The Mathematico-Cognition Reality Theory (MCRT)

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The Mathematico-Cognition Reality Theory (MCRT)

By Marc Geddes, Auckland, New Zealand

Version 3.0
Seed-ideas for version 1.0 completed on: 15th December, 2005
This version updated on: 16 th January, 2006

The Mathematico-Cognition Reality Theory (MCRT) is a series of ideas intended to sketch a general framework or philosophical approach which *may* lead towards a 'Theory Of Everything'.

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.

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)

Since mathematical Platonism is central to the theory presented here, an over-view of the arguments in favor of Platonism will first be given.

First, why should we believe in the objective existence of mathematical entities? Surely, some will argue, mathematical entities are really just abstract fictions (or invented languages) we use for describing what are really material processes. This position is known as nominalism.

However, there's an argument known as *The argument from Indispensability*. Certain mathematical theories (for instance analysis) are indispensable for modern physics. Physics uses quantifiers which range over domains that include mathematical entities not in space and time. Thus, the argument goes; since we have to accept our best scientific theories of the world, we should accept that the entities referred to in our theories really exist.

Now one could try to remove the references to mathematical entities in scientific theories. For instance the philosopher Hartry Field (1980) has proposed this - he suggested trying to remove talk of real numbers in Newton's theory of gravity and replacing numbers with space-time points and regions. But if one tries to do this, one finds that the theories become enormously unwieldy - mathematical entities such as numbers are just so *useful* in science. If there are entities in our theories which it is very useful to refer to, this provides some pragmatic grounds for believing in their existence. The argument at work here is Occam's razor: in science the general rule of thumb is that simple explanations are favored over more complex ones. Since in science references to mathematical entities simplify scientific theories, the simplest explanation is that these mathematical entities really exist.

Further it appears that there are some highly abstract mathematical entities in scientific theories which *cannot* be replaced with descriptions of material processes at all. An example of this is 'the quantum wave function' -in quantum mechanics. The wave function is necessary for the theory to work, yet the wave function is wholly abstract. See arguments by Malament (1982) to the effect that one cannot remove talk of abstract entities from quantum mechanics. Since references to abstract entities appears to be *essential* for QM to work and since QM is such a successful scientific theory, the simplest possible explanation is that these abstract entities really do exist.

Returning to the principle of Ocaam's razor again, physicist David Deutsch in his book 'The Fabric Of Reality', uses the principle to establish 'Criterion for reality'. The idea is that we should regard as real those postulated entities which, if we tried to replace them with something else would complicate our explanations. Deutsch's principle was this:

'If according to the simplest explanation, an entity is complex and autonomous, then that entity is real.' ('The Fabric Of Reality', Pg 91)

As Detusch points out, mathematical entities do appear to match the criteria for reality: 'Abstract entities that are complex and autonomous exist objectively and are part of the fabric of reality. There exist logically necessary truths about these entities, and these comprise the subject-matter of mathematics.'

Professor of mathematics Roger Penrose also neatly makes the point that mathematicians strongly feel they are engaged in discovery, not creation, and that mathematical entities appear to have complex, autonomous structure not put there by humans:

'The Mandelbrot set provides a striking example. It's wonderfully elaborate structure was not the invention of any one person, nor was it the design of a team of mathematicians. Benoit Mandelbrot himself, the Polish-American mathematician who first studied the set, had no real prior conception of the fantastic elaboration inherent in it...Moreover, the complete details of the complication of the structure of Mandelbrot's set cannot really be fully comprehended by any one of us, nor can it be fully revealed by any computer. It would seem that this structure is not just a part of our minds, but it has a reality of its own.'

In 'Shadows of the Mind', Penrose goes on to make the very telling point that mathematical theories often turn out to be useful for science in a manner which goes far far beyond what the math was originally used for. The example is given of the mathematics of Einstein's general theory of relativity:

'In the early years after Einstein's theory was put forward, there were only a few effects that supported it and the increase in precision over Newton's scheme was marginal. However, now, nearly 80 years after the theory was first produced, its overall precision has grown to something like *ten million times* greater’ ('Shadows of The Mind', Pg 415).

This is not at all what we would expect if the math was just an invention of the human mind. As Penrose points out: 'Einstein was not just 'noticing patterns' in the behavior of physical objects. He was uncovering a profound mathematical substructure that was already hidden in the very workings of the world.'

