Sunday, December 30, 2018

Non-Dualism in East and West: An Introduction

“You are a woman; you are a man; you are a boy or also a girl.
 As an old man, you totter along with a walking-stick.
As you are born, you turn your face in every direction.
You are the dark blue bird, the green one with red eyes,
the raincloud, the seasons, and the oceans.
You live as one without a beginning because of your pervasiveness,
you, from whom all beings have been born.”
(Svetasvatara Upanishad 4.3-4)


Non-Dualism is a type of spiritual philosophy based on a type of spiritual experience, that of non-duality, the complete absence of separation (duality) between you and the world you observe. In non-dual awareness, the subject experiences reality as one whole of which the subject itself forms an integral part. Thus, subject-object duality is overcome. As a type of philosophy, Non-Dualism tries to make sense of this non-dual experience, to interpret it, to explain it, to gauge its value, to place it in a broader world view. However, Non-Dualism is not just one philosophy but a family of different philosophies, mostly Eastern, though the West has produced some significant forms of Non-Dualism as well, but here it usually goes by the name “Monism” (more about this terminological difference below). In Eastern philosophy, non-duality is a central feature of Vedanta, Buddhism, Daoism, Sufism, and Shaivite Tantrism. In Western philosophy, elements of non-dual thinking can be found in Eleatic Monism, Neoplatonism, Spinozism, Absolute Idealism, and Schopenhauer´s metaphysics of the Will to Life.
 
Whereas the Western approaches to non-duality are mostly theoretical, more focused on the epistemological, ontological, political and theological aspects of non-duality, the Eastern approaches – though certainly not devoid of theory – focus more on the experience of non-duality as an existentially transformative experience, to be more precise, as the key to “Enlightenment” and the ultimate “Liberation of Suffering”. Here the non-dual experience brings to an end the suffering inherent in being a (seemingly) separate individual
, standing over against an independent world, in which the individual must struggle to maintain him-/herself. As the illusion of the separate ego falls away, its petty worries and ambitions, its bickering likes and dislikes, its fears and unfulfilled desires – all these obstacles to peace of mind fall away as well. And what remains is just peace of mind, a tranquil bliss, and a deep feeling of loving unity with everything and everyone. In Eastern philosophy, this liberating aspect of non-dual awareness is traditionally theorized as bringing to an end the suffering of samsara, the karmic cycle of reincarnation.

In Eastern philosophy, the enlightening aspect of non-duality is often illustrated in terms of the comparison of the human mind with a lake that mirrors the sky above it. Normally, the water on the lake is rippled, as the ever-variable winds of our thoughts and emotions create smaller or greater waves, causing a distorted reflection of the sky in the water. But with the experience of non-duality, the waves on the lake calm down, as the storm of thoughts and emotions settles, and the water becomes as smooth as a mirror, finally reflecting the blue sky above it, with the radiant Sun at its centre. Here, of course, the ‘Sun’ is a metaphor for the creative essence of reality-as-a-whole, the source of all energy and life, which you now realize to be your true identity.

Origin of Non-Dualism in the Upanishads
The oldest texts that explicitly thematize non-duality, and its connection with Enlightenment and Liberation, are the Upanishads, the fountainhead of Indian philosophy. The earliest Upanishads, the Brihadaranyaka and the Chandogya, date roughly from 800 BCE, although they are based on much older oral traditions. The philosophy expounded in the Upanishads is called “Vedanta” because these texts form the closing books of the sacred Hindu scriptures, the Veda. Thus, the Upanishads constitute the “end / culmination of the Veda” (“Veda-anta”). But this can also be read as the “highest knowledge” since in Sanskrit “veda” means “knowledge”. Vedanta in general, however, is not to be confused with Advaita Vedanta, which is a special case of Vedantic philosophy. Advaita Vedanta emerged much later as a recognizable school in Indian philosophy, around 800 CE, and develops just one of the many strands that can be found the Upanishads. Thus, Advaita Vedanta is certainly not representative of the entire range of Vedantic philosophy – a point that is often sadly ignored, not least by proponents of Advaita itself. I will say more about the difference between Advaita Vedanta and Vedanta in general below when I discuss the difference between Cosmic and Acosmic Non-Dualism.

The Upanishads develop concepts that proved to be fundamental to subsequent Indian philosophy and religion – concepts such as reincarnation, the law of karma that regulates rebirth, and the techniques for achieving liberation from the samsaric cycle of rebirth, such as Yoga, meditation, ascetism and world renunciation. In this way, the Upanishads prepared the way for new spiritual movements, notably Buddhism and Jainism, which emerged not long after the composition of the oldest Upanishads. With the concepts of reincarnation and karma, a profound pessimism creeped into Indian culture: earthly life was seen as a prison of suffering from which there is no escape, since due to the karmic effects of our actions we are reborn again and again into this ‘vale of tears’. The Upanishads, however, not only introduced this pessimism into Indian culture but at the same time presented a solution, a “Path to Liberation” by way of non-dual identification with the divine ground of reality-as-a-whole, the “Brahman” that underlies everything and everyone. By the non-dual awareness of Brahman as one’s innermost Self (“Atman”) – i.e. by realizing that “Atman is Brahman” – one breaks the power of karma and the cycle of reincarnation, becoming one with the Highest Bliss which is Brahman. This non-dual awareness of Brahman-Atman is the “highest knowledge” which, as we have noted, the term “Vedanta” indicates. More about the development of Vedantic thought in the Upanishads can be found here.

“This finest essence here, son, that you can’t even see, look how
on account of that finest essence this huge banyan tree stands here.
Believe, my son: the finest essence here – that constitutes the Self
of this whole world; that is the truth; that is the Self.
And you are that, Svetaketu.” (Chan.Up. 6.12)
The Dialogue between Uddalaka and Svetaketu
A clear illustration of non-dual awareness in the Upanishads can be found in the famous dialogue between the sage Uddalaka Aruni and his son Svetaketu in the Chandogya Upanishad. Having told Svetaketu to cut open one of the tiny seeds of the fruit of the banyan tree, Uddalaka asks: “What do you see there?” “Nothing, sir,” Svetaketu replies. Then Uddalaka tells him: “This finest essence here, son, that you can’t even see – look how on account of that finest essence this huge banyan tree stands here. Believe, my son: the finest essence here – that constitutes the Self of this whole world; that is the truth; that is the Self. And you are that, Svetaketu.” (Chan.Up. 6.12) Brahman, the “finest essence” of the whole world, cannot itself be seen or thought because it is the underlying unity of all the different beings in reality; as such, Brahman differs from nothing and thus cannot be conceptually determined in contrast to anything else. As Uddalaka explains to his son: just as a chunk of salt dissolved in water can no longer be seen but nevertheless pervades all of the water, so Brahman is the indescribable essence pervading everything, thereby giving everything reality (Chan.Up 6.13). With this ineffable essence of reality Svetaketu is declared to be identical by Uddalaka: “You are that” (“Tat tvam asi”) – which is one of the four “Great Sayings” (Mahavakyas) traditionally seen as expressing the core message of the Upanishads, the other three being “Atman is Brahman”, “Conscious is Brahman”, and “I am Brahman”. Each saying is a formulaic expression of the same non-dual insight: that the single and all-encompassing Brahman is in essence identical with the human Self – or, in other words, that the empirical plurality of individual human selves is really an illusion, because in reality there is only one Self, the Atman which is Brahman, the Absolute Subject underlying the universe.

Western Monism and Spinoza’s Supreme Joy
Earlier we noted that Non-Dualism is more usually known as “Monism” in the context of Western philosophy. This has to do with the difference between Western and Eastern forms of Non-Dualism: that the former are more theoretical, whereas the latter are primarily aimed at the practical-existential aim of Liberation. Monism means first of all the theoretical claim that all of reality is fundamentally a single ‘thing’, one seamless all-including Whole. Non-Dualism indicates this overarching unity of reality as well but focuses attention primarily on what this means for the subject: the falling away of its separation from the world in the liberating experience of non-duality. This is not to say that the liberating aspect of non-duality has gone totally unnoticed in Western philosophy, but the role it plays there is considerably less pronounced than in Eastern philosophy, where it is indeed the central interest.

