Sunday, 30 December 2012

Secular Buddhism, Materialism, Physicalism, Naturalism and other vague and ambiguous terms.

'Secularist' means whatever I choose it to mean

Call me old-fashioned, but I always thought that 'secularism' meant a political belief in the separation of church and state.  The government doesn't meddle in religion and vice versa.  Secularism in this sense doesn't imply the endorsement of any particular philosophical or metaphysical view. But it seems that 'secularism' is now becoming a loaded word that, due to sloppy usage, is gradually accumulating a lot of baggage.

For example, this gem of wisdom comes from the Christian Peoples Alliance

"Creeping secularism has brought with it policies that have ravaged the planet, exploited vulnerable workers, caused financial meltdown, abused the sanctity of the person and marginalised family life."

Secularists ravaging the planet

Hundreds of Catholic Bishops have recently held a conference to denounce and campaign against secularism, and members of The Religion of Peace™ shot Malala Yousafzai, a fourteen-year-old girl, for 'promoting secularism'.   She survived, though is now seriously injured in a Birmingham hospital.   The brave jihadists have threatened to shoot her again to finish the job.

And it isn't just the Abrahamics who get their undergarments in a helix about secularism.  Consider the strange phenomenon of 'Secular Buddhism', which prides itself on being  'post-metaphysical' (whatever that may mean)  and whose assertions about what the Buddha really intended to say just happen to correspond to the materialistic assumptions of scientism.

B. Alan Wallace describes Secular Buddhism thus:

"There would be nothing wrong if Batchelor simply rejected the authenticity of the Buddha’s enlightenment and the core of his teachings, but instead he rejects the most reliable accounts of the Buddha’s vision and replaces it with his own, while then projecting it on the Buddha that exists only in his imagination.

Perhaps the most important issue secularists ignore regarding the teachings attributed to the Buddha is that there are contemplative methods – practised by many generations of ardent seekers of truth – for putting many, if not all, these teachings to the test of experience. Specifically, Buddhist assertions concerning the continuity of individual consciousness after death and rebirth can be explored through the practice of samadhi, probing beyond the coarse dimension of consciousness that is contingent upon the brain to a subtler continuum of awareness that allegedly carries on from one lifetime to the next.

Such samadhi training does not require prior belief in reincarnation, but it does call for great determination and zeal in refining one’s attention skills. Such full-time, rigorous training may require months or even years of disciplined effort, and this is where the Buddhist science of the mind really gets launched. If one is content with one’s own dogmatic, materialist assertions – content to accept the uncorroborated assumption that all states of consciousness are produced by the brain – then one is bound to remain ignorant about the origins and nature of consciousness. But if one is determined to progress from a state of agnosticism – not knowing what happens at death – to direct knowledge of the deeper dimensions of consciousness, then Buddhism provides multiple avenues of experiential discovery. Many may welcome this as a refreshing alternative to the blind acceptance of materialist assumptions about consciousness that do not lend themselves to either confirmation or repudiation through experience."


Both the 'secular' Buddhists and Evangelical Christians are misusing the words 'secular' and  'secularism' to mean 'materialist' and  'materialism', though in slightly different ways. 

The Secular Buddhists are trying to reduce all aspects of the mind to the mechanistic activities of matter, and are thus denying the existence of the spiritual or transcendental aspects of Buddha's teaching.  Their main motivation is the false belief that they are somehow making Buddhism more compliant with science by doing so.  The evangelical Christians are equating another aspect of materialism with secularism: that aspect being the excessive desire to acquire and consume material goods.

It would be more honest if the Secular Buddhists referred to themselves as 'Materialist Buddhists', though even this terminology is not unambiguous. Maybe calling yourself a 'Materialist Buddhist' could give the impression that you were obsessed with goodies, gadgets and gizmos

So how can we describe the world view of the 'Secular Buddhists if 'secularism' is a misuse of the English language, and 'materialism' is ambiguous and ill-defined? (It's surprisingly difficult to get a definition of matter - 'It is fair to say that in physics, there is no broad consensus as to a general definition of matter, and the term "matter" usually is used in conjunction with a specifying modifier. )


Another near synonym for 'Materialism' is 'Naturalism'. However this is highly ambiguous, even when understood in its philosophical sense rather than as people studying the habits of birds and bees while possibly running around stark naked.  Naturalism is also rather ill-defined and incoherent, since phenomena such as qualia, intentionality and free-will might be regarded as natural, while defying any physical explanation.


Physicalism is a better term to describe the Secular Buddhists' beliefs, though even this is not quite precise enough. To quote Wiki
"Physicalism is a philosophical theory holding that everything which exists is no more extensive than its physical properties; that is, that there are no kinds of things other than physical things. The term was coined by Otto Neurath in a series of early twentieth century essays on the subject, in which he wrote:

"According to physicalism, the language of physics is the universal language of science and, consequently, any knowledge can be brought back to the statements on the physical objects."

In contemporary philosophy, physicalism is most frequently associated with the mind-body problem in philosophy of mind, regarding which physicalism holds that all that has been ascribed to "mind" is more correctly ascribed to "brain" or the activity of the brain. Physicalism is also called "materialism", but the term "physicalism" is preferable because it has evolved with the physical sciences to incorporate far more sophisticated notions of physicality than matter, for example wave/particle relationships and non-material forces produced by particles.

The related position of methodological naturalism says that philosophy and science should at least operate under the assumptions of natural sciences (and thus physicalism). Physicalism is a strong form of metaphysical naturalism.

The ontology of physicalism ultimately includes whatever is described by physics — not just matter but energy, space, time, physical forces, structure, physical processes, information, state, etc. Because it claims that only physical things exist, physicalism is generally a form of ontological monism."

The reason why physicalism is still too imprecise is that it lacks a coherent definition of physics itself. 

A more precise term than physicalism would be Mechanistic Reductionism, which is obtained by coupling physicalism with the Church Turing Deutsch Principle.