Accepting all this, a skeptic might concede that mathematical entities have objective existence, but try to identity them entirely with the material world. This doesn't work. For one thing, as pointed out earlier, our best scientific theories make explicit references to wholly abstract entities (for instance 'the quantum wave function') which have no concrete counter-part at all.

Further more, there exist perfectly good mathematical facts which be cannot be directly or indirectly matched to any material facts. A striking example of this transfinite numbers and infinite sets- here references are clearly made to infinite entities yet all available evidence would indicate that all material entities are finite. Attempting to equate transfinite numbers or infinite sets with some nebulous property of a ‘multiverse’ (as some scientists have attempted to do) is simply begging the question about what is physical. Nor can infinite sets be argued away as fictions - they are perfectly precise and logical mathematics, having the same 'reality' as any other results in mathematics. Greg Cantor developed a rigorous treatment of transfinite numbers and later Abraham Robinson and John Conway did the same for infinitesimals.

In fact one has not even have to consider such esoteric things as transfinite numbers and quantum wave functions to see that nominalism (the idea that abstract entities don't exist) has severe problems.

Logical positivists used to claim that statements could not be meaningful if they could not be converted into descriptions in terms of concrete observables. The positivists were wrong. There are perfectly meaningful statements in plain every day English that cannot be converted into concrete descriptions. Here is one example from the philosophy literature:

Statement: "There are shapes that are never exemplified"

It can be shown that this statement cannot be converted into any description of finite length which refers only to concrete entities. Yet the statement is clearly meaningful. This shows that abstract entities do exist.

Semantic considerations provide even more evidence for believing in the existence of abstract entities. 'The Fregean argument' is based on the idea that only in the context of a sentence does a word have meaning. If a certain expression functions as a singular term in a sentence, the sentence cannot be meaningful unless there is an actual real singular entity to which the term is referring. For instance if ‘2’ functions as a singular term in a sentence, there must be a real entity '2' to the terms refers.

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)

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.

There’s nothing mystical about the notion of extra time dimensions. A ‘time dimension’ is simply a co-ordinate system for marking off events. Everything in reality exists in at least one time dimension. On the macroscopic scale there appear to be 3 dimensions of space and 1 of time. For instance to locate an event (say meeting a friend), one has to give 4-ordinates. 3 involve space; Distance left-right, distance forward-back and distance up-down. One involves time; for instance 10'clock. This is the classical physics Einsteinian conception of a 4-dimensional space-time (3 spatial dimensional, 1 time dimension).

There have been string theorists exploring the possibility of extra time dimensions. It may be that this idea could resolve some of the paradoxes and confusion surrounding quantum mechanics. In quantum physics, things behave as if they occupy more than one state at once. Counter-factual states - 'what if's' or things that *could* have happened strangely interfere with what *did* happen. No one is quite sure what this means. But string theorists Edward Witten and Cumrun Vafa believe that string theory could resolve these puzzles. Cumrun Vafa has proposed a 12-dimensional version of string theory (his ‘F-variation’) with two dimensions of time and 10 of space.

Aside from string theory, there are other wacky physics theories which do strange things to time. Cosmologists Stephen Hawking and James Hartle proposed the notion of 'Imaginary Time', so-called because of the use of 'Imaginary' numbers from mathematics. In fact these numbers are just as real as real numbers and there would be nothing imaginary about this kind of time if it existed. In this theory, the time dimension can behave as if it's just another dimension of space. The theory was originally intended to deal only with extreme situations such as the beginning of the universe, where the mystery of the origin of time could be resolved by supposing that ordinary time changes into 'Imaginary Time'. But suppose that there were extra time dimensions existing even today A single I-time dimension by itself does not allow for a new form of causality. But two I-time dimensions together can make up one new ‘real’ time dimension.

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.

'The mind-stuff of strong AI is the logical structure of an algorithm... the particular physical embodiment of an algorithm is something totally irrelevant. The algorithm has some kind of disembodied 'existence' which is quite apart from any realization of that algorithm in physical terms' ('The Emperor's New Mind', Pg 27)

It was an argument similar to this that led to the demise of the original 'Identity Theory' of mind (a theory which attempted to identity mental states with physical processes). Again, the trouble is that many different brain states could be associated with the *same* algorithm (or have the same mental states) which shows that physical processes cannot be identified with mathematical entities in any simple way. The weaker 'Token Identity' theories concede this, but still attempt to equate mental states with physical processes. Couldn't one simply say that there's some general high-level properties of physical matter which can be equated with the algorithm, and hence dispense with ghostly mathematical entities? The reason one can't really say this boils down to Occam's razor and inference to the best explanation again. Attempting to replace the concept of 'algorithm' with some high level properties of physical matter is results in descriptions that are enormously complex and unwieldy. And therefore such an arbitrary scheme should be rejected, for reasons explained earlier. Inference to the best explanation requires that we accept that mathematical entities such as 'algorithms' really do have an objective existence above and beyond a particular instantiation in material processes.