Baruch Spinoza, 1632-77
Spinoza is probably the Western philosopher who comes closest to this Eastern appreciation of the liberating power of non-duality. Baruch Spinoza, born a Sephardic Jew in Amsterdam during the Dutch “Golden Century”, was excommunicated from the Jewish community at the age of 23 for proclaiming heretical opinions. Exactly what these opinions were is unknown, but – given his later monist philosophy of the single, all-including “Substance” which can be called “God or Nature” – these opinions probably involved a denial of the dualistic conception of God as standing apart from and above His creation (a conception common to the three Abrahamic religions: Judaism, Christianity, Islam). No doubt, the excommunication made life extremely difficult for Spinoza, who was still a young man at the time, cut off from his family, having to fend for himself, since fellow Jews were explicitly forbidden to help or even to contact him. So when Spinoza – in his first piece of philosophical writing, the Treatise on the Emendation of the Intellect – speaks of the vanity of mundane existence and his longing for a supreme joy independent of the vicissitudes of daily life, we know he is speaking from the heart: “After experience had taught me the hollowness and futility of everything that is ordinarily encountered in daily life […], I resolved at length to enquire whether there existed a true good […] whose discovery and acquisition would afford me a continuous and supreme joy to all eternity.” (Treatise on the Emendation of the Intellect, para.1)

The problem, as Spinoza goes on to diagnose, is that people normally desire “perishable things” which “can be reduced to these three headings: riches, honour, and sensual pleasure” (idem: para.3&9). As these things are “perishable”, they cannot afford lasting happiness; in fact, they worsen our existential situation, since their acquisition more often than not requires compromising behaviour and their consumptions makes us even more dependent on perishable goods. “But love towards a thing eternal and infinite feeds the mind with joy alone, unmixed with any sadness.” (Idem: para.10) Thus, in his mature masterpiece, the Ethics, Spinoza finds lasting happiness only in the “intellectual love of God”, which is the mystical, non-dual vision of the single “Substance” underlying everything and everyone. The non-dual nature of this vision is clearly announced by Spinoza when he says that “[t]he mind’s intellectual love of God is the very love of God by which God loves himself” (Ethics, Part 5, Prop. 36). Since, for Spinoza, God is the Whole that includes everything, it also includes your love for God, and thus God can be said to love Itself through you.

Non-Duality and the Problem of the Ego
As Non-Dualist therapists stress, the conviction of being a separate individual, who must assert him-/herself in the outside world, brings with it a sense of contraction and straining, experienced physically as contracted breathing and a tightening of the body, felt specifically in the solar plexus, the throat, the back of the head, and as a strain around the eyes. This feeling of contraction into a separate being sets in when we’re still very young and builds up as strain and stress throughout our lives. No wonder burn-out is reaching epidemic proportions in our hyper-individualized societies!
In the experience of non-duality, this stress and straining falls away, as you experience yourself as basically one with the world. Hence the therapeutic value of Non-Dualism. In the non-dual experience, the sense of separation between ‘me’ and ‘not-me’ disappears, and the restless drive to be a self-standing, self-asserting individual is given up. The separate ego is felt to dissolve in the cosmic Whole. This sense of letting go is experienced physically and emotionally as a great relaxation, a great sigh of relief, like the final breath of a dying man. With this difference, of course, that you do not die – on the contrary, you are in a sense reborn in a liberated state, born into freedom for the first time in your life.

Freud described the oceanic feeling as
the "
feeling of oneness with the universe".
Or, rather, for the second time. For, in a way, what happens in the experience of non-duality is that you return to the state of oneness you experienced as a baby. That feeling of being absolutely one with your mother when still in the womb, and later, after birth, of being held in the arms, that feeling of total safety and surrender, of undivided unity and love, what Freud called the “oceanic feeling” which he described as a “feeling of oneness with the universe” – that primal feeling of undifferentiated bliss is what we lose when we grow up and are taught to see ourselves as separate beings, each with his/her own free will and moral responsibilities, having to live up to society’s expectations. We lose this bliss, but we never lose the memory of it, and that basically is why we suffer – in the sense of suffering that plays such an important role in Eastern philosophy. We suffer because we want, more than anything else, to return to that original state of blissful unity which we experienced as babies, and because – as separate individuals – we can never have it again. We want, therefore, the impossible – as long as we remain in the dualist mode of being.

From a Non-Dualist perspective, this is the secret of human desire. Seemingly separated from the Whole, we feel radically incomplete, radically insecure, and then we try to fill this inner lack by seeking something outside ourselves, something that will make us whole again. That’s why we never stop buying stuff, running desperately after wealth and success, love and sexual pleasure, physical health and beauty. We think: “If only I could buy that new car…”, or: “If only I could find the right partner…”, or: “If only I could finish my education…”, or:  “If only I could have that breast enlargement…” – in short: “If only I could get my hands on this elusive thing X, THEN I would be happy, THEN I would be complete, THEN I would be fulfilled.” But, as we all know – deep down, even if we don’t admit it – it simply doesn’t work that way. The ‘Inner Hole’ left by the ‘Original Whole’, which we lost when we became (or thought we became) separate beings, can never be filled by anything short of the Whole itself. Trying to fill it by external things – be it material objects, public success or loving partners – is like trying to fill a sieve with water. And that’s what suffering is: trying to retrieve the Whole while remaining separate.

In this way we can make sense of the cycle of samsara without having to buy into the ancient metaphysics of reincarnation, which to modern eyes is bound to appear as unscientific superstition. The cycle of samsara can simply be understood as the cycle of desire: each attempt to satisfy the inner need to be whole again by means of some finite thing, a “perishable good” (Spinoza), is bound to fail and thus to reproduce the same desire again and again. Samsara is the ceaseless reproduction of dualist desire, because nothing finite and temporal can ultimately satisfy us. Only the Whole can do that, and thus it is only in non-dual awareness – when we realize our original oneness with the Whole – that the samsaric cycle of desire finally stops. This ending of dualist desire is Enlightenment, the Liberation from Suffering, or – as Buddhists say – nirvana. This does not mean we become totally desireless, without any need or want. Only a certain type of desire falls away, “Desire” writ large, the desire to “fix” ourselves, to become whole by chasing finite things in the world. That desire falls away, because we realize that we never left the Whole in the first place.

"The self continues in samsara only as long
as it retains attachment due to ignorance
or Maya. If it casts off the veil of Maya
through knowledge, it will realize its identity
with the Brahman and get merged into it."

(Shankara, the founder of Advaita Vedanta)
Cosmic versus Acosmic Non-Dualism
Earlier we noted an important distinction in Non-Dualist thinking between Eastern approaches, which focus above all on the liberating aspect of non-duality, and Western approaches, which focuses more on the theoretical side of non-dualism qua monism (with the significant exception of Spinoza). A second distinction, which runs across both Eastern and Western forms of Non-Dualism, is between ‘cosmic’ and ‘acosmic’ forms of Non-Dualism. In philosophy “acosmism” means the denial of reality to the empirical world of plurality. The universe we observe around us appears to consist of many different individual objects, from atoms and molecules up to trees, cars, people, planets, stars and galaxies. According to acosmism, this plurality of individual objects is ultimately unreal, non-existent, a mere appearance or illusion. Non-Dual philosophers are particularly prone to acosmism, given their overarching emphasis on the fundamental unity of reality: since reality is one Whole, the empirical world of plurality must be unreal – or so it is argued. Such acosmic forms of Non-Dualism often go hand in hand with a monkish ethics of renunciation: to achieve the final Liberation of Suffering, the individual must renounce the empirical world of plurality – only then will she realize the liberating insight into “the One” that alone is truly real. Since the individual, qua individual, is part and parcel of the world of plurality, this renunciation of the world is also a radical self-renunciation: even one’s own individual existence must be rejected as illusory! Such acosmism affects both Eastern and Western forms of Non-Dualism. In the East, acosmism is a dominant feature of Advaita Vedanta and, perhaps to a lesser extent, Buddhism. In the West, acosmic tendencies can be found in Parmenides, Spinoza, Schelling (at the time of his “Identity System”) and the British Idealist Bradley.

