[extropy-chat] The Mathematico-Cognition Reality Theory (MCRT)

[Marc Geddes]

Summary of the Mathematico-Cognition Reality Theory
(MCRT)
By Marc Geddes, Auckland, New Zealand

Version 1.0
Seed-ideas for the MCRT completed on: 15th December,
2005


What follows is a series of ideas intended to sketch a
general framework or philosophical approach which
*may* lead towards a 'Theory Of Everything'.  It is
*not* intended as a scientific theory as of yet.  The
ideas do not yet meet the requirements for a
scientific theory.  The ideas are only intended as
entertaining speculations. 

---

Theory Of Everything (TOE) - A Definition

A TOE is a logical scaffolding or framework which is
universal in scope and capable of integrating all
general classes of knowledge under a single
explanatory umbrella.  Specifically, one would like a
framework which integrates (explains the relationship)
between Mathematical, Mental and Physical concepts. 
It is not required that such a theory literally
'explain everything', nor it is assumed that all
aspects of the universe are comprehensible.  


Assumptions (AS)

AS 1 - Mathematical Platonism

Mathematical Platonism is the idea that mathematical
concepts have objective reality.  The basic position
is that human mathematicians are engaged in
*discovery* of mathematical facts that exist *out
there* in reality.  Mathematical facts are not created
by humans, but are things which exist external to
human society and are discovered.  Mathematical
entities are patterns, or abstractions derived from
concrete facts.  Mathematical Platonism is the idea
that these abstractions have a real existence external
to the human mind.

See 'Platonism':
http://plato.stanford.edu/entries/platonism/


The main argument for Mathematical Platonism is the
'Argument from Indispensability’: the fact that
mathematics appears to be indispensable to science: 

"Certain mathematical theories, such as arithmetic or
real analysis, are indispensable for modern
physics...But these mathematical theories are
ontologically committed to abstract entities...And
since we have no adequate grounds for rejecting these
physical theories - they are part of our overall best
theory of the world - we should acquiesce to the
existence of abstracta" (The Oxford Handbook of
Metaphysics)


AS 2 - Functionalism

"Functionalism is a theory in the philosophy of mind
that thinks of mental states rather as we think of
patterns.  A pattern - say a six-pointed star - can be
made out of anything...The thing that makes the
pattern a star and not a circle or a crescent is the
mutual relation of its constituent parts, not the
material out of which those parts are made."
(Consciousness:  Guide to the Debates)

See 'Functionalism':
http://plato.stanford.edu/entries/functionalism/


The assumption is that mental states are constituted
in *computations* and that there is no esoteric
non-computational physics involved.  There's good
evidence for this, based on the fact that all known
laws of physics are computational in nature.

Key TOE principle 1: 3 time dimensions

The first principle of the TOE is derived from
assumptions (1) and (2).  The combination of
Mathematical Platonism and Functionalism can be used
to make an argument that time is 3-dimensional.  The
first part of the argument is given below.

Definition:

'Time' is here being used to mean 'Causality' - or
ordered cause and effect relations between things. 
'Time dimension' is defined to mean a particular
linear ordering of causal events.  Multiple time
dimensions mean that there's more than one valid way
to define cause and effect.

Argument:  Mathematical entities are processes in
multi-dimensional time

Brain processes are *mathematical* in nature (they are
'algorithms' ? See ‘Functionalism’.    Mathematical
entities are abstracted patterns.  But abstracted
patterns (like 'algorithms') don't exist directly
inside physical causal networks, only particular
instances of them do.  This is clear by pointing to
the fact that many different brains could enact the
*same* computation (algorithm).  So the physical
processes in the brain can't be *identical* to the
mathematical entity (the algorithm) itself.

