematical existence if you don't believe in a multiverse. 

> 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.

Stathis Papaioannou
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