By contrast with “acosmism” we can define “Cosmic Non-Dualism” as a position that recognizes the fundamental oneness of reality yet does not deny the reality of the empirical world of plurality. The cosmos – the infinite universe with its countless stars, planets, living and non-living beings – is rather seen as somehow manifesting the One that alone truly is. For Cosmic Non-Dualism, the One somehow ‘appears’ as the world of plurality: reality is a unity-in-diversity, an integrated whole with inner complexity, rather than a featureless blob of undifferentiated Oneness – which is the view to which acosmism tends. Consequently, Cosmic Non-Dualism does not tend to world renunciation but rather to the exact opposite, world affirmation, a celebration of empirical existence as the manifestation of divine reality, and an associated ethics of universal compassion and solidarity. Enlightenment is achieved not by rejecting the world, but by embracing it as your own Self. This leads to an ethics of active involvement in the world rather than aloofness from the world. With the separation between Self and Other overcome, you can no longer remain indifferent to the suffering and injustice in the world. You have to act, simply because in helping others you are actually helping yourself – perhaps not, directly, your individual self, your empirical persona, but first and foremost your underlying Self, the creative essence of the universe, of which everything and everyone is an integral part. In the East, such Cosmic Non-Dualism, with its celebration of empirical reality as manifesting the Divine and its ethics of universal solidarity, can be found in Shaivite Tantrism and the Qualified Non-Dualism of the Vedantic philosopher Ramanuja. In the West, cosmic Non-Dualism is a prominent feature of the Neoplatonism of Plotinus, who explicitly rejected the extreme world renunciation of Gnosticism, and the philosophy of Hegel, who developed his version of Absolute Idealism partly in criticism of Schelling’s acosmism.

The Superiority of Cosmic Non-Dualism
In my view, the spiritual philosophy of Cosmic Non-Dualism is exactly right for our time. Not only is the factual truth of some form of Cosmic Non-Dualism strongly suggested by what contemporary physicists and philosophers tell us about the holistic unity of the universe, and the place of consciousness in it, Cosmic Non-Dualism also satisfies an urgent ethical and spiritual need that is felt worldwide. As such, it is far superior to Acosmic Non-Dualism, which tends to a nihilist indifference towards the world. This comes out forcefully in Robert Pirsig’s cult novel Zen and the Art of Motorcycle Maintenance (which is partly autobiographical), where the protagonist – the analytically minded Phaedrus – goes to India to find wisdom but ends up taking classes in Oriental philosophy taught by a professor with a predilection for Advaita Vedanta:

“But one day in the classroom the professor of philosophy was blithely expounding on the illusory nature of the world for what seemed the fiftieth time and Phaedrus raised his hand and asked coldly if it was believed that the atomic bombs that had dropped on Hiroshima and Nagasaki were illusory. The professor smiled and said yes. That was the end of the exchange.” (Zen and the Art of Motorcycle Maintenance, Vintage 1999, p. 144)

This is why the difference between cosmic and acosmic forms of Non-Dualism is so utterly crucial! An activist ethics of universal solidarity is precisely what our suffering world needs, torn as it is by ever widening divisions – between the haves and have-nots, between different ethnic groups, between secular society and religious fundamentalism, between mass society and the isolated individual, between the dangerous lure of populism and the aloofness of the political elite, between the interests of economic growth (necessary to feed an ever-growing world population) and the interests of a defenceless nature choking in the mind-numbing garbage heap produced by economic growth. It is now, after all, generally acknowledged that environmental pollution is the driving cause behind catastrophic climate change and diminishment of biodiversity. This is a global problem, affecting our whole planet and everyone on it, requiring a global solution and thus global solidarity.

Here Cosmic Non-Dualism could just be the right stimulus triggering people into collective action, not only to save the precious ecosystem of our planet, but also to eradicate poverty, war, racism, injustice, and the extreme wealth inequality that has become rampant due to 40 years of neoliberal capitalism. What, in the light of these challenges, could be more inspiring and motivating than to learn that you, a seemingly separate and isolated human being, are really not separate at all, that you and the other(s) are actually the same, the same suffering being which is suffering precisely because it hasn’t yet realized what it is, namely, a single being? What could be more conducive to global responsibility and solidarity than the knowledge that you are non-different from the world around you? The Non-Dualist teacher and therapist Jeff Foster puts this wonderfully well:


“It’s myself in Burma, it’s myself in the earthquake. It’s myself starving in Africa. People sometimes hear the message of non-duality and they think that it’s about sitting back and doing nothing. They think it’s about arrogantly sitting back and saying, “Oh, it’s just a dream, it’s just a story, there’s nobody there suffering so what’s the point in doing anything at all?”… Oneness recognises itself in the face of that starving child and can move to help itself, not out of pity, not because it needs to be a good person, that’s nothing to do with it. It doesn’t come from a set morality. But in seeing that it’s all One – and this is the mystery of the universe – somehow it moves to help itself.” (Jeff Foster in Conversations on Non-Duality, p.37)

Monday, August 20, 2018

Some Thoughts on the Mathematical Unfolding of Absolute Self-Awareness

In various posts on this blog I have sketched the rough outlines of a contemporary version of Absolute Idealism, which I like to call – for lack of a better term – “Absolute Idealism 2.0”. The philosophical tradition of Absolute Idealism, stretching from the Upanishads in the East and Plotinus in the West to the German and British Idealists, can be summarized by the claim that everything exists because it is thought and/or experienced by an Absolute Mind, which in turn exists because it thinks/experiences itself. Thus, the Absolute Mind makes itself exist by being aware of itself, and it should as such be defined as Absolute Self-Awareness (ASA). This self-causing capacity of ASA (developed especially by Plotinus and Fichte) is in my view one of the strong features of Absolute Idealism, as it provides a possible (and, perhaps, plausible) answer Leibniz’s famous question why something exists rather than nothing.

This answer, however, is only worth anything if the concept of ASA can also explain why reality is the way it is. For we do not just want to explain the existence of reality; we also want to explain its nature. Why did reality take the form of this universe we see around us, developing in space and time, governed by physical laws? This is where Absolute Idealism 2.0 comes in. Taking its cue from modern physics, which shows the thoroughly mathematical nature of physical reality, Absolute Idealism 2.0 stresses the intimate connection between mathematics and the structure of (absolute) self-awareness. In earlier posts I already developed some ideas about this connection (see here, here and here). This post takes these ideas to a (somewhat) higher level.

I will end with some speculations about a mathematical solution to the problem of evil (the theodicy problem): given the randomness of by far the most real numbers, is it possible that the Absolute simply ‘lost itself’ in what Leibniz called the “labyrinth of the continuum”? Does this explain why the universe is not perfect, despite being the mathematical image of ASA?

ASA’s awareness of the natural numbers and real numbers
The basic idea is that ASA, due to its inner recursivity, generates an infinite sequence of reflection levels (namely: self-awareness, awareness of self-awareness, awareness of awareness of self-awareness, ...) isomorphic to the sequence of the natural numbers N={0, 1, 2, 3, …}. Presupposing a structuralist account of mathematics (such that mathematical objects are numerically identical iff they are isomorphic), we can conclude that the natural numbers exist because ASA, through its inner recursivity, thinks them. N, then, is ASA’s first creation beyond its immediate self-awareness.