Mechanistic reductionism

Mechanistic reductionism is the belief that all phenomena (including the human mind) can in principle be simulated by, and explained in terms of, algorithmic models running on general purpose computing machines.  This, whether they realise it or not, is the logical consequence of what the secular Buddhists are advocating.

Simulation implies prediction.  An effective computational simulation of a real-world system is one that, given a set of input values, will predict output values within some arbitrary limits of accuracy deemed 'useful' or 'acceptable'.

Explanation requires the ability to lead the enquirer through a chain of effects assigned to their causes by mathematical or logical statements. The most exhaustive version of an explanation would be a high-level listing of the program running the simulation.

'General purpose computing machines' include both the theoretical (universal Turing machine) and the practical (stored program computers as actually constructed). 

Hence systems that can't be simulated by a machine can't be explained in physical terms.

The opposing view to Mechanistic Reductionism is Ontological Mysterianism, which states that no algorithm is capable of simulating or explaining the processes of the mind.   Mental phenomena include non-procedural processes, which will forever be beyond the limits of understanding in terms of physics, though as Alan Wallace points out, they are directly accessible to experiential discovery through meditation.

There is no alternative to Mechanistic Reductionism apart from Ontological Mysterianism, because if you could explain in a stepwise logical and mathematical manner how something worked, it would be algorithmic and hence mechanistic.   Epistemological Mysterianism is not really an alternative, because it is a form of reductionism which assumes an unknown mechanism, whereas Ontological Mysterianism requires no mechanism.


In describing Secular Buddhists as Mechanistic Reductionists in disguise, maybe I've set up a strawman that misrepresents their views.  If so, could someone please explain where I have gone wrong.

Secular Buddhism isn't Rational Buddhism.

Secular Buddhists may claim that they are reforming Buddhism to make it compatible with science, but all they are actually doing is making it compatible with scientism.  

Scientism is a misuse of scientific methodology beyond the limits of its applicability, including attempts to reduce all knowledge to only that which can be understood by mechanistic models. Scientism is a totalizing view of science as if it were capable of describing all reality and knowledge, or as if it were the only true way to acquire knowledge about reality and the nature of things.

While Buddhism is quite happy with science in general, and especially with evolution, it does not agree with scientism, and disputes claims that the mind can be explained or understood in physical terms, because its ultimate nature is non-physical: 'when the body dies the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later, perhaps immediately.'  - Alan Turing (Code Breaker, Mathematician and Buddhist Philosopher)

The Limits of Science

The Church-Turing-Deutsch principle helps to demarcate the limits of science.

The domain of science concerns those aspects of the world that can be modelled effectively and efficiently in terms of algorithms and data-structures.

'Effectively' means that the models have predictive power.

'Efficiently' means that the models are simpler and more general than the phenomena that they model (they embody 'algorithmic compression', Kolmogorov-style )

All non-algorithmic phenomena, are, by their very nature, outside the scope of science.

Consequently, the 'materialists', 'physicalists' reductionists and other practitioners of scientism are committed to trying to represent the three-dimensional world of causality, composition and mind, in terms of the two dimensions of algorithms and datastructures. This process requires them to insert various square pegs (qualia, semantics, intentionality, etc) into the round hole of computationalism . The lack of progress with The Hard Problem  is one of the best illustrations of the failure of their project.

Non-Procedural Processes

The physics-based sciences construct their models, predictions and explanations by abstracting and reducing the numerous natural instances of processes operating on structures, into a few generic procedures operating on data.

Hence physical explanations will be impossible to construct, will fail, or will be innapplicable as 'category errors' for any phenomena where

(i) Processes cannot be reduced to procedures
(ii) Structures cannot be reduced to data

I suspect that one of the intractable features of The Hard Problem is that some of the processes of consciousness are not even in principle reducible to procedures (they are 'non-algorithmic'). Consequently, attempts at physical explanations may be a category error. The non-physical mind will forever remain a riddle, wrapped in a mystery, inside an enigma. See this New Scientist video (preceded by a short sponsor's ad).

For a discussion of why the mind is a non-physical, fundamental aspect of the universe which is not derived from anything else, see Confronting Materialism and the Delusion of the Mechanistic Mind.

- Sean Robsville

Related Posts

Mind and Mechanism – Buddhism and the Turing Machine

Evolution, Emptiness and Delusions of the Darwinian Mind

The non-physical mind

How do we bridge the gap between mind and brain?

How do we reconcile non-physical mind with the theory of evolution?

Buddhism and Quantum physics: does quantum weirdness produce the mind, or vice versa?

Mysterians, Mysterianism and the Mystery of the Mind


Saturday, 15 December 2012

Evolution and Islam Debate at Imperial College London

Can Buddhist Philosophy provide a Middle Way between Antiscience and Scientism?

Geology Lecture at Imperial College

From The Independent, by Jerome Taylor

"Organisers behind a British conference on Islam and evolution say they nearly had to cancel the event after receiving a torrent of opposition from Muslim students at one of the country’s top scientific universities, The Independent has learned.

The Deen Institute, a Muslim debating forum which promotes critical thinking, had hoped to hold a conference entitled “Have Muslims misunderstood evolution?” early next year. Among the speakers invited to attend included Muslim scientists, imams who have promoted the compatibility of Islam and evolution as well as those who preach a form of Islamic creationism.

The initial plan was to hold the event next month at Imperial College London, one of the country’s foremost universities for scientific exploration and debate, in cooperation with the local Islamic student society. But the Deen Institute said it was forced to pull out when it became clear that opposition to the event from supporters of creationism began mounting. It is now being held without input from any Muslim student society at Logan Hall, a conference centre owned by the University of London.

“We eventually had to give up of getting any support from student societies because it was seen as simply too controversial,” Adam Deen, co-founder of the institute, told The Independent. Deen, who describes himself as a “conservative Muslim” who encourages critical thinking, said he was surprised to receive such opposition at a place of scientific study, particularly as he had made sure to invite all sides of the debate including those who preach creationism...

