On 26 Oct 2014, at 16:47, spudboy100 via Everything List wrote:
And now in physics we have this-
http://stardrive.org/stardrive/index.php/news2/science/14152-when-parallel-worlds-collide-quantum-mechanics-is-born
MWI worlds interact
Then QM is wrong. Weinberg but also Plaga (on this list) showed that
[QM is non linear, but approximatively correct] is equivament with QM
worlds can interact.
Bruno
-----Original Message-----
From: Bruno Marchal <marc...@ulb.ac.be>
To: everything-list <everything-list@googlegroups.com>
Sent: Sun, Oct 26, 2014 10:13 am
Subject: Re: Why is there something rather than nothing? From
quantum theory to dialectics?
On 24 Oct 2014, at 19:35, Peter Sas wrote:
Hi Brent,
On my account, beings (i.e. all things that are) lack intrinsic
qualities because they are defined through their differences from
each other.
I guess you love category theory, which is mathematics based on that
idea. It is also a quite functionalist and sort of constructivist
view, like an employee will be defined by its job, and not by the
particular individual having that job.
It works very well for many branch of math, but it is in trouble for
computer science, and some other branch of logic.
Some mathematical object can have intrinsic quality. Modal logic is
a good tool for handling this.
Note also that a "universe" is usually considered only for its
intrinsic quality. A universe has a priori no relation with
something else, as everything is or should be part of a universe, by
definition.
I could argue that it is the same for a dreamer, of any closed
system in which we are interested.
Thus a being is what it is simply by not being something else. So
in themselves, abstracted from their relations to other beings,
beings 'are' just nothing, indeterminate, hence they lack intrinsic
qualities (all properties are relational). If you like you can also
say there are just relations and not relata, or alternatively that
there are only internal relations of which the relata are
functions. The next question would then be: but what kind of
relations are ontologically most basic? I would say: mathematical
relations.
That follows from the computationalist hypothesis. You can read the
references in my URL. Or the posts to this list. If we assume that
the brain (or whatever my consciousness supervene on) is Turing
emulable, we must recover physics from a special self-referential
statistics on the computations. Physics becomes a branch of
machine's psychology, or better machine's theology (in the greek
original sense of the word) itself branch of arithmetic or
mathematics.
According to me, saying that a being is what it is because it
differs from something else is the same as saying that all being is
mathematical. For if beings lack all intrinsic qualities, they can
only be distinguished quantitatively, and that's basically what
mathematics is about, isn't it?
You are quick and a bit vague on this.
This seems to me to be the reason why the whole of mathematics (and
everything that can be described mathematically) can ultimately be
described in binary terms, as compositions of the difference
between 1 and 0, which is just difference as such.
I doubt you will get more than the numbers, or than the computable.
In fact all attempt to define mathematically the hole of mathematics
fails. In fact, already for the arithmetical reality, it follows
from Gödel's incompleteness that all axiomatizable theories will
fail to unify it. The arithmetical reality is inconceivably large.
It seems to me that mathematics is what you get when you take a
structuralist view of things, where you say that a thing IS just
its differences from something else.
You get category theory.
I think this also the view Tegmark takes in his Mathematical
Universe book, although he speaks of "relation" instead of
"difference":
"the only properties of these entities would be those embodied by
the relations between them... To a modern logician, a mathematical
structure is precisely this: a set of abstract entities with
relations between them.
That is more the view of an algebraist. A logicien studies such
strcture as model of theories (set of sentences or propositions).
The algebraists and categoricians study the relation between
structures. The logician study the relation between those relations
and theories or machines (syntactical beings).
Take the integers, for instance, [...] the only properties of
integers are those embodied by the relations between them." (p.259)
"5 has the property that it's the sum of 4 and 1, say, but it's not
yellow, and it's not made of anything." (p.268) " the entities of a
mathematical structure are purely abstract, which means that they
have no intrinsic properties whatsoever..." (p.264)
We can doubt this, notably for the numbers where many particular
numbers can be individuated through its special property.