This idea, that ASA through its inner recursivity generates a sequence isomorphic to N, was first put forward systematically by the American Idealist Josiah Royce, influenced by Dedekind’s notorious Gedankenwelt proof of the existence of infinity (see the “Supplementary Essay” in Royce
1959 [1899]). Anticipations of this idea, however, can already be found in the Neoplatonic philosopher Plotinus (as I explain more fully here). Virtually the same idea was later developed by the Husserlian phenomenologist and mathematician Oskar Becker, who shows in some detail how the inner unfolding of self-awareness exhibits the same principles as the ones used by Cantor in his construction of the transfinite hierarchy (see Becker 1973 [1927]).

It is sometimes objected that this infinity of levels of self-awareness is humanly impossible: we can be aware that we are self-aware, and perhaps we can also be aware of this awareness of our self-awareness, but this is where the buck stops for most of us. Russell, for example, comments as follows on Dedekind’s idea that self-awareness implies infinitely many reflection levels: “Now it is plain that this is not the case in the sense that all these ideas have actual empirical existence in people’s minds. Beyond the third or fourth stage they become mythical.” (Russell 1970 [1919]: 139)

In response to this objection, it should be remembered that we are not speaking of human self-awareness, but of absolute self-awareness (ASA) qua self-causing cause of all reality. The assumption that this ASA exists is admittedly not a matter of course, and I can see why a philosopher like Russell would reject that assumption out of hand (after all, Russell and Moore started analytic philosophy as a revolt against the Absolute Idealism of their teachers). Nevertheless, the idea that self-awareness has a self-causing capacity can be defended, and I see no other equally plausible answer to Leibniz’ question “Why does reality exist?” on the table. Once we accept the assumption that ASA is the self-causing cause of reality, then the above objection to the infinity of levels falls away. For, surely, such infinite complexity would be no problem for the Absolute, i.e. that which explains everything else? We should also keep in mind here that, since self-causation is obviously impossible in time, the ASA can only exist timelessly. So the infinite hierarchy of reflection levels cannot be conceived as a merely potential infinity, unfolding in time; it must be conceived as a timelessly existing actual infinity, accomplished ‘at once’ by the ASA, in the nunc stans of its timeless reality.



Georg Cantor (1845 - 1918)
I note here in passing that this idea of an infinite hierarchy of reflection levels inside the ASA (a hierarchy which even extends into the transfinite, as Oskar Becker argues) fits Cantor’s original vision of transfinite set theory wonderfully well. Cantor was a deeply religious man, interested in theology and metaphysics no less than in mathematics. For him, the existence of the transfinite hierarchy was guaranteed by God, in whose mind all the infinite sets exist as separate ideas. These sets, as Cantor wrote, “exist in the highest degree of reality as eternal ideas in the Intellectus Divinus” (quoted in Dauben 1979: 228). Obviously, other mathematicians generally disapprove of Cantor’s theological views (sometimes interpreting them as signs of Cantor’s mental illness, which had a touch of religious insanity). For most mathematicians, transfinite set theory can do just fine without a grounding in theological metaphysics. But from the perspective of Absolute Idealism 2.0, Cantor’s theological views are not so strange. One could even say that by arguing for the self-causation of ASA and its inherent recursivity (which generates the infinite hierarchy of reflection levels), we give a philosophical foundation to Cantor’s belief in the existence of the transfinite hierarchy in the Divine Mind.

Be that as it may, the next step is the realization that ASA, through its awareness of the natural numbers, is also aware of all possible mappings from the natural numbers to the natural numbers, i.e. ASA is aware of all total functions f:N
N. (Formally, the set of all functions from A to B is defined as BA = { f : f є P(AXB) and f is single-valued}.) To see why, we need to keep in mind what ASA essentially is, namely, absolute self-awareness. From this it follows that on each reflection level n from N ASA is aware of its identity with itself on every reflection level m from N (with the possibility that n=m). Such an awareness of self-identity between different reflection levels n and m, then, amounts to a mapping from n to m, that is, a function f such that f(n)=m. And since, as indicated, this holds for all n and m from N, it follows that ASA ‘performs’ or ‘executes’ all total f:NN. (When I speak of functions in the following, I always mean total functions as opposed to partial functions; for the distinction see here.)
 
Now, the set of all f:N
N is basically the set of all (positive) real numbers R+, i.e. the positive continuum (cf. Burrill 1967). This follows from the facts that each f:NN can be seen as the definition of a real number, and that each real number can be seen as the output of some f:NN as it progressively evaluates its domain N. This turns on the fact that each real number can be defined as a natural number (i.e. the integer part) followed by a unique and infinite decimal expansion, for example, π=3.141592654…. The point is that among all the f:NN there is at least one f that outputs π as it progressively evaluates N. That is: there is at least one f such that f(0)=3, f(1)=1, f(2)=4, f(3)=1, and so on. Thus, one possible definition of π is in terms of this f, namely: π=f(0).f(1)f(2)f(2)f(3)f(4)f(5)…

In this way, each positive real number can be defined in terms of some f:N
N. And conversely, each f:NN defines some positive real number. Thus, as said, the set of all f:NN is basically identical with the set R+. This, of course, requires the convention that for each such f we see f(0) as the integer part of the real number defined by f, but this is unproblematic. There is, however, one minor complication with this definition of R+ in terms of all f:NN, namely: it implies that different functions sometimes define the same real number. For example, we saw that π is defined by the function f such that f(0)=3, f(1)=1, f(2)=4, f(3)=1, f(4)=5,… But there is also another function (let’s call it g) from the set of all f:NN that outputs π as follows: g(0)=3, g(1)=1415, g(2)=9, and so on. Thus π can also be written as g(0).g(1)g(2)g(3)… In fact, it is easy to see that infinitely many functions from the set of all f:NN define the same real number.

To avoid such multiple definitions of the same real number, the definition of R+ in terms of functions on N is usually limited to all f:N
{0, …, 9}. In this way, each positive real number is defined by only one such f. This is admittedly much more economical, but not strictly necessary. What matters is that the set of all f:NN basically is (i.e. defines) the set R+. I will stick to this latter definition of R+ because it fits the above account of ASA as generating N through its inner recursivity. It makes little sense to say that ASA, through this recursivity, generates only reflection levels 0 to 9 and then stops, or that ASA indeed generates all reflection levels n from N but is only aware of its interlevel self-identity on the first 10 levels (and thus of all f:N{0, …, 9}). No, ASA generates all reflection levels n from N and is aware of its interlevel self-identity on all these levels, thereby performing all f:NN. As we have seen, this means that ASA is also aware of all positive real numbers, i.e. the set R+. The fact that multiple f’s from the set of all f:NN then define the same real number is irrelevant; it is a redundancy built into the nature of ASA.

Patterns in the continuum and algorithmic information theory
The next step is somewhat more speculative, but not unreasonable. We have established that ASA is aware of all positive real numbers. So now what? What does ASA ‘do’ with the real numbers? What does the continuum ‘mean’ to ASA? Because the essence of ASA is to be aware of itself, it must use its awareness of R+ to further increase its self-awareness. This, it seems to me, can only mean that ASA looks for patterns (i.e. ordered number sequences) in the continuum in which it recognizes itself, i.e. patterns that somehow mirror its own nature.

What does this mean? It basically means that there are algorithms that mirror the nature of ASA, for example the algorithms inherent in the functioning of the human brain. We know from algorithmic information theory (developed around 1970 by Andre
ï Kolmogov and Gregory Chaitin, among others) that a number sequence is patterned (i.e. ordered, regular, as opposed to random) iff there is an algorithm, shorter in length than this sequence, which outputs this sequence. This is a definition of what order is. The shorter the algorithm, the more ordered the sequence it outputs. If for some sequence S no algorithm shorter than S can be given, then S is random. In that case, the only way to describe S is simply to reproduce S in full. S is not algorithmically compressible in that case, i.e. it contains no regularity that allows the formulation of a rule (i.e. algorithm), shorter than S itself, for the generation of S.