...Mr Deen’s public Facebook account illustrates many of the concerns people raised. In one comment Mohammad Ali Harrath, the founder of the highly influential Islam Channel, wrote: “This debate is a big mistake. It is shifting debate to make it a Muslim issue rather than an issue between atheists and creationists...”

...Another commenter, Zeshan Sasjid, added: “Evolution is not Islamic. Prophet Adam did not have parents. A Muslim can’t believe that Prophet Adam...

...Muslims believe the Qur’an is the indisputable word of God and therefore any scientific discovery which risks proving something within their holy book as incorrect is highly controversial, particularly among the more literalist schools of thought. For example, most Muslim scholars have long accepted scientifically proven cosmology but even up until his death in 1999, Sheikh Ibn Baaz, the Grand Mufti of Saudi Arabia, continued to insist that the Sun revolved around the Earth based on his interpretation of Islamic texts...

...Much of this newfound enthusiasm for attacking evolution has been pushed by Harun Yahya, a prominent Turkish theologian whose writings have been seized upon by literalists and those who exhibit a theological suspicion of science. Dr Oktar Babuna, a representative from the Harun Yahya movement, is scheduled to speak at the conference alongside Shaikh Yasir Qadhi, an influential imam who accepts evolution at a micro level but refuses to countenance the idea that man evolved from anything other than Adam himself...   
Read it all here.

(As an aside, observers of the interfaith dialog scene may remember the Harun Yahya organization as having some definite opinions on Buddhism)

Pseudoscience, Antiscience, Irrationalism and Anti-rationalism

In a previous article I noted how Christianity is deteriorating rapidly, with a headlong retreat into obscurantism, anti-science and general dumbing-down.  

However, it would be erroneous to conclude that the same thing is happening to Islam, because orthodox Islam has never attempted to emerge from anti-science and obscurantism. So for the Koran-believing jihadist, fundamentalist creationism is business as usual .    In fact, Islam goes further than Christianity in not only rejecting science when it conflicts with scripture, but rejecting rationalism itself!

Philosophical Debate at Imperial College
Al-Ghazzali, the prominent Sufi jihadist, anathematized rational belief in causality by preaching that what is perceived as cause and effect between objects is mere appearance, not reality. Instead, only Allah truly acts with real effect; all seemingly natural observances of causation are merely manifestations of Allah's habits, for Allah simultaneously creates both the cause and the effect according to his arbitrary will.    . This, of course, undermines the rational basis of all sciences, and for some religious people this is their only way of coping with modernity.  All science is wrong and evil. 

However not all Muslims reject evolution, though they do tend to have a rather unusual understanding of the theory.


Although we laugh at the way the creationists try to defend their religious beliefs, they may have genuine concerns, though expressed in a very incoherent way.    What may be motivating them subconsciously is the need to reject materialism  - the belief that all phenomena in the universe, in particular the human mind, are explainable in terms of matter. In other words, such concepts and experiences as beauty, love, spirituality, pleasure and pain are reducible to nothing but physical and chemical interactions.

Materialism leads to a rejection of spirituality, both in terms of declining religious belief, and also in the arts, where the cult of ugliness, with its obsessions with the sordid and brutalistic, works to reduce humans to nothing more than biological automata .  Of course all religions reject materialism as an article of faith, but none apart from Buddhism attempts to offer any rational philosophical refutation of the materialist worldview.

The religious motivation to reject science as a whole may derive from a need to reject materialism, coupled with a confusion of science with scientism. 


Scientism is a misuse of scientific methodology  beyond the limits of its applicability, including attempts to reduce all knowledge to only that which can be understood by mechanistic models. It is an overreaching view of science as if it were capable of describing all reality and knowledge, or as if it were the only true way to acquire knowledge about reality and the nature of things.

While Buddhism is quite happy with science in general, and especially with evolution, it does not agree with scientism, and disputes claims that the mind can be explained or understood in physical terms, because its ultimate nature is non-physical: 'when the body dies the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later, perhaps immediately.'  - Alan Turing (Code Breaker, Mathematician and Buddhist Philosopher)

For a discussion of why the mind is a non-physical, fundamental aspect of the universe which is not derived from anything else, see Confronting Materialism and the Delusion of the Mechanical Mind.


Buddhist Philosophy - the Middle Way between Scientism and Antiscience

All physicalist/materialist explanations are algorithmic ( Church-Turing-Deutsch Principle).

However. the 'Hard Problem' of the mind seems incapable of any algorithmic understanding, as no progress has been made since the problem was first formulated by the eminent Victorian physicist John Tyndall 140 years ago.

It is therefore a reasonable working hypothesis that the mind is non-algorithmic, and is thus a good candidate for being non-physical.

A phenomenon that is non-algorithmic is not reducible to the 20 or so fundamental algorithmic building blocks that comprise the instruction set of a general purpose computer, these are SET, MOVE, READ, WRITE, ADD, SUBTRACT, MULTIPLY, DIVIDE, AND, OR, XOR, NOT, SHIFT, ROTATE, COMPARE, JUMP, JUMP-CONDITIONALLY, RETURN.  

In particular, the causal JUMP-CONDITIONALLY (usually implemented as IF...THEN...ELSE...) is not applicable to any non-algorithmic phenomenon, for if we could describe in a stepwise manner how the phenomenon functioned, then the phenomenon would be algorithmic!

This puts non-algorithmic systems, such as the mind, beyond the limits of science and scientism without violating any scientific principles, or abandoning rationalism, or otherwise degenerating into antiscience.

Thus Buddhist philosophy can protect spirituality from destruction by the bleak and barren doctrines of materialism and scientism, without the need to believe six impossible things before breakfast, or the truth of Genesis and the Koran as the literal 'word of God'.