So what is primary, "relation" or "difference"? I would say
neither, both terms seem equally primordial. For to be able to
specify which relations hold between, say, 5 and 4, you first have
to specify how they differ from each other, e.g. by saying 5 = 4
+1. But that's the same as saying what relations hold between these
entities? Thus it would seem that mathematical relations are just
relations of difference, indeed, ultimately the 'pure', binary
difference of 1 and 0.
Brouwer founded mathematics on something similar, but he get the
constructive mathematics (and only one of a special kind). Most of
the arithmetical reality is bigger than what such subjectivist
theories are about. Of course the ability to accept the difference
between 0 and 1 is fundamental and very important.
According to me, such a mathematical view of being as defined by
difference (ultimately 1 and 0) follows from reflection on nothing.
Nothing is inconsistent, hence it differs from itself. Being then
is the (self-)negation of nothing, hence it must be difference (not
from itself but) from something else. This then is what "being"
means: to differ from something else, and as we have just seen this
is just what mathematics is about.
As for the fact that you and I both differ from Bruno but we are
obviously not the same, that's because you and I differ as well...
If you like, in terms of the above account, you could say Bruno,
you and me are all qualititatively indistinguishable units which
nevertheless have different values only because of our different
positions in a quantitative structure, e.g. spacetime.
Spinoza famously said, and Hegel repeated it: every determination
is a negation,
That is interesting, and, I think, well illustrated by formal
provability (which is on the determination part) and acts formally
as a negation for many propositions: like []<>t -> []f (proving
self-consistency entails proving a falsity). Also, the Löb rule or
axiom shows also that provability is a form of negation.
In fact even the simple formal implication is also a sort of
negation p -> q is really put for NOT p ... or q. But this is
weaker than the illustration just above.
i.e. saying what something is is saying what it is not,
OK, but the reverse is not true.
God and the protegorean virtues are defined only negatively. You can
not define them by saying what they are, only by what they are not.
God is not this, neither that, nor ... (cf the greek negative
theologies).
i.e. a thing IS its difference form something else.
OK, you might say God is what is different from all beings.
You can call this dialectics, but according to me it converges with
a mathematical view of being, so to that extent there is a strong
dialectical aspect to mathematics. Or at least so it seems to me.
OK.
Then another question arises, which relates to the topic of
consciousness and how it fits in the physical (= mathematical) world.
I stringly disagree with making the physical = to the mathematical.
The physical might have a mathematical origin, but the mathematical
is larger than the physical. mathematical objects are not physical
objects. The beliefs in physicc are mathematical object, and they
should arise from some mathematical special relation. In fact, to
put it crudely, the physical might be the border of the mathematical
when seen from internal (to math) beings.
If all beings are ultimately mathematical (quantitative)
I would also be careful not to identify math and the study of the
quantitative. In computer science qualities arise from the
intensional part of arithmetic, where an object can refer to its own
code, and see the difference with truth to which he has some access,
without being able to capture them in pure third person relations.
in nature,
Well, what is that? (Especially if you agree that math is more
fundamental than physics).
then where does quality come from? It would seem to me that quality
is precisely an intrinsic property, which does not depend on
relation to something else. Take as a thought experiment someone
who right after birth was given red colored glasses so that
everything looks red to him, and he has been wearing the glasses
all of his life, so he has never seen any other color, all he sees
are shades of red. Obviously, then, it must be possible to be aware
of red without being aware of other colors.
I don't see why that would be necessary.
Hence it is an intrinsic quality. In contrast, you cannot be aware
of 1 without being aware of other numbers, for knowing what "1"
means is simply knowing that 1 is more than 0, that 1+1=2 etc.
Ultimately, then, I think we can pose the problem of consciousness
in terms of the quantity/quality opposition. If reality is
ultimately mathematical (quantitative), how then are qualities
possible?
By being some semantical fixed point. It is where the map is
confused with the territory, and that happens when the map is part
of the territory. What is nice is that such fixed points obeys
logics already suggested for the Qualia (and it generalizes a bit
quantum logic). See for example the paper by J.L. Bell (the
logician, not the physicists).
Bruno
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