The number
π provides a good example of a sequence that is highly ordered in the sense of algorithmic information theory. This may come as a surprise, since π is often considered to be a typically random number, whose decimal expansion evinces no clear order. It is true that π is a normal number, i.e. an irrational number whose decimal expansion features all possible number strings with equal frequency irrespective of the chosen base, which is a kind of statistical randomness. Nevertheless, the normality of a number does not per se imply its algorithmic randomness, as is shown by the computability of π. For, as is well-known, there are a number of relatively short algorithms that calculate π’s decimal expansion up to its n-th digit for some arbitrary n. From the perspective of algorithmic information theory, then, π is in fact highly ordered, since some arbitrarily long (but obviously still finite) stretch of it its decimal expansion can be generated by an algorithm much, much shorter than this string. On second thought, this is really not so surprising. For as we all learn in high school, π is just a circle’s circumference divided by its diameter. If one were to live forever and continued this division endlessly, one would eventually calculate every digit of π. Hence the computability of π and hence its orderedness in the sense of algorithmic compressibility.

Algorithmic compressibility offers an objective and universal measure of order. This can be seen from two facts: (1) that the thermodynamic concept of entropy can also be understood in terms of algorithmic compressibility (see Baez & Stay 2013), and (2) that the algorithmic compressibility of any sequence is more or less invariant between different formal languages. To make the intuitive concept of algorithm precise, after all, we need to unpack it in terms of some formal language, such as the language of Turing machines, lambda calculus, or programming languages such as Pascal, C or LISP. Algorithms, therefore, are notation dependent, relative to some formal language. One of the strengths of the notion of algorithmic compressibility is that such differences between formal languages are more or less irrelevant to it: the algorithmic compressibility of some sequence in a formal language is the same (up to an additive constant) as its algorithmic compressibility in any other formal language. This means that algorithmic compressibility is indeed a universal and objective measure of order.

For algorithmic information theory, then, each ordered sequence of numbers represents the shortest algorithm that outputs it. This enables us to make sense of the above claim that ASA recognizes itself in some patterns in the continuum, for we can now unpack this as the claim that the algorithms represented by these patterns mirror ASA’s essence. It stands to reason that these are the algorithms that simulate intelligent agency, e.g. the algorithms that describe the functioning of human brains (and the functioning of intelligent organisms in general). We know from physics that physical reality is thoroughly computable (i.e. algorithmic). Moreover, the anthropic principle in cosmology tells us that the universe is surprisingly well-suited for the evolution of life, and thus of those physically realized algorithms that mirror ASA’s essence. Perhaps, then, we can explain the universe as that hugely complex pattern in the continuum (which, remember, exists in our view only as the structure of ASA’s self-awareness) in which ASA sees its essence best reflected? The universe, then, would simply be an extremely complicated pattern in the recursive unfolding of ASA’s self-awareness, namely, that pattern whose (shortest) algorithm simulates intelligent agency to the highest degree.

Did God lose Himself in the “labyrinth of the continuum”?
A second reason why I like this theory is that it enables us to explain why the universe is not perfect, despite being the mathematical image of ASA (or ‘God’ if you prefer). For, as Turing showed (as part of his proof of the undecidability of the halting problem), by far most of the real numbers are uncomputable and therefore transcendental. This means that their decimal expansions cannot be generated by any algorithm. Thus, from the perspective of algorithmic information theory, their decimal expansions are totally random. In being aware of the continuum, therefore, ASA is aware of something that is for the most part unordered, a kind of primordial chaos. ASA’s attempt to find patterns in the continuum (in order to mirror itself in those patterns) must therefore be extraordinarily difficult, indeed virtually impossible, since the ordered part of the continuum is infinitesimally small compared to the unordered part. In fact, if one could randomly pick out a real number (say, by pricking somewhere in the real number line with an infinitely sharp needle), the probability of getting an uncomputable number is approximately 1 (cf. Chaitin 2005: 113)! Perhaps this explains why the universe, despite being an image of ASA, is not perfect? It must, after all, be close to impossible for ASA to find order in the continuum.

Since, as we have seen, R+ and the set of all f:N
N are basically the same set, the fact that most real numbers are uncomputable also means that most of the f:NN are uncomputable. To see why most of the real numbers are uncomputable, remember that the notion of algorithm is always relative to some formal language. This language must have a finite set of basic symbols (i.e. a vocabulary) and a finite set of syntactical rules for the combination of these symbols into larger expressions. This means that the language can generate only a countably infinite number of expressions, since we can list them in order of length (i.e. we can have a bijection f:NE where E is the set of all expressions generatable in the language). Since the set of algorithms is a proper subset of the set of all expressions generatable in this language, the set of all possible algorithms too must be countably infinite. So if we assume, for contradiction, that all positive real numbers are computable, then R+ must be countably infinite as well. But we know this is not the case, given Cantor’s proof of the uncountability of the real numbers: already in the unit interval [0,1] there are uncountably many numbers (in fact, as Cantor’s sun theorem shows, there are as many reals in [0,1] as in the entire continuum!). Thus, the set of real numbers is said to be “maximally larger” than the countable set of all possible algorithms. So there simply aren’t enough algorithms to compute all the real numbers; by far most of the real numbers are uncomputable and have therefore totally random decimal expansions.

Could this, perhaps, explain why the universe is imperfect, despite being (on our account) the mathematical self-image of God, i.e. self-causing Absolute Self-Awareness? Having generated the continuum through the recursivity of its self-awareness and its interlevel self-identity (which, as we have seen, gives all f:N
N and thus all real numbers), ASA looks for those patterns in the continuum in which it can mirror its own essence (which is self-awareness), only to find that patterns form an infinitesimally small portion of the continuum, since almost all real numbers are uncomputable. So ASA’s trying to find its own image in the continuum is a bit like trying to find a needle in a haystack… only much more difficult! As said, the probability of randomly selecting a computable number out of the continuum approaches zero. One could say that ASA, trying to see its own mathematical mirror image, instead lost itself in the “labyrinth of the continuum” (as Leibniz called the complex of unsolved problems and paradoxes surrounding the real numbers). And still, we are here, there is this ordered universe in which we find ourselves. True, it is not perfect, that is, it is the not the true image of the Absolute, but still it is there and it is computable. So, despite its near impossibility, the Absolute must nevertheless have succeeded in finding order in the arch-chaos of the continuum which the Absolute had itself created. It’s a bit like that old question: what happens when an unstoppable force meets an immovable obstacle? Well, what happens is the creation of this refractory miracle which we call the universe…

 References
-Baez, J.C & Stay, M. (2013), “Algorithmic Thermodynamics”, http://math.ucr.edu/home/baez/thermo.pdf
-Becker, O. (1973 [1927]),
Mathematische Existenz: Untersuchungen zur Logik und Ontologie mathematischer Phänomene. Tübingen: Max Niemeyer Verlag.
-Chaitin, G. (2005), Meta Maths: The Quest for Omega. London: Atlantic Books.
-Burrill, C. (1967), Foundations of Real Numbers. New York: McGraw-Hill.
-Dauben, J.W. (1979), Georg Cantor: His Mathematics and Philosophy of the Infinite. Cambridge, Mass.: Harvard University Press.
-Royce, J. (1959 [1899]), The World and The Individual, First Series: The Four Historical Conceptions of Being. New York: Dover Publications. 

-Russell, B. (1970 [1919]), Introduction to Mathematical Philosophy. London: George Allen and Unwin.

Sunday, April 29, 2018

The Epistemological Nature of Early Modern Idealism

Modern Idealism, as developed by Berkeley and Kant and their successors, was mainly epistemological in nature. That is to say: the arguments they used to establish the central Idealist thesis – that reality exists only in or for the mind – were mainly epistemological arguments, based on analyses of knowledge and sense experience. They reasoned basically as follows: Since we can know reality only insofar as it is sensed and conceptualised by us, we literally can have no evidence of any reality beyond our sensations and concepts, and thus beyond our consciousness. All that we are justified in postulating, therefore, is the reality internal to our consciousness, the organized whole of sensations and concepts we ordinarily call “reality”. This, arguably, is the master argument for modern Idealism.