However, it seems unlikely that anything can protect the once-prestigious Imperial College from being dumbed down by Islamic intimidation, stealth jihad and creeping Sharia.  Western academia cannot withstand attack by the traditional Islamic debating tactics of ignorance, arrogance and aggression.


Related articles

Mysterians, Mysterianism and the Mystery of the Mind

Algorithmic compression and the three modes of existence

Non-algorithmic phenomena

Buddhism and Mathematics

Buddhism and Science 

Evolution, Emptiness and Delusions of the Darwinian Mind

Bridging the Explanatory Gap of the Hard Problem 

The Church-Turing-Deutsch Principle and Buddhist Philosophy

All Watched over by Machines of Loving Grace

Is Richard Dawkins a Buddhist? 

THE CLOSING OF THE MUSLIM MIND:How Intellectual Suicide Created the Modern Islamist Crisis

- Sean Robsville



Sunday, 21 October 2012

Mysterians, Mysterianism and the Mystery of the Mind

Progress on The Hard Problem will come not by trying to understand consciousness in physical terms, which is impossible, but by explaining WHY it is impossible to understand consciousness in physical terms... 

Mysterianism is the philosophical position that the mind cannot be explained in terms of physical structures and processes.

It comes in two varieties:

(i) Physical Mysterianism  (also known as epistemological Mysterianism)
(ii) Non-physical Mysterianism
(also known as ontological Mysterianism)

Physical Mysterianism states that the mind is indeed a purely physical process, but we humans lack the ability to understand how it works.

Non-Physical Mysterianism claims that attempting to explain the mind in terms of physical processes is a category error, like attempting to explain the operation of a steam engine in terms of the rules of chess.

Physical Mysterianism

Physical Mysterialism is the philosophical position that although mind is purely physical in origin, humans do not have the intellectual ability to explain consciousness in physical terms.  Any such explanation, although theoretically possible, is in practical terms 'cognitively closed' to us.

Cognitive closure refers to the possibility that certain problems cannot be understood or explained by the human mind. 

In the philosophy of science, physicalist mysterians have adopted the position that some problems are forever outstanding, and not because their solutions do not exist, but rather because the solutions cannot be properly conceived. 

This philosophical position is also sometimes called transcendental naturalism or anti-constructive naturalism. It proposes that the human mind is unavoidably limited, or "closed" in some areas of thinking, and so these areas are forever mysteries.

Philosophy Student Tom of Oxford gives an excellent explanation of Colin McGinn's views on the limits of explanation:

"McGinn has formulated ‘Transcendental Naturalism’: the view that due to our biological and evolutionary background, we are inherently limited to some extent in our cognitive abilities, and thus there will be problems (both scientific and philosophical) that we will never be able to solve or explain in our current status as human beings. To many, this view will at first sight appear extremely pessimistic, but I think it holds a lot of plausibility.

McGinn describes conscious beings as each having a ‘cognitive space.’ This is analogous to our perceptual space, or our physical space: areas within which we can ‘move’, so to speak. Our perceptual space is our visual and auditory field, outside which we cannot see or hear anything. Our physical space is the space within which we can move, and outside of which we cannot. So too with our ‘cognitive space’ - the intellectual area within which we can think, reason, and form concepts; and outside which, we cannot reason.

We have cognitive limitations just as we have perceptual and spatial limitations

If we accept that we are cognitively limited in this sense (and this seems likely, since as McGinn states, ‘we are not Gods, cognitively speaking’), then we should expect that some of the problems of philosophy we will be unable to solve. McGinn most famously treats the problem of consciousness as such a problem, not unsolvable in principle, but unsolvable to us, due to its solution falling outside our cognitive space. After 2000 years of thought and experiment, the basic nature of consciousness continues to remain mysterious: it is a Hard problem with a capital H, and raises a significant explanatory gap. The natural explanation for this mystery, McGinn argues, is not that consciousness itself is inherently mysterious, or is made up of new ‘mental, non-physical stuff’, as Descartes thought. Consciousness is probably as grounded in the physical world as tables or chairs. However, its nature lies outside our cognitive space: our biologically limited concept-forming abilities do not extend to grasping it. We can no more understand consciousness than a slug can understand mathematics.

McGinn also applies his transcendental naturalist view to other problems, such as the problem of Free Will (a response also shared with Noam Chomsky). On reflection, these conclusions may be extremely disappointing: after all, if we agree with McGinn that these problems are in principle unsolvable to us, then we must admit that they could only in principle be solved by a higher intellectual race, 1000s of years of evolution in the future. This is not a nice conclusion to draw, certainly if one is a philosopher.

However, as is often pointed out, the unpleasantness of a view is not a reason not to hold it, especially if one has good philosophical reasons to hold it. And I think we do: why assume that we are intellectually so superior as to solve profound philosophical problems such as the problem of consciousness? Our powers must stop somewhere; and there is good reason to think that consciousness does indeed lie outside our cognitive space. It’s not all so bleak though; McGinn’s view does allow the physicalist/materialist a good response to the arguments for dualism drawn from the explanatory gap between the mental and the physical. The explanatory gap exists not because there is a gap in the world, between physical and mental stuff; it exists because there is a gap in our cognitive abilities to grasp the physical world, and the conscious states that arise from it.

McGinn's more substantial defence of his position as applied to consciousness can be found here, in his classic paper."

Non-Physical Mysterianism

In contrast to physical mysterianism, non-physical or 'ontological' mysterianism (typified by Buddhism) claims that the mind cannot even in principle be explained or understood in physical terms, because its ultimate nature is non-physical.

Here is the traditional Buddhist view:

'when the body dies the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later, perhaps immediately.'  - Alan Turing 

Or, as Geshe Kelsang Gyatso explains in more detail:

"The brain is a physical object that can be seen with the eyes and that can be photographed or operated on in surgery. The mind, on the other hand, is not a physical object. It cannot be seen with the eyes, nor can it be photographed or repaired by surgery. The brain therefore is not the mind but simply part of the body. There is nothing within the body that can be identified as being our mind because our body and mind are different entities. For example, sometimes when our body is relaxed and immobile our mind can be very busy, darting from one object to another. This indicates that our body and mind are not the same entity.