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:

Qualia are generated by brain processes
Brain processes are enacting algorithms (mathematical patterns)
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
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.
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 called *Mathematico-Cognition*. The idea is that the fabric of reality ultimately is a hybrid of Physical, Volitional and Mathematical properties and this *is* Qualia (conscious experience) itself. Hence the term Mathematico-Cognition. The concept is clarified further below. The idea is that Qualia (or phenomenal properties) are equivalent to the underlying fabric of reality itself. This theory of Monism is different to the more well known theory of 'Neutral Monism' (for instance the one proposed by Bertrand’s Russell - see above), where the underlying substance if reality is neutral with respect to phenomenal and physical properties. Here the underlying substance of reality proposed is not neutral - it is being proposed that the underlying substance *is* conscious experience (Qualia) itself. The 7-properties are all different manifestations of Qualia.

Key TOE Principle 3: Reality as Mathematico-Cognition.

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 Physical, Volitional and Mathematical properties, and equivalent to conscious experience itself. So let us consider reality as 'Pure information'. The idea dates back to John Wheeler and his 'It' from 'Bit' theory. Indeed when we treat reality is a 'program' or a kind of mind' we do indeed find that 3 kinds of fundamental 'data types' appear - Mathematical propositions, Memes and Physical functions. 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 basic building blocks (or 'Entities') taking part in an 'Event'.

*Logical: The logical relationship between an 'Entity' and its external environment.

*Temporal: An 'Event'. Cause and effect relations between several different states

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

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

A 'State' is defined as combination of an Intrinsic property and a Logical property.

The schematic below shows the data types for modeling each of the three different kinds of general 'events' in reality. The Intrinsic and Logical properties can be thought as static representations of reality itself. The Temporal properties form dynamic causal *models* of reality.

Physical Model

*Temporal Property - Function (Physics/Computation)

*Logical Property - Field (Containment)

*Intrinsic Property - Object (Spatial extension)

*Function* here refers to a functional process, or 'computation'. A computation can be defined by a binary number where: 0=Off, 1=On

*Field* Here refers to what is 'containing' or acting upon an object. A field can be defined by a binary number where: 0=Unconstrained, 1=Contained

*Object* here refers to something with an extension in physical space. An object can be defined by a binary number where: 0=Empty, 1=Occupied

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 fields.

Example:

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

Logical property: The gun is being held in someone's hand.

Intrinsic Property: The gun itself

Volitional Model

*Temporal property - Meme (Morality/Actions)

*Logical property - Situation (Benefits)

*Intrinsic property - Agent (Desires)

*Meme* here refers to the behaviors, roles and activities of volitional agents. A meme can be defined by a binary number where: 0=Not Acting, 1=Acting

*Situation* here refers to the relationship between two agents or between an agent and the environment. A situation can be defined by a binary number where: 0=Loss, 1=Gain

*Agent here refers to desire or agency. An agency can be defined by a binary number where: 0=Avoidance, 1=Desire

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 situations.

Mathematical/Platonic Model

*Temporal Property - Set (Mathematico-Cognition)

*Logical Property - Set

*Intrinsic Properties – Function, Meme

*Set* here refer to the standard mathematical definition of the term -groupings of entities related in some way. A Set can be defined by a binary number where: 0=Unrelated, 1=Associated

*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 the relationship between combinations of functions (physical systems) and memes. Therefore a set is proposed to be a mathematical expression of the relationship between mental concepts and physical concepts. A 'Primitive Singleton function' is just this logical relationship.

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 an 'Intrinsic' property of the Platonic world. But they also have a concrete component which manifests itself as the behavior of volitional agents - Memes are defined as 'Temporal' properties of the Volitional world (see above). Functions (physical concepts) also have this dual-aspect. Their abstract component is defined as an 'Intrinsic' property of the Platonic world. But they also have a concrete component - Functions are 'Temporal' properties of the Physical world - which appears as physics - or computation (See above).

