On 10/21/2018 7:11 AM, Tomas Pales wrote:
I am generally sympathetic to Tegmark's mathematical multiverse idea,
but I have two comments/criticisms to it:
1) I am not sure whether Tegmark is aware of the so-called
"instantiation" relation. In philosophy, the instantiation relation is
the relation between a general and a particular object, where the
particular object is an instance of the general object. In other
words, the general object is a property of the particular object.
Example: general triangle (or triangle "in general") is the property
of any particular triangle, and any particular triangle is an instance
of general triangle. Another example: number 2 is a general relation
that is instantiated in the particular relation between any two
objects. I am not sure whether Tegmark realizes the difference between
general objects and their instances, because he said something like:
when we probe matter we only find numbers (and hence reality is just
mathematics). But numbers cannot be found in our world; you cannot
find number 2 sitting on a tree or in the atomic nucleus. You can only
find instances of number 2, as relations between particular objects.
Mathematical objects are usually thought to be general objects, but in
that case there is more in reality than mathematical objects: there
are general objects /and/ their instances. And in our physical world
there are /no/ general objects, only their instances. If we want to
say that there are mathematical objects in our physical world, we
should include among mathematical objects also non-general objects,
that is, objects that have no instances. (By the way, there is a
hierarchy of generality: more general objects are instantiated in less
general objects and those are ultimately instantiated in non-general
objects. Non-general objects are often called "concrete", while
general objects are also called "abstract".)
This appears not to be a well-order hierarchy. The thing I am sitting
on is an instance of a chair, and it's concrete. But it's also an
instance of a matter, i.e. a collection of particles of the Standard
Model (which may or may not be the most general category). It's also an
instance of things I own.
2) While I agree with Tegmark that reality contains all mathematical
objects (both general and non-general), I think there is also a
non-mathematical aspect of reality. That's because mathematical
objects are relations or structures of relations, but relations cannot
exist without objects between which they hold. While it is true that
relations can hold between other relations, there should also be
objects that are non-relations, which ultimately make sense of all
relations. These non-relations are the non-mathematical objects and
they (or at least some of them) may be the qualities of consciousness
(qualia) - because (1) they have an unanalyzable/unstructured nature,
and (2) they stand in relations to other objects (relations or
non-relations) that we call "correlates of consciousness".
Can you clarify with some examples?
Brent
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