Although I am greatly attracted by Idealism, I am critical of modern, i.e. epistemological Idealism. In my view, we should accept Idealism on ontological grounds, i.e. because it offers the best explanation of reality, and not primarily on epistemological grounds. As I intend to argue in a following post, epistemology alone can never provide a sufficient justification for the Idealist thesis. In particular, the master argument for modern Idealism remains vulnerable to skeptical attacks. For from the mere fact that knowledge of objects is only possible of objects within consciousness, it does not follow that all objects are within consciousness; there might still be unknown or even unknowable objects


To this skeptical retort, modern Idealism has no satisfactory answer, precisely because it rests its case on our epistemological confinement to consciousness. If we are indeed trapped within the circle of consciousness, then – as the epistemological Idealist emphasizes – we cannot prove the existence of a reality outside of consciousness; but then neither can we disprove that existence. This is the weak spot of modern Idealism, the point at which it remains vulnerable to skeptical counter-attacks. To prepare the way for this critique of epistemological Idealism, this post explains why the Idealisms of Berkeley, Kant, and their successors took this epistemological form.

The Way of Ideas and Its skepticism
To understand why modern Idealism took this epistemological form, we have to place it in the context of its origination, namely, the Way of Ideas developed by Descartes, Locke and their followers, and the radical epistemological skepticism to which it led. As explained in a
previous post on this blog, the Way of Ideas led to skepticism because it had ‘imprisoned’ the knowing subject within the “circle of consciousness”, hiding external reality behind a “veil of perception”. As the Cartesian philosopher Arnauld put it: “We have no knowledge of what is outside us except by mediation of the ideas within us.” (Arnauld 1964 [1662]: 31) Thus arose the skeptical question: If all we know directly are the ideas within our consciousness, how can we know if these ideas correspond to a reality outside our consciousness, indeed, how can we know there is an external reality at all? We cannot, after all, step outside our consciousness in order to inspect its correspondence, or lack thereof, with external reality. This threat of skepticism was sharply felt by Descartes, Locke, and their successors, some of whom – most famously Hume – went on to argue that skepticism was indeed inescapable.

It was to counter this threat of skepticism that Berkeley and Kant developed their respective versions of Idealism. As both of them pointed out, the skepticism induced by the Way of Ideas turned on the assumption of a reality external to consciousness; strike that assumption, they argued, and the threat of skepticism vanishes. If reality is ‘just’ a product of the mind itself, then surely its knowability can pose no problem for us?

George Berkeley (1685 - 1753)
Berkeley’s Idealist Rescue of Common Sense
Berkeley had designed his Idealism particularly with the intent to save common sense from skepticism. Common sense says that the objects we perceive by our senses are indeed as we perceive them: they have the colours, smells, tastes, auditory and tactile qualities we perceive in them. The Way of Ideas, however, had placed all such “secondary qualities” within consciousness, locating the real object outside the latter, as the external cause of those sensations. When we eat an apple, for example, we see its redness, taste its sweetness, feel its smooth skin, etc. But according to the Way of Ideas, all these sensations are not qualities of the apple itself; the real apple is just some material structure in space and time of which we know nothing except what physical science tells us (and even the truth of physics became doubtful after Hume’s critique of causality). For Berkeley, this skeptical doubt concerning common sense, induced by the Way of Ideas, was absurd: 


Upon the common principles of philosophers, we are not assured of the existence of things from their being perceived. And we are taught to distinguish their real nature from that which falls under our sense. Hence arises Scepticism and Paradoxes. It is not enough that we see and feel, that we taste and smell a thing. Its true nature, its absolute external entity, is still concealed.” (Berkeley 1969 [1713]: 3)

It was therefore to redeem common sense that Berkeley argued for Idealism, which in his case amounted to the thesis that sensible objects do not exist unperceived: “Their esse is percipi,” as Berkeley famously put it (1995 [1710]: §3). Perceptible objects, he argued, are nothing but bundles of sensible qualities in consciousness. Thus, through his Idealism (or “Immaterialism” has he called it),
Berkeley could restore the common-sense belief that when we eat an apple, and see its redness, taste its sweetness, etc., we are eating, seeing and tasting the apple itself, not just its appearance as distinct from the real thing. The real apple, for Berkeley, is this bundle sensations; there is nothing beyond it. Berkeley made the same point by contemplating a cherry (fruit, apparently, lending itself very well for Idealist argumentation…):

“I see this cherry, I feel it, I taste it […]: it is therefore real. Take away the sensations of softness, moisture, redness, tartness, and you take away the cherry. Since it is not a being distinct from sensations; a cherry, I say, is nothing but a congeries of sensible impressions, or ideas perceived by various senses: which ideas are united into one thing (or have one name given them) by the mind; because they are observed together.” (Berkeley 1969[1713]: 117)

In his Three Dialogues between Hylas and Philonous, Berkeley makes his alter-ego Philonous (Greek for “Lover of mind”) respond as follows to the insensible matter beyond sensory experience defended by Hylas (Greek for “matter”):

“I am of a vulgar cast, simple enough to believe my senses, and leave things as I find them. To be plain, it is my opinion that the real things are those very things I see and feel, and perceive by my senses… A piece of sensible bread, for instance, would stay my stomach better than ten thousand times as much of that insensible, unintelligible, real bread you speak of… Away then with all that Skepticism, all those ridiculous philosophical doubts. What a jest is it for a philosopher to question the existence of sensible things, till he hath proved it to him from the veracity of God1; or to pretend our knowledge in this point falls short of intuition or demonstration! I might as well doubt of my own being, as of the being of those things I actually see and feel.” (Berkeley 1969 [1713]: 90-1)

As Berkeley admitted (see idem: 110), it is a bit strange to defend common sense by declaring that perceived objects exist only within the mind – a view that directly violates common sense, for which perceived objects ‘evidently’ exist outside the mind – but, according to Berkeley, it is the only way to save the reality of the sensible object within the context of the Way of Ideas. Idealism is the bitter medicine that common sense must take in order to cure it from the illness of skepticism.

Immanuel Kant (1724 - 1804)
Kant’s Idealist Rescue of Causality
For Kant, it was a different aspect of the skepticism induced by the Way of Ideas that brought him to accept Idealism. What worried him was not so much the affront to common sense as the affront to physical science presented by Hume’s skeptical attack on causality. As Kant noted in the Prolegomena, it was Hume’s attack on causality that first aroused him from his “dogmatic slumber” and stimulated the development of his “transcendental Idealism” (Kant 2001 [1772]: 5). Hume had shown, convincingly according to Kant, that our causal claims about reality are thoroughly unsupported by the sensations caused in us by external objects. We say, e.g., that fire causes smoke, but all the evidence we have is that sensations of smoke regularly follow sensations of fire. In the sensations themselves we find no reason why one should follow the other. Moreover, we cannot generalize from a finite number of past observations to universal claims: the fact that up till now sensations of smoke have followed sensations of fire does not guarantee that this will be so in the future as well (the problem of induction). As Hume put it:

Thus not only our reason fails us in the discovery of the ultimate connection of causes and effects, but even after experience has informed us of their constant conjunction, 'tis impossible for us to satisfy ourselves by our reason, why we should extend that experience beyond those particular instances, which have fallen under our observation.” (Hume 2003 [1739-40]: 66)

Kant was deeply disturbed by Hume’s attack on causality. His respect for the physical science developed by Copernicus, Galileo and Newton was so great that he simply could not stomach Hume’s dismissal of causal laws. The stunning success of the new science, especially Newton’s discovery of the laws of motion and gravitation, meant that Hume had to be wrong. And where he went wrong, according to Kant, was in his assumption that causality, if it exists at all, must be a feature of external reality, in other words, that causal connections must be connections between real objects, independent of our consciousness. But, as Kant argued, such external objects are “nothing to us”. Objects become something for us, i.e. they become accessible to us as experienceable and knowable objects, only if they conform to our forms of cognition, and causality is one such form. Raw sensations do not yet give us experiences of objects. The sensations have to be ordered by our forms of sensory intuition (space and time) and our forms of conceptual understanding (the categories, prime among which is causality); only then do we experience a single, ordered, integrated reality consisting of interconnected objects. This, according to Kant, explains our ability to make objective causal claims: because causality is not a feature of external reality but rather a cognitive form in our mind, a form to which objects must conform in order to become experienceable and knowable.