In Buddhist scriptures our body is compared to a guest house and our mind to a guest dwelling within it. When we die our [deepest level of] mind leaves our body and goes to the next life, just like a guest leaving a guest house and going somewhere else. If the mind is not the brain, nor any other part of the body, what is it? It is a formless continuum that functions to perceive and understand objects. Because the mind is formless, or non-physical, by nature, it is not obstructed by physical objects." 
Buddha & the Brain

Does non-physicality imply mysterianism?
According to the Church-Turing-Deutsch principle,  to state that something is non-physical necessarily implies that it is non-algorithmic.  The possibility that the mind may (in part) be non-algorithmic was first explicitly stated by Roger Penrose in The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics .   Penrose presented the argument that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital computer. More controversially, Penrose hypothesized that quantum mechanics  plays an essential role in the understanding of human consciousness.

How does a phenomenon being non-algorithmic limit our understanding of it?
What if the mind is indeed non-algorithmic?  All physicalist explanations are by their very nature algorithmic, so attempting a physical/computational/procedural/quantitative/Boolean explanation for non-algorithmic mind would be a category error.

Non-algorithmic phenomena (if they exist) present a profound challenge to scientism, because some/most/all of  the basic algorithmic operations and data structures may not be relevant or applicable to any 'reductionist' explanation.  

To see just how profound this challenge to physicalist/computationalist understanding might be, consider that...

AND may not be applicable

NOT may not be applicable

OR  may not be applicable

IF... THEN... (and its reverse aspect 'because' ) may not be applicable

Numbers and logical states may not be applicable

TRUE and FALSE may not be applicable

The great difficulty in talking about nonalgorithmic phenomena is that although we can say in general terms what they do, it is impossible by their very nature to describe how they do it. (If we could describe in a stepwise manner what was going on, then the phenomenon would be algorithmic!).

Non-algorithmic phenomena

So what phenomena would be applicable in the non-algorithmic realms? Qualia? Semantics? Introspection? Mysticism?  

If any progress in solving the The Hard Problem of the Mind is to be made, it will have to come from the non-algorithmic side of the mind, rather than from the physics-based sciences, such as neurobiology, molecular biology, biophysics etc.  The biophysical sciences are completely stalled in furthering our understanding of the mind, and have been for over a century.

Science cannot explain how events in the brain produce mental experiences, nor how mental intentions produce effects in the brain, such as those which are transmitted via the nervous system to give rise to the voluntary movement of muscles.  

Over 140 years ago, the eminent Victorian physicist John Tyndall wrote:

"... the passage from the physics of the brain to the corresponding facts of consciousness is unthinkable. Granted that a definite thought, and a definite molecular action in the brain occur simultaneously; we do not possess the intellectual organ, nor apparently any rudiment of the organ, which would enable us to pass, by a process of reasoning, from the one to the other. They appear together, but we do not know why. 

Were our minds and senses so expanded, strengthened, and illuminated, as to enable us to see and feel the very molecules of the brain; were we capable of following all their motions, all their groupings, all their electric discharges, if such there be; and were we intimately acquainted with the corresponding states of thought and feeling, we should be as far as ever from the solution of the problem, "How are these physical processes connected with the facts of consciousness?" The chasm between the two classes of phenomena would still remain intellectually impassable. 

Let the consciousness of love, for example, be associated with a right-handed spiral motion of the molecules of the brain, and the consciousness of hate with a left-handed spiral motion. We should then know, when we love, that the motion is in one direction, and, when we hate, that the motion is in the other; but the "Why?" would remain as unanswerable as before." 

It isn't that there are no causal relationships between mind and brain, it's just that we can't model (and hence understand) the causality.

The Hard Problem is hard precisely because it tries to apply an algorithmic model of causality to a non-algorithmic process.

All algorithmic models of causality take the form of IF x THEN y ELSE z, where x, y and z are logical and arithmetic functions, assignments and values.

Thus all algorithmic models of causality can be reduced to the state transition table and one dimensional array comprising a Turing machine.

The Kadampa Buddhist view of Mind
In contrast to the mechanistic materialists with their computer model of the mind, the Kadampa Buddhist view is that the mind is (i) Clear and Formless (ii) Cognizing and (iii) Devoid of 'inherent existence' (any defining essence).

Consequently, because algorithms have form (Turing machine or equivalent) they are not attributes of the mind, though the mind may cognize algorithms.

Cognizing implies intentionality or 'aboutness'. Algorithms themselves are not 'about' anything. The apparent 'aboutness' of an algorithm is projected onto it by the mind of its user.

The lack of inherent existence of the mind means that it has no defining essence, nothing to 'keep it as it is', so it can unobstructedly apprehend all objects including those of its own creation. The mind can be 'about' anything whatsoever. The lack of defining essence allows the mind to change, expand, have freewill, and be creative.

The materialists' mechanistic/algorithmic model of the mind breaks down beyond Tyndall's molecular and neuronal states, because this is the territory in which the formless mind operates, projecting meaning/semantics/intentionality onto what it cognizes. 

There is no algorithmic progression for information beyond neural states. All further mental activity comes 'from the other side'. The mind is drawn or driven, either voluntarily or involuntarily (by attachment or aversion), to meet and apprehend its objects.

'The mind is not the brain'
 - Geshe Kelsang Gyatso
For a discussion of why the mind is a non-physical, fundamental aspect of the universe which is not derived from anything else, see Confronting Materialism and the Delusion of the Mechanistic Mind. 