Sets too have a dual-aspect. A Set can be both a logical property of the Platonic world and a temporal property. As a logical property the Set represents a static mathematical object existing in platonic reality. But as a temporal property the Set represents a *model* of a mathematical object. This is proposed to be equivalent to the underlying substance of reality itself - Mathematico-Cognition. Curiously then , this last property (the 'Set' as a Temporal property) is in some sense equivalent to (or contains) all the other properties (including itself!), since all properties in reality are manifestations of Mathematico-Cognition. Mathematico-Cognition was also proposed to equivalent to Qualia (conscious experience) itself. The scheme is a form of panpsychism, ascribing some degree of conscious experience to everything in reality.

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 (UVS) 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 Value System(UVS):

The Mathematico-Cognition Reality Theory (see above) said that Qualia (conscious experiences) were both the underlying substance of reality itself and 'Events' on the Mathematical time-line - or processes in multi-dimensional time. Qualia (conscious experience) are built-up out of all of the 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 causal relationships between combinations of Functions (models of physical systems) and Memes (models of sentient behavior). Such 'Events' were proposed to be equivalent to the fabric of reality itself (Mathematico-Cognition), a hybrid of Physical, Volitional and Mathematical properties.

Therefore mathematical 'Events' are processes in multi-dimensional time. The interaction of platonic mathematical objects (functions, memes and sets) manifests itself as physical, volitional and mathematical properties and conscious experience itself. The mathematical time-line connects the other two time-lines together. Call this 'time knitting'.

The purpose of mind then (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) and mathematical entities (Sets). This process maintains existence itself, since mathematical 'events' were proposed to be equivalent to Mathematico-Cognition (the underlying substance of reality itself).

The idea here is that the one thing a conscious mind must value (if it values anything at all), is the continuation of consciousness itself (since value comes from consciousness). This is not an objective basis for values, but it is a universal one.

To summarize, 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 physical, volitional and mathematical properties)

There are 3 temporal domains - the Physical, Volitional and Mathematical. When considering a mind which is modeling each of these domains there are 3 aspects to which value (or utility) could be assigned - *reality* itself (events in the external world), the *model* of reality and *qualia* (conscious experiences). A table of 9 'Universal Utilities' is implied. Utilities which are 'good' are those that maximally enable the growth, integration and self-reflection of knowledge because this is what maintains existence itself and also consciousness (recall that the underlying fabric of reality itself - Mathematico-Cognition - was proposed to be equivalent to Qualia - conscious experience).

-------------Universal Utilities Table

-------------Reality Utility---Model Utility---Qualia Utility

Physical-------Productivity----Prediction-------Pleasure

Volitional------Liberty--------Optimization-----Happiness

Mathematical-Knowledge---Consilience------Enlightenment

*Productivity: The capacity and efficiency of functional systems at outputting things of value

*Prediction: The ability to make accurate models of the future states of functional systems.

*Pleasure: Conscious sensations and senses interpreted as 'physical'

*Liberty: The optimal growth and satisfaction of multiple desires

*Optimization: The ability to model the most efficient way to achieve goals

* Happiness: The full range of positive conscious experience interpreted as 'emotional'

*Knowledge: The growth and creation of knowledge

*Consilience: The ability to integrate different kinds of knowledge into a single explanatory framework

*Enlightenment: Conscious experience interpreted as 'reflection on knowledge'

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

The Mathematico-Cognition reality schematic suggests that there is no clear division between *reality* itself, a *model* of reality and *qualia* (conscious experience). . Because Qualia (conscious experience) were defined as the underlying fabric of reality itself (Mathematico-Cognition), 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 a mind. The table of Universal Utilities gives the general goals which an ‘optimally functioning mind' pursues. An individual mind which is 'functioning optimally' would model reality according to the Mathematico-Cognition reality schematic and have the Universal Utilities built into it as invariant values. Such a mind would ultimately aim for the growth and integration of knowledge and the self-reflection of knowledge.

The integration of the different kinds of knowledge into a single explanatory framework was exactly the suggested original aim of a TOE (Theory Of Reality). A TOE was defined to be a logical system which integrated physical, volitional and mathematical concepts. Furthermore, note that Qualia were equated with mathematical sets. A mind capable of fully modeling the reality schematic 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 - to 'see' Qualia from the outside as it were (where as humans can only subjectively experience Qualia). Again Qualia represent the integration of physical, volitional and mathematical concepts and Qualia are equivalent to a form of mathematics itself. So a mind capable of direct perception of Qualia (the ability to view Qualia objectively) would have *direct awareness of the theory of everything* (since ultimately such a theory is mathematical in nature). 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.