Kant’s Idealism, then, extends only to the forms of empirical reality, not to the sensory material structured by these forms. This is why Kant calls his philosophy “transcendental Idealism”, the term “transcendental” being his technical term for what pertains to the a priori forms of consciousness: “I call all cognition transcendental that is occupied not so much with objects but rather with our a priori concepts of objects in general.” (CPR: A12) In extension, Kant speaks of the “transcendental subject” as the subject who applies the a priori forms of cognition to the sensory material.

Ultimately, the necessity of the object to conform to our forms of cognition has to do with the fundamental role Kant accords to self-consciousness in experience and knowledge. This point is often described, rightly, as the cornerstone of Kant’s Idealism. According to Kant, a process or state in my consciousness counts as an experience or belief only if I can be aware of it as my experience or my belief, thus only if it belongs to the unity of my consciousness (a consciousness that forms a unity precisely because it is mine, i.e. because all episodes and states in it are related to me as their underlying subject). For a mental episode or state to be mine, then, I must as it were be able to prefix it with the qualifier “I think…”. By prefixing “I think…” to a mental content, such as an impression of redness, thus by thinking “I think (or rather I see) redness”, I indicate that the content belongs to the unity of my consciousness. As Kant puts it:

“The I think must be able to accompany all my representations; for otherwise something would be represented in me that could not be thought at all, which is as much to say that the representation would either be impossible or else at least would be nothing for me… The thought that these representations […] all together belong to me means, accordingly, the same as that I unite them in a self-consciousness […].” (CPR: B132, B134) 

According to Kant, the ultimate function of the forms of space and time and the categories of the understanding is to effectuate this unity of self-consciousness (a unity that Kant therefore calls “transcendental”, since it underlies the application of the transcendental forms of cognition). Thus only by placing all my mental episodes and states within a unified spatiotemporal network of causal relations can I recognize those episodes and states as mine, as belonging to my (self-)consciousness. The resulting integrated unity of empirical reality, then, is for Kant only a reflection or projection of the transcendental unity of self-consciousness unto the unorganized manifold of raw impressions. The unity of the object, and thereby the object as such (because there is no object without unity), is really a manifestation of the unity of the subject’s self-consciousness. In this sense, as later German Idealists would put it, the principle of subject-object identity is the central principle of Kant’s Idealism.

The Epistemological Nature of Idealism after Kant and Berkeley
Although the Idealisms of Berkeley and Kant differ greatly, they have roughly the same goal – to counter the epistemological skepticism engendered by the Way of Ideas – and use roughly the same strategy to achieve that goal, namely: argue that we can only know objects which are in or for consciousness, such that supposedly external reality falls away as irrelevant and unknowable, in which case the skeptical threat, too, falls away. The only reality left standing, then, is the reality inside consciousness. This, to repeat, is the master argument for modern Idealism – an argument either explicitly repeated or at least implicitly accepted by later German and British Idealists. They all stood on the shoulders of Berkeley and Kant, striving to improve or complete their ground-breaking but still imperfect Idealist systems (for the Germans, of course, Kant was more important, but the British Idealists drew on both Berkeley and Kant). As such, the German and British Idealists took over the epistemological agenda of Berkeley and Kant and remained within their epistemological mode of reasoning. For all of them, epistemology remained the prima philosophia, the foundational “first philosophy” that had to precede and ground all other theoretical endeavours. And even if later Absolute Idealists (such as Schelling, Hegel, Green and Bradley) went on to draw more ontological and metaphysical conclusions concerning the mind-dependence of reality, they did so ultimately because Idealist epistemology demanded it. As Frederick Beiser notes: “Although absolute idealism is indeed metaphysics, and in the very sense prohibited by Kant […], its metaphysics is necessary to solve the outstanding problem of Kant’s philosophy according to its own guiding principle.” (Beiser 2002: 369)

Notes
1. An obvious reference to Descartes’ appeal to God as the guarantor of the veracity of our perceptions, PS.

References
-Arnauld, A. (1964 [1662]), The Art of Thinking. Indianapolis: Bobbs-Merrill.

-Beiser, F. (2002), German Idealism: The Struggle against Subjectivism, 1781-1801. Cambridge, Massachusetts: Harvard University Press.
-Berkeley, G. (1995 [1710]), A Treatise Concerning the Principles of Human Knowledge. Indianapolis: Hackett Publishing.
-Berkeley, G. (1969 [1713]), Three Dialogues Between Hylas and Philonous. Chicago: Open Court.
-Kant, I (1998 [1781-87]), Critique of Pure Reason. Cambridge: Cambridge University Press.
-Kant, I. (2001 [1772]), Prolegomena To Any Future Metaphysics. Indianapolis: Hackett Publishing.

Thursday, April 5, 2018

The Problem of Skepticism in Early Modern Philosophy of Consciousness

This post is part of a larger project I am working on: a critique of the epistemologically motivated Idealisms of Berkeley, Kant, and the post-Kantians. I am greatly attracted to Idealism, but I think we should accept it primarily on ontological grounds, i.e. because Idealism gives the best explanation of why reality exists and why it is as it is. Hence my criticism of the Idealisms of Berkeley, Kant, et al., because for them Idealism was primarily epistemologically motivated, Idealism being their solution to the problem of epistemological skepticism as it arose within the early modern philosophy of consciousness advanced by Descartes, Locke, and their followers. As I will argue in a next post, modern Idealism, as an answer to this threat of skepticism, fails miserably (thus the only remaining reasons for accepting Idealism must be ontological). To prepare the way for this critique of epistemological Idealism, this post explains how the problem of skepticism arose in the early modern philosophy of consciousness, or the “Way of Ideas” as it was known to Descartes, Locke and their contemporaries. 

The Way of Ideas
There were two main, interconnected forces driving early modern philosophers towards the Way of Ideas and its epistemological centralization of consciousness. One of these forces was the desire for certain knowledge, which arose from the quarrels between the Church and the new natural science of Copernicus and Galileo, which rose all kinds of thorny issues concerning the authority of Faith and the powers of Reason. Here, famously, Descartes used the cogito ergo sum argument as a way to ground the certainty of knowledge on the self-evidence of consciousness’ knowledge of itself. Thus, the range of certain knowledge became limited to individual consciousness and its ‘contents’ (generically called “ideas” or “representations”; Kant spoke of “Vorstellungen”). According to the proponents of the Way of Ideas, then, the subject knows primarily what is inside the “circle” of his consciousness; only those contents are immediately present to it. All things outside consciousness are known mediately, by conjecture on the basis of what is inside consciousness (sensations, feelings, concepts, thoughts).

The other force that drove early modern philosophers to embrace the Way of Ideas was the atomism – or “corpuscular philosophy” – of the new natural science. Reviving (and transforming) the atomism of Democritus, the proponents of the new science advanced the hypothesis that all natural phenomena are explainable in terms of tiny particles of matter, “corpuscles”, interacting mechanically in space. This, however, led to the question of how to explain sensory qualities such as colour, smell, sound, and taste, which are notoriously subjective. What colour something appears to have or how it sounds, tastes or smells can differ from person to person, depending on one’s physical constitution and the surrounding environment (thus, a thing’s colour changes with the light falling on it; things can taste and smell differently when you are sick, etc.). However, like the atoms of Democritus, the corpuscles of the new science were supposed to exist objectively, independently of our consciousness of them. They were, moreover, supposed to be so small as to be imperceptible and thus as being in themselves without colour, taste, smell, etc. Hence, like Democritus, the corpuscularians – including Descartes and Locke – concluded that such sensory qualities were merely the effects in our minds of the collisions of corpuscles on our sense organs. Such sensory qualities, then, are only subjective and do not reveal the objective qualities of the corpuscles, which consist merely of solidity, spatial form and position, and motion. This distinction between subjective and objective qualities became known as the distinction between secondary and primary qualities. Whereas the primary qualities, such as spatial position and motion, are objective, measurable, and mathematizable, and thus are crucial to natural science, the secondary qualities convey no trustworthy information about the reality outside our consciousness.