- Sean Robsville

Related articles

Algorithmic compression and the three modes of existence

Non-algorithmic phenomena

Buddhism and Mathematics

Buddhism and Science 

Evolution, Emptiness and Delusions of the Darwinian Mind

Bridging the Explanatory Gap of the Hard Problem 

The Church-Turing-Deutsch Principle and Buddhist Philosophy

All Watched over by Machines of Loving Grace

Mind and Mechanism – Buddhism and the Turing Machine



Saturday, 15 September 2012

Buddhism and Mathematics

The Empty Set

Six aspects of mathematics which are relevant to  Buddhist Philosophy

(i) The foundations of mathematics have parallels (and differences) with the Buddhist concept of emptiness (sunyata)

(ii) The bootstrapping  of the integers out of the empty set provides a simple illustration of how causes and components can be expressed as algorithms and datastructures.

(iii) The further development of mathematics from its empty foundations creates computational algorithms and datastructures that can simulate all physical phenomena.  

(iv) These simulations epitomize the 'unreasonable effectiveness' of mathematics in physics and engineering, which suggests that there may be aspects of the mind  which are not explainable as the products of evolution.

(v)  The concept of 'algorithmic compression', which is an aspect of the unreasonable effectiveness of mathematics,  leads on to the Church-Turing-Deutsch principle, which gives us a workable philosophical demarcation between physical and non-physical phenomena, including physical and non-physical aspects of the mind.

(vi) The deep interconnection between the mind contemplating emptiness, and the workings of the physical world, suggests that mathematics may provide a bridge between ultimate and conventional truths.

John von Neumann

1) What are the origins of numbers?

In what way do numbers exist? Have they always been present as 'Platonic' abstractions, or do they require a mind to bring them into existence? Can numbers exist in the absence of matter or things to count?

The mathematician  John von Neumann, who was one of the founders of computer science, demonstrated that the whole numbers could be bootstrapped out of the Empty Set by mental operations without reference to any physical entities.

A set is a collection of things.  The empty set is a collection of nothing at all.  The empty set can be thought of as nothing with the potential to become something (that is to be become a set with at least one member).

The procedure is as follows:
The mind observes the empty set. The mind's act of observation causes the appearance another set - the set of empty sets. The set of empty sets is not empty, because it contains one non-thing - the empty set. The mind has thus generated the number 1 by producing the set containing the empty set.

Next the mind perceives the empty set and the set containing the empty set, so generating a new set encapsulating two non-things. The mind has generated the number 2 out of emptiness. And so it goes on, all the way up through the integers, to 42 and beyond.

So, the three modes of existential dependence (causes, components and mental designation) postulated by Kadampa Buddhist philosophy are apparent even at the very deepest level of mathematics.

- Numbers are dependent upon causes - the operations on the sets.

- Numbers are dependent upon components. The number 1 is defined as the set which contains the empty set and so on.

- And in the final analysis the entire number system is dependent upon the play of mind on an empty datastructure, in the complete absence of the need to refer to any material thing, or things, which are being counted.

Hence numbers are non-physical phenomena that make no reference to physical systems for their existence.  But they are not inherently-existent entities from the 'Platonic realms'. Numbers are dependently-related manifestations of the working of the mind.

Note - the Empty Set is not synonymous with Emptiness (Sunyata)  in the Buddhist sense, though there are parallels.   Buddhist emptiness refers to the ultimate unfindability of all objects existing 'from their own side' .  The subjective experience of Emptiness results from the exhaustion of all procedures to find an object (eg the classic meditations which try to find the real 'self').  

Buddhist Emptiness is a philosophical conclusion, not a 'thing', state or attribute.    The Emptiness of phenomena should not be confused with the delusion of a self-existent void.
Emptiness is the logical conclusion of the unfindability of a 'thing in itself' once every cause and component that is 'not the thing' has been removed from its basis of imputation.   Buddhist Emptiness always refers to an object whose 'inherent existence' has been refuted, for example the emptiness of a chariot.   Emptiness too is empty, and Nagarjuna warned against reifying it.  

The empty set, on the other hand, is what is left when everything has been removed, regardless of any original starting object.  This emptiness is then 'encapsulated', and in a sense it is reified, to make it logically and mathematically manipulable.

What the empty set represents is an 'encapsulation' of emptiness which renders it logically and mathematically manipulable for certain defined purposes. According to Wiki  "While the empty set is a standard and widely accepted mathematical concept, it remains an ontological curiosity, whose meaning and usefulness are debated by philosophers and logicians. The empty set is not the same thing as nothing; rather, it is a set with nothing inside it and a set is always something. This issue can be overcome by viewing a set as a bag—an empty bag undoubtedly still exists."  

Just as the defining characteristic of a chariot is its chariotness, which can't be found within the chariot itself, so the defining feature of the empty set is its emptiness, which similarly can't be found within the empty set; for if the empty set contained anything whatsoever it would no longer be empty.  So the emptiness of the empty set must itself be empty.

As with the failure to find the definitive chariot,  the failures of ones attempts to find a 'thing' is not an attribute of that thing. Nothing is to be found in the empty set beyond the conclusion that there is nothing to be found.

The procedure for mentally generating numbers by bootstrapping out of the empty set can be set out symbolically:  

0 = {} (empty set)
1 = {0} = { {} }
2 = {0,1} = { {}, { {} } }
3 = {0,1,2} = {{}, { {} }, { {}, { {} } }}
4 = {0,1,2,3} = { {}, { {} }, { {}, { {} } }, {{}, { {} }, { {}, { {} } }} }

See also  and  

2) The simplest algorithm acting on the simplest datastructure.

The bootstrapping of the integers is one of the simplest illustrations of an algorithm acting on a datastructure.   There can't be any simpler datastructure than an empty set, and the iterative procedure of nesting the sets is one of the simplest algorithms one can envisage.   However neither the datastructures nor the algorithms contain any 'meaning'.
Their meaning, as it appears in terms of named integers (one, two, three etc used for counting objects)  has to be designated by the mind of the observer.    There is no concept of number, indeed no concept of singularity or plurality existing 'from its own side'.   Singularity and plurality have to be designated by the mind of the observer over some chosen object(s) or subdivisions of objects, eg leaves, branches, trees, forests.  