If we are prepared to grant objective reality to
‘Abstracted patterns’ (See ‘Mathematical Platonism’
the only way to make sense of this is to generalize
the notion of causality to include *abstract* kinds of
causality.  Then an
algorithm can be defined as a process taking place in
multi-dimensional
time.  This *includes* physical time (physical
causality) but extends beyond
it.  So long as a postulated entity (like a 'Quale')
is defined as being at
least *partially* inside the network of physical
causality, there'll be
observable consequences and scientific evidence for
the existence of the
Quale can be gathered.   But this does *not* mean that
the Quale fits
completely inside physical causal networks.  .  Take
the analogy of a
three-dimensional object (say a cube) passing through
a 2-dimensional plane
which we'll call Flatland.  The inhabitants of
Flatland can only see in
2-dimensions and they might argue that 'we can only
ever gather evidence of
something if it exists in our 2-d space.  Therefore
only 2-d objects exist'.
Did you spot the gross error in the reasoning?  Just
like a cube passing
through a 2-d plane has part of itself intersecting
the plane, a Quale could
be *part* of physical causality without fitting
entirely into physical
reality.  The argument summarized again:

(1) Qualia are generated by brain processes

(2) Brain processes are enacting algorithms
(mathematical patterns)

(3) The algorithm itself (the mathematical pattern)
can't exist totally
inside physical reality, because mathematical patterns
are abstractions and
many different types of brain processes can enact the
same algorithm.  So
the brain processes themselves can't be identical to
the mathematical
algorithm

(4) An algorithm is a process.  But as demonstrated
above, it can't be a
process which is confined to physical reality - since
it's an *abstract* 
process.  Therefore it must be a process taking place
at least partially
outside physical reality.

(5) Processes are events along time dimensions.  As
demonstrated above,
there are processes at least partially taking place
outside physical
reality, in the form of mathematical patterns. 
Therefore these processes
must be taking place in multiple time dimensions

Ergo, extra time dimensions exist.  And consciousness
is a process taking
place in multi-dimensional time.



AS 3 - Non-reductive Physicalism.

"Non-reductive physicalism is the idea that there
exists in association with the physical realm a mental
realm that is *dependent* on it, but not reducible to
it."  (Consciousness: A Guide To The Debates)

The idea here is that mental concepts are constituted
in (or dependent on) physical processes, but
descriptions of mental concepts cannot be completely
converted into descriptions of material processes. 
(i.e. Mental concepts have a reality *above and above*
the material processes in which they are constituted).

The assumption has been adopted because of the
argument for multiple time dimensions (see above).  If
mathematical entities are processes in
multi-dimensional time, then such entities don't exist
completely inside physical reality.  And from
assumptions (2) - Functionalism, if mental states are
based on mathematical entities (computations), then
mental states can't exist entirely within physical
reality either.

The philosophical position known as 'Eliminative
Materialism' - the idea that everything (including
what we think of as mental states) is really just
material is based on weak premises and non sequiturs

To try to explain away Qualia by demanding that
everything be fully describable in terms of physical
causality is simply to presuppose the very thing you
are trying to prove (circular reasoning).  A believer
in Qualia could easily rebut simply by redefining the
definition of 'causality' and demanding that
everything be explained, not in terms of physical
causality, but in terms of direct experience.  Now it
*may* well prove to be the case that talk of Qualia
can be eliminated and replaced entirely by
explanations in terms of physical causality
(eliminative materialism).  But it may not.  The facts
of the matter can only be determined through a
combination of theory and observation, just like
everything else in science.  

Suppose for instance that there's some kind of
fundamental law of cognitive science and information
theory such that no explanation phrased entirely in
terms of physical causality can fully predict sentient
behavior?  For instance suppose that for some *in
principle* theoretical reason computational
intractability prevents accurate real-time predictions
of sentient behavior if these predictions are phrased
solely in terms of physical processes?  Suppose that
in order to achieve an accurate model of sentient
behavior one needs to introduce mental concepts into
one's explanations right from the start - i.e. suppose
this is an *in principle* requirement?  Then one would
have to conclude that some mental concepts are just as
'real' and fundamental as physical ones.   