The general picture that thus arose was of a knowing subject locked inside his “circle of consciousness”, with external objects impinging on it from the outside, causing perceptions within the circle. “We have no knowledge of what is outside us except by mediation of the ideas within us,” as the Cartesian philosopher Arnauld (1964 [1662]: 31) summarized it. Such was the overall conceptual framework within which the Way of Ideas operated. And although this focus on consciousness was partly motivated, notably in Descartes, to provide a secure foundation for knowledge, the irony of the situation was that the Way of Ideas ended up fostering a radical epistemological skepticism. For if certainty pertains only to what is inside consciousness, how then can we know what is outside consciousness, the external reality? If all we know with certainty are the contents of consciousness, how can we know that these contents correspond to external objects? After all, as the problem was frequently put, we cannot step outside our consciousness in order to inspect its correspondence, or lack thereof, with external reality. 

The Veil of Perception and the Cartesian Circle
The problem is sometimes put in terms of a veil-of-perception theory which has been attributed to Descartes, Locke, and other philosophers of the Way of Ideas. On this theory, our sensory experiences of external objects do not give us cognitive access to these objects but rather form a ‘veil’ or ‘screen’ hiding them from our view. So the medium we use to know external objects, our sensations and ideas, blocks our very access to them. Thus Barry Stroud describes Descartes’ sceptical conclusion in his First Meditation as “implying that we are permanently sealed off from a world we can never reach”: “We are restricted to the passing show on the veil of perception, with no possibility of extending our knowledge to the world beyond. We are confined to appearances we can never know to match or deviate from the imperceptible reality that is forever denied to us.” (Stroud 1984: 33-4) Similar veil-of-perception theories have been attributed to Locke, Berkeley and Hume (cf. Bennett 1971).

The radical nature of the epistemological problem created by this veil-of-perception theory is well illustrated by the desperate solution offered to it by Descartes. In his Meditations on First Philosophy he famously argued that the only way to ‘pierce through’ the veil of perception, in order to reach the objects in themselves, is by evoking God, whose goodness would guarantee the veracity of our perceptions, such that “all things which I perceive very clearly and distinctly are true” (Descartes 1996 [1641]: 24). But to this solution, of course, the skeptic can easily respond by asking how Descartes can know for sure that God exists. If our ideas form a screen between us and external reality, then surely they would also screen us from the true nature of God, if He exists at all. Descartes had an answer to this, but few would find it convincing. It could even be argued that it is downright circular. Descartes argued that we find within our minds an idea of an infinite being, thus an idea which we as finite beings cannot possibly have produced; thus, it can only have been put in our minds by our Creator, “like the mark of the workman imprinted on his work” (Descartes 1996 [1641]: 35). Descartes’ assumption, however, that a finite being cannot form any idea of infinity, is rather questionable. Therefore Descartes also had recourse to a version of the ontological proof of God’s existence. But, as was already pointed out by critics in Descartes’ time, this makes his argument for the veracity of clear and distinct ideas rather circular. For Descartes cannot know that this proof of God does not contain any error unless he assumes that his clear and distinct perception of the steps of his reasoning guarantees that the proof is correct. So Descartes has to presuppose the veracity of clear and distinct ideas in order to prove the existence of God, which he then invokes as the guarantee of this very veracity – a conundrum known as the “Cartesian circle”.

The Problem of Primary and Secondary Qualities in Democritus, Locke, and Berkeley
The Way of Ideas, then, fostered epistemological skepticism by imprisoning the knowing subject within the circle of his consciousness, hiding external reality behind a veil of perception. It is often said that this type of skepticism was exclusively modern and cannot be found in premodern times. This is by and large true, but not entirely. It is true that for Pyrrhonism, the dominant form of epistemological skepticism in antiquity, the gap between what is in consciousness and what outside it didn’t matter much (Pyrrhonism was mainly concerned with showing that we can have no definitive criterion of truth, since every proof of such a criterion must either be circular or presuppose another criterion of truth, for which then the same problem arises). Nevertheless, the problem of the gap between consciousness and external reality was not completely unknown in classical philosophy, as shown by the remarkable case of Democritus, the "laughing philosopher". Not only did Democritus, with his atomism, anticipate the modern scientific worldview, he also anticipated the modern distinction between primary and secondary sensory qualities, as well as the epistemological skepticism induced by this distinction. In one of the few surviving fragments of his work, Democritus stages a striking dialogue between the Intellect and the Senses:

“Intellect: By convention there is sweetness, by convention bitterness, by convention colour, in reality only atoms and the void.
 Senses: Foolish intellect! Do you seek to overthrow us, while it is from us that you take your evidence?” 

In other words: if the secondary qualities do not convey objective information about the atoms, how can we ever know about them? How, in particular, can we know their primary qualities, since we cannot experience a thing’s spatial position and motion apart from its colour, sound, etc. If we disregard all secondary qualities, external objects become utterly unobservable to us. This means, as Democritus realized, that the atomic theory undermines the very credibility of the empirical evidence on which it rests. Democritus’ point was later repeated by early modern philosophers, notably Berkeley in his critique of Locke. 

Locke conceded that secondary qualities give us no insight into the true nature of external objects, but like Descartes he remained steadfast that we can nevertheless know these objects by observing their primary qualities, e.g. spatial position and motion. Thus Locke claimed that “the ideas of primary qualities of bodies are resemblances of them, and their patterns do really exist in the bodies themselves, but the ideas produced in us by these secondary qualities have no resemblance to them at all” (Locke 1996 [1689]: 51). Berkeley objected – much as Democritus had argued some 2000 years earlier – that we can observe a thing’s primary qualities only through its secondary qualities, and thus that our beliefs about the primary qualities of external objects are as problematic as the secondary qualities we attribute to them. Thus, Berkeley writes: “In short, extension, figure, and motion, abstracted from all other qualities, are inconceivable. Where therefore the other sensible qualities are, there must these be also, to wit, in the mind and nowhere else.” (Berkeley 2003 [1710]: 35)

Locke and the Problem of the ‘Thing in Itself’
In this way, however, Berkeley only aggravated a skepticism that was already present in the inaugurators of the Way of Ideas. We have already seen how Descartes felt the sceptical challenge and how he attempted to meet it by invoking God as the guarantor of the veracity of his “clear and distinct ideas”. Locke, too, felt this challenge. Although Locke thought (pace Berkeley) that we can know an external thing’s primary qualities, he also thought that we could not know what that thing is in itself, independent from its relation to us and other objects. Primary qualities, after all, are thoroughly relational, pertaining to a thing’s position in space and motion relative to other things. But what is an external thing in itself, apart from those relations? This, as Locke conceded, we cannot know, since we are ‘locked’ (pun unintended) inside our consciousness and cannot inspect objects as they exist outside of consciousness. Thus, what a thing is in itself, what the Aristotelians called its “substance”, was for Locke merely a “supposed” something “I know not what” (Locke 1996 [1689]: 123). For Locke, therefore, even the new natural science, despite its huge empirical success in the work of Galileo and Newton, yielded only opinion, not knowledge. Such sceptical modesty concerning the success of the new physics was in fact widely shared in early modernity, even by those who were directly involved in the development of the new science, such as Mersenne and Gassendi in France and John Wilkins in England. For all of them, our ‘imprisonment’ in consciousness precluded any knowledge about the true nature of external reality. 

Hume’s Critique of Causality
The authority of epistemological skepticism was further cemented by David Hume, who specifically undermined the causal claims of natural science, i.e. the claim that the scientist’s “laws of nature” refer to real causal connections within external reality. Hume followed Locke in holding that all