Counting is a mental projection, things do not count themselves,  see 'The Emptiness of the Eight Extremes' in Modern Buddhism.
God gave us the integers


3) "God gave us the integers"

"God gave us the integers, all else is the work of man" is a famous statement attributed to the mathematician Leopold Kronecker.  I'll let the theologians decide whether it was actually God or John von Neumann who gave us the integers, but what the statement is saying is that once you have the foundation of the integers, you can derive the rest of mathematics using a very small repertoire of operations. 

In fact, the integers (represented as binaries) plus the instruction set of a computer are capable of representing any other kind of numbers and simulating and modelling any physical system (Church-Turing-Deutsch principle)

It's quite remarkable just how few operations are required to equip a general purpose computer with universal physical modelling capabilities - fewer than twenty:  SET, MOVE, READ, WRITE, ADD, SUBTRACT, MULTIPLY, DIVIDE, AND, OR, XOR, NOT,  SHIFT, ROTATE, COMPARE, JUMP, JUMP-CONDITIONALLY, RETURN


 4) The unreasonable effectiveness of mathematics in science and engineering.

The remarkable efficiency of mathematics in predicting the behavior of physical systems has fascinated many scientists.

Einstein is said to have remarked that "The most incomprehensible thing about the universe is that it is comprehensible." This observation was elaborated by Eugene Wigner in his famous paper in Pure Mathematics (Volume 13, Number 1, February 1960) entitled 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences'

The theme was further developed in 'The Unreasonable Effectiveness of Mathematics' by R. W. Hamming in The American Mathematical Monthly (Volume 87, Number 2, 1980), which considered the predictive, as well as descriptive powers, of mathematics in relation to engineering.

Two surprising conclusions appear from these papers:

(i) Although it is a product of the human mind, mathematics is also involved in some strange metaphysical way at the deepest levels of physical existence. To quote Wigner:

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."

(ii) There is no Darwinian explanation for the presence of mathematical abilities within the mind. The ability to understand physics could not have arisen by evolution. Although our bodies may well be the product of random mutation and selection all the way from amoeba to man, our minds have some 'unevolved' dimension. To quote Hamming:

"But it is hard for me to see how simple Darwinian survival of the fittest would select for the ability to do the long chains that mathematics and science seem to require".

"If you pick 4,000 years for the age of science, generally, then you get an upper bound of 200 generations. Considering the effects of evolution we are looking for via selection of small chance variations, it does not seem to me that evolution can explain more than a small part of the unreasonable effectiveness of mathematics."

Or Wigner again:

"Certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess."

So we are left with something of a mystery. According to the materialist worldview, the mind (including mathematicians' minds) is an epiphenomenon of matter which has evolved solely to ensure the survival of the selfish genes which code for it. So why should this 'top-level' phenomenon have such intimate access to the 'bottom level' phenomena such as quantum physics? After all, the two levels are supposedly separated by less well-understood (in some cases) explanatory layers such as evolutionary psychology, neurology, cell biology, genetics, molecular biology, and chemistry.

Buddhists don't dispute that some aspects of the mind have been determined by evolution of the brain,  but there also seem to be highly functional attributes of the mind that have no evolutionary explanation. The unusual effectiveness of mathematics is one of these.


5) Algorithmic compression.

A very powerful aspect of the unusual effectiveness of mathematics in the physical sciences, is what is known ''Algorithmic compression'.

The laws of physics may be regarded as being analogous ('isomorphic') to algorithms, with the physical objects being analogous to the datastructures the algorithms act upon.  All physical systems can thus be simulated by a general purpose computer. This is known as the Church-Turing-Deutch principle

Algorithmic compression is explained in this excerpt from an article by Gregory Chaitin :

'My story begins in 1686 with Gottfried W. Leibniz's philosophical essay Discours de métaphysique (Discourse on Metaphysics), in which he discusses how one can distinguish between facts that can be described by some law and those that are lawless, irregular facts. Leibniz's very simple and profound idea appears in section VI of the Discours, in which he essentially states that a theory has to be simpler than the data it explains, otherwise it does not explain anything. The concept of a law becomes vacuous if arbitrarily high mathematical complexity is permitted, because then one can always construct a law no matter how random and patternless the data really are. Conversely, if the only law that describes some data is an extremely complicated one, then the data are actually lawless.

Today the notions of complexity and simplicity are put in precise quantitative terms by a modern branch of mathematics called algorithmic information theory. Ordinary information theory quantifies information by asking how many bits are needed to encode the information. For example, it takes one bit to encode a single yes/no answer. Algorithmic information, in contrast, is defined by asking what size computer program is necessary to generate the data. The minimum number of bits---what size string of zeros and ones---needed to store the program is called the algorithmic information content of the data. Thus, the infinite sequence of numbers 1, 2, 3, ... has very little algorithmic information; a very short computer program can generate all those numbers. It does not matter how long the program must take to do the computation or how much memory it must use---just the length of the program in bits counts...

...How do such ideas relate to scientific laws and facts? The basic insight is a software view of science: a scientific theory is like a computer program that predicts our observations, the experimental data. Two fundamental principles inform this viewpoint. First, as William of Occam noted, given two theories that explain the data, the simpler theory is to be preferred (Occam's razor). That is, the smallest program that calculates the observations is the best theory. Second is Leibniz's insight, cast in modern terms---if a theory is the same size in bits as the data it explains, then it is worthless, because even the most random of data has a theory of that size. A useful theory is a compression of the data; comprehension is compression. You compress things into computer programs, into concise algorithmic descriptions. The simpler the theory, the better you understand something'

In summary: If a computer program or algorithm is simpler than the system it describes, or the data set that it generates, then the system or data set is said to be 'algorithmically compressible'.  