‘Eliminative materialism’(the idea that ‘qualia’ don’t
exist but are simply misrepresentations of what are
really entirely material processes is based on
arguments by philosophers Paul and Patricia Churchland
and Daniel Dennett (in fact the position traces back
to earlier arguments by philosophers Paul Feyerabend
and Quine), to the effect: that (a) qualia are simply
abstract (or theoretical entities) and (b) should be
replaced by the objective scientific viewpoint.  But
the argument undermines itself.  One can agree that
‘Qualia’ are ‘theoretical abstractions’ and also agree
that the correct view-point requires an objective
scientific account, but the conclusion that Qualia are
fictions doesn’t follow from (a) and (b) at all!  It’s
a total non-sequitur.  In fact the very arguments
applied by Eliminative materialism to argue *against*
Qualia can be used to argue for them!  Let’s examine
the first argument of the Qualia skeptics: (a)
'Qualia' are abstractions!  But this doesn’t prove a
thing against Qualia.  On the contrary, we could take
a Platonic view of these abstractions just as some
philosophers do for mathematics.  

There are examples of abstract entities (mathematical
concepts) that many (Platonists) take to be
objectivity real, yet clearly don't directly fit into
the causal networks of the brain at all.  As Kripke
showed (1972) such entities don’t require causal
contact.  They can be referenced through meaningful
descriptions.  Nor is causal contact required to
obtain evidence of such entities.  Evidence for the
existence of something is based on the explanatory
power of the postulated entities for our theories of
the world. 

It appears that humans can only have ‘subjective’
awareness of Qualia.  But this could be merely a
limitation of the human brain.  If it’s possible to
objectivity view Qualia, the second argument of the
Qualia skeptics is also exposed as a total
non-sequitur.  Recall that the eliminative
materialists argue that (b) The most accurate
view-point of something is the objective scientific
view-point.  The believer in Qualia can just say: well
of course I agree with (b), but so what?  For *Qualia
themselves are a part of objective science* !  As
suggested earlier, if it proves that accurate models
of sentient behavior are *in principle* impossible
without introducing mental concepts into one’s
explanations (perhaps due to some theorem involving
computational intractability), then one would have to
conclude that some mental concepts are just as
fundamental and real as physical concepts and the
ontology of objective science would have to be
broadened to include these mental concepts. 

So the arguments of Eliminative materialists are
simply without philosophical merit.


---

AS 4:  Many-aspect Monism (Fundamental Property
Dualism)

Many-Aspect monism is a variant of Non-reductive
physicalism.  The idea is that reality has only one
underlying substance (monism) but this substance takes
on the appearance of multiple forms or properties. 
All of these different properties are really
reflecting (approximately) the same reality however. 
They only *appear* to be different things.  The idea
is that mental and physical concepts are really just
different manifestations of a single underlying
reality.  Many-aspect monism is also known as
'Fundamental Property Dualism', because although only
one underlying reality is postulated, fundamental
reality is granted to multiple properties.

The idea has similarities to an earlier theory known
as 'Identity Theory'.  That theory originated with
Ullin Place (1956 paper, "Is Consciousness A Brain
Process?).  It was defended by philosopher Jack Smart
(1959 paper, "Sensations and Brain Processes'.  The
defense makes use of a distinction from philosopher
Gottlob Frege (1848-1925) between the sense (Sinn) of
an expression and what the expression refers to
(Bedeutang).  For instance the terms "morning star"
and "evening star" have different senses - one refers
to a bright star seen early in the day, another to a
bright star seen later in the day - but in fact they
both refer to the *same* entity - the planet Venus. 
Similarly, material brain processes and consciousness
may *seem* to be different things (we use mental and
physical concepts in different senses), but they are
not.  The difference between Identity Theory and
Many-Aspect Monism is that in Many-Aspect Monism the
different properties cannot be totally reduced to (or
identified with) each  other.

The theory of Monism dates back to Baruch Spinoza
(1632-1677), and a variant known as Dual-aspect Monism
was championed by Bertrand Russll (1872-1970). 
Russell pointed out that reality consists of two
general types of properties - Intrinsic - or what
objects are constituted out of - and Relational - or
the relations between different objects.  Russell
proposed to equate Intrinsic properties with Mental
things and Relational properties with Physical things.
 So the idea was everything had these two properties
associated with it - mental and physical.  (Hence the
expression 'Dual-aspect Monism').