This concept of algorithmic simplicity/complexity can be extended from the realms of mathematics into physical systems.   The complexity of a physical system is the length of the minimal algorithm than can simulate or describe it.    Thus the orbits of the planets, which seemed so complex to the ancients, were shown by Newton to be algorithmically compressible into a few short equations.

Related to algorithmic compression is the fact mentioned earlier, that the small repertoire of opcodes acting on binary encoded integers is capable of describing and predicting the behavior of all physical systems.

The computer model of the three levels of dependency
So causal dependency can be modelled as algorithms, and compositional/structural dependency can be modelled as datastructures, but where does that leave conceptual dependency?

According to Buddhist philosophy, the function of the mind cannot be reduced to physical or quasi-physical processes.

In Buddhist psychology, the mind is clear, formless, and knows its object.  Its knowing the object constitutes the conceptual dependency, which is fundamental, axiomatic and cannot be explained in terms of other phenomena, including algorithms and datastructures.

So the issue that separates the Materialist from the Buddhist is whether there is anything left to explain about reality once algorithms and datastructures have been factored out.  

The Materialist would answer that algorithms and datastructures offer a complete explanation of the universe, without any remainder. The mind is included in the overall scope of this 'computationalist' explanation.  

In contrast, the Buddhist would claim that the mind is a third fundamental factor irreducible to algorithms and datastructures. Hence the mind itself is not algorithmically compressible, but is responsible for carrying out algorithmic compression. 

Supporting this view one may point out that algorithms, as executed, do not contain within themselves any meaning.  For example, the following two statements reduce to exactly the same algorithm within the memory of a computer

(i) IF RoomLength * RoomWidth > CarpetArea THEN NeedMoreCarpet = TRUE

(ii) IF Audience * TicketPrice > HireOfVenue THEN AvoidedBankruptcy = TRUE

Neither do datastructures as stored in machine format contain any meaning.

Such considerations have led critics of philosophical computationalism to claim that algorithms can only contain syntax, not semantics. Hence computers can never understand their subject matter. All assignments of meaning to their inputs, internal states and outputs have to be defined from 'outside the system'.

This may explain why the process of writing algorithms does not in itself appear to be algorithmic. The real test of computationalism would be to produce a general purpose algorithm-writing algorithm. A convincing example would be an algorithm that could simulate the mind of a programmer sufficiently to be able to write algorithms to perform such disparate activities as controlling an automatic train, regulating a distillation column, and optimising traffic flows through interlinked sets of lights.

According to the computationalist view this 'Mother of all Algorithms' must exist as an algorithm in the programmer's brain, though why and how such a thing evolved is rather difficult to imagine. It would certainly have conferred no survival advantage to our ancestors until the present generation (even so, do programmers outreproduce normal people?).

The Mother of all Algorithms
The proof of computationalism would be to program the Mother of all Algorithms on a computer. At present no one has the slightest clue of how to even start to go about producing such a thing.

According to Buddhist philosophy this is hardly surprising, as the Mother of all Algorithms is itself NOT an algorithm and never could be programmed. The mother of all algorithms is the formless mind projecting meaning onto its objects (i.e. conceptually  designating meaning on to the sequential and structural components of the algorithm as it is being written).

The non-algorithmic dimension of mind, of understanding of meaning, is needed to turn the programmer's (semantically expressed)  requirements and specifications into the purely syntactic structural and causal relationships of the algorithmic flowchart or code.

[For people with a scientific education, the Turing Machine provides one of the most easily understood refutations of materialism, physicalism and the mechanistic model of the mind.  The argument is as follows:

- The behavior of all machines, computers and physical systems is reducible without remainder to the operations of a Turing machine.

- The behavior of the mind shows at least two functions - 'aboutness' (intentionality)  and qualitative experience (qualia) - that cannot in principle be reduced to the operations of a Turing machine.

- Therefore, there are some aspects of the mind that are non-mechanistic and non-physical.

See  Mind and Mechanism – Buddhism and the Turing Machine for a full explanation.]


6) Ultimate and conventional mathematics

The question remains of how mathematics, which is derived from the mind contemplating emptiness, gives such an excellent predictive description of conventional physical reality.  It may be that mathematics, in some strange way, acts as a bridge between ultimate and conventional truths.  Or maybe the bridge actually is just part of a loop, and what goes around comes around...

42) Conclusion: The ultimate, fundamental nature of life the universe and everything

So let's combine reductionism with the fundamentals of mathematics:
- The structures and operations of mathematics are reducible to the structures and operations of the mind.

- The structures and  operations of the mind are reducible to the structures and operations of biological macromolecules.

- The structures and operations of biological macromolecules are reducible to the structures and operations of organic chemicals.

- The structures and operations of organic chemicals are reducible to the structures and operations of atoms.

- The structures and operations of atoms are reducible to the structures and operations of mathematics.

- The structures and operations of mathematics are reducible to the structures and operations of the mind.

-  which is where we came in!

This allows us to draw the following equally valid conclusions:

(i)  Matter is fundamental
(ii)  Mind is fundamental
(iii)  Both mind and matter are fundamental
(iv) Neither mind nor matter are fundamental
(v) Nothing is fundamental
(vi)  Forty two

- Sean Robsville

Related posts

Confronting Materialism and the Delusion of the Mechanistic Mind

Mind and Mechanism – Buddhism and the Turing Machine

The Four Philosophical Foundations of Buddhism

Buddhism and Science

Evolution, Emptiness and Delusions of the Darwinian Mind  

The Church-Turing-Deutsch Principle and Buddhist Philosophy

Nonalgorithmic phenomena

Ultimate and Conventional Truths

Algorithms, Data Structures and Mental Attribution

Sunyata - the emptiness of all things

Bridging the Explanatory Gap of the Hard Problem 

Minds, Machines and Meaning

All Watched over by Machines of Loving Grace

Buddhism, Sentience, Dukkha, Evolution and the Mind