See the section 'Type-F Monism' in this David
Chalmer's paper:
http://consc.net/papers/nature.html



Key TOE Principle 2:  7-fold aspect monism

I'm here postulating a variant of Many-aspect monism
which has an underlying substance with 7 different
properties.  The idea is that everything in reality
has 7-fundamental properties associated with it. 
There are, if you like, 7 different valid perspectives
through which one could view the whole of reality (see
summaries of 'Many Aspect Monism' above).

Why 7?  It follows the argument for 3-time dimensions
(See Key TOE Principle 1 and associated arguments). 
The idea is that everything in reality can be defined
as part of an 'event' (a cause and effect relations in
time).  If there are really 3 different kinds of
causality, 'events' along each of the 3 time-lines
will have their own fundamental sub-properties
associated with them.

What are the fundamental properties associated with
'events' then?  I here draw on ideas associated with
philosopher Jaegwon Kim (1966, 1969, 1976).  "The
view, which takes the Aristotelian conception of
change as its starting point, sees an event as the
exemplification by an object or several objects of an
attribute (property or relation) at a time or over a
period.  Schematically, if we consider P to be the
attribute, s the object, and t the time, we can
specify the event of s's having P at t as the triple
[s, P, t]."  (The Oxford Handbook Of Metaphysics).

Since there 3 different time dimensions, there are 3
different kinds of events and each 'event' requires a
'triple' co-ordinate to specify it, the initial total
is for 9 fundamental properties.  It shall be
explained shortly how this is reduced to 7. 

The underlying 'substance' of reality is here
postulated to be something *Mathematico-Cognition*. 
The idea is that the fabric of reality ultimately is a
sort of combination (or hybrid) of mathematics (see
Mathematical Platonism for a justification) and
Cognition (Information processing).  hence the term
Mathematico-Cognition.  The concept will be clarified
below.


Key TOE Principle 3:  Reality as
Mathematico-Cognition.  The Basic Reality Schematic

The schematic below is intended to represent: (a) Both
the structure of Reality itself (in terms of the
fundamental properties making up reality AND (b) A
model of Reality.  Since the fabric of reality was
postulated to be Mathematico-Cognition (a hybrid of
mathematics and Information), there is no clear
division between a *model* of reality (which would
require a mathematical description) and *reality
itself* (which IS mathematics).

The key ideas behind this schematic are: (a) the 3
time dimensions (see Key TOE Principle 1), and (b)
7-fold aspect Monism (see Key TOE Principle 2) where
reality was proposed to consist of an underlying
substance called Mathematico-Cognition - a hybrid of
mathematics and information processing and everything
in reality could be defined as an 'event' on the 3
time-lines and the sub-properties associated with
these events. 

The big idea is to connect the 3 time dimensions to
each other, so they are no longer totally independent
of each other.  There are 3 general kinds of property
represented below, each with 3 sub-properties.  The
three general properties ('Temporal' properties)
represent the three time dimensions.  The big idea is
to connect them together by making 2 of the
Temporal-properties (Physical and Volitional)
sub-properties of the other one (Mathematical).  Then
the total number of fundamental properties in reality
is reduced from 9 to 7 and all aspects of reality are
linked together in the most 'natural', aesthetically
pleasing way.  For justification of this move see the
original argument for multiple time dimensions (Key
TOE principle 1) and 'Mathematical Platonism’:
mathematical properties appear to be 'processes'
taking place in all three time dimensions, whereas
Mental and Physical properties do not.  Therefore the
Mathematical time-line must be fundamental and must
encompass the other two time-lines.

It was proposed that the basic underlying substance of
reality was something called Mathematico-Cognition ? a
hybrid of mathematics and information processing.  So
let us consider reality as 'Pure information' and
‘Pure Mathmatics’.  The idea dates back to John
Wheeler and his ‘It’ from ‘Bit’ theory.  The idea is
to pretend that reality is a 'program' or a kind of
mind', and when we do this we find that  3 kinds of
fundamental'data types' appear - Mathematical
propositions, Memes and Physical states. We are
justified in treating each kind of Information
separately because
that is what we need to do in order to fully *explain*
reality in *informational* terms.

Recall that we proposed to define all properties in
reality as sub-properties of ‘Events’.  Each of the
three general types of property (events on one of the
three time-lines) has 3-sub properties. 



*Intrinsic:    The form of the basic building blocks
(or individual 'entities’) taking part in an ‘Event’.

*Action:       The internal states of the entities
taking part in an ‘Event’.

*Temporal:  An ‘Event’.  Cause and effect relations
between two states of an entity (or two different
entities).

The '*Temporal* aspect of an event is an ordered
relationship (or in mathematical jargon a 'mapping')
between two states of an entity.

Temporal Event =  Mapping (State 1 >>>>>>>>> State 2)

State = Combination (Intrinsic property, Action
property)

The schematic below shows the data types for modeling
each of the three different kinds of general ‘events’
in reality.


Physical Model


*Temporal Property - Function (Physics/Computation)

*Action Property    - Translation (Motion)

*Intrinsic Property - Object (Spatial extension)



*Physics* here refers to a functional process - a
system passing through
a succession of on/off states.

*Translation* Here refers to the movements of a body

*Object* here refers to something with an extension in
physical space

The schematic above is a strategy for modeling
physical events.  It says that
a physical system is defined as a series of
computational 'events' composed
of serially ordered combinations of objects and their
motions.

Example:

Temporal property :  A gun firing (this is a function
-  an 'event').

Action property:    The particular movements of the
gun needed (i.e. cocking trigger, bullet exiting etc)

Intrinsic Property: The gun itself


Volitional Model


*Temporal - Meme (Morality)

*Action       - Situation (Activities)

*Intrinsic    - Agent (Intentions)


*Morality* here refers to a system of memes -
referring to behaviors resulting in gains and losses
for volitional agents.

*Situation* here refers to the activities of a
volitional agent

*Agent here refers to volitional agent ? an agent with
intensions ? goals which can be signaled or
communicated to other agents.



The schematic above is a strategy for modeling events
involving volitional agents.  It says that Memes are a
series of mental events consisting of a
combination of agents and activities.  


Mathematical/Platonic Model


*Temporal Property - Sets (Qualia)

*Action Property      -Memes (Morality)

*Intrinsic Property - Function (Physics).


Sets* here refer to the standard mathematical
definition of the term -
groupings of entities related in some way.  

*Memes* is here is referring to beliefs modeling the
behavior of volitional agents

*Function* is here referring to models of functional
systems (Physics/Computation)

This scheme represents the 'Platonic' or abstract
world (See 'Mathematical Platonism').  The basic
‘event’ on the mathematical time-line is here
postulated to be the 'Set'.  According to David Lewis
(1991) set theory comes from three things: (a) A
Primitive singleton function (a logical 'lasso'), (b)
Plural quantification and (c) Mereology (collections
of objects).  A 'Set' is a collection of objects with
a logical 'lasso' thrown over them, or even a *single*
object with such a lasso.  The nature of such
'Singleton' sets has been puzzling.  What is the
difference between an object and a set containing only
that object?  The schematic here proposes an answer. 
A set is here defined as a combination of a physical
model (a function) AND an intentional model (a meme). 
Therefore a set is proposed to be a mathematical
expression of the relationship between a mind (or
mental concepts) and physical reality.  A 'Primitive
Singleton function' is proposed to be equivalent to a
Meme.  Note that the proposed fundamental unit of
mathematics is the Function.  Sets supervene on (are
dependent on) Functions and Memes.

The really radical idea here is to equate Qualia
(conscious experience) with mathematical sets.  Since
the set is a general unit of mathematics and many
properties of reality could defined as a Set, the
scheme is a form of panpsychism, ascribing some degree
of conscious experience to everything in reality.

Note how the Platonic world subsumes the other aspects
of reality.  Memes (mental concepts) have a
dual-aspect.  They have an abstract component which is
defined as the 'Action' properties of the Platonic
world.  But they also have a concrete component which
manifests itself as the behavior of volitional agents
- Memes are also defined as the 'Temporal' properties
of the Volitional world (see above).  Functions
(physical concepts) also have this dual-aspect.  Their
abstract component is defined as the 'Intrinsic'
properties of the Platonic world.  But they also have
a concrete component - the 'Temporal' properties of
the Physical world - which appears as physics - or
computation (See above).  This is based on the idea of
3-dimensional time (See 'Key TOE Principle 1). 
Mathematical (Platonic) entities have extensions in
multiple time dimensions.  They project into the
concrete world but also extend beyond it.


Key TOE Principle 4:  Universal Value System

The Reality schematic above, if it's accurate,
establishes the basis for a Universal Value System.  

Definition:

A Universal Value System (UV) is a set of values that
*all* intelligent minds would converge upon, if they
were smart enough and thought about it for long
enough.  This does *not* imply Objective Morality (the
idea that there exist objectively 'good' values
independently of minds), only the weaker claim of
Universal Morality.  

Universal Morality (UV):  Actualization

The Mathematico-Cognition Reality Schematic (see
above) said that Qualia (conscious experiences) were
'events' on the Mathematical time-line.  Qualia
(conscious experience) is built-up out of (dependent
on) all of the other unconscious processes which make
up an integrated mind.  Therefore the purpose of
Qualia is equivalent to the purpose of Mind in
general.  

'Events' on the mathematical time-line (or Qualia)
were defined to consist of a combination of Functions
(models of physical systems) and Memes (models of
sentient behavior).  Since the mathematical time-line
connects the other two time-lines together, the
mathematical time-line is what connects models of
physical systems with models of sentient behavior. 
Call this 'time knitting'.  The purpose of mind (or if
one wishes to be dramatic, the meaning of life itself)
is precisely this 'time knitting': the integration of
models of physical systems (functions) with models of
sentient behavior (memes).  This could be called
'Actualization', since it maintains existence itself
(by ordering time itself).  Recall that there is no
clear distinction between a *model* of reality and
*reality itself*.  The schematic implies some
variation of panpsychism (the idea that everything in
reality has some degree of consciousness associated
with it).  This follows from the fact that the
schematic is representing a 7-fold aspect monism (see
earlier definition of many-aspect monism) and Qualia
are represented in the schematic as one of the 7
aspects. 

The ultimate imperative (if the scheme is correct),
appears to be 'maintain the existence of the
universe', which is apparently achieved through the
integration and growth of knowledge (ultimately the
integration of memes with functions).  This process is
also equivalent to 'achieving better awareness of the
theory of everything', where 'theory of everything'
was defined as 'the integration of mental, physical
and mathematical concepts into a single explanatory
framework' (See below -Key TOE Principle 5 - for
further explanation).


Key TOE Principle 5-  A transhuman intelligence has
awareness of the TOE (Theory Of Everything)

Recall that the Mathematico-Cognition Reality
Schematic suggests that there is no clear division
between a *model* of reality and *reality itself*. 
Because Qualia were defined as the most fundamental
'aspect' of reality, the schematic represents not only
'objective reality' but also any individual mind.

If the theory is correct then, the schematic tells us,
in very general terms, how to build an 'optimally
functioning mind'.  An individual mind which is
'functioning optimally' would model the reality
schematic shown.  Such a mind would optimally
integrate models of sentient behavior (memes) and
models of physical systems (functions).  But this was
exactly the suggested original aim of a TOE (Theory Of
Reality).  A TOE was defined to be a logical system
which integrated physical and mental concepts. 
Furthermore, note that Qualia were equated with
mathematical sets.  A mind capable of fully modeling
the reality schematic then, would be a mind capable of
direct perception of mathematical entities (something
the human mind is not capable of).  Such a mind would
presumably be able to objectively view Qualia
themselves (where as humans can subjectively
experience Qualia). To summarize again, these Qualia
represent the integration of physical and mental
concepts and qualia are equivalent to mathematics
itself.  *In other words such a mind would have direct
awareness of the theory of everything*.  This appears
to *define* what a transhuman intelligence is - a mind
capable of modeling the Mathematico-Cognition Reality
schematic  - or a mind with direct awareness of the
theory of everything.    


"Till shade is gone, till water is gone, into the shadow with teeth bared, screaming defiance with the last breath, to spit in Sightblinder’s eye on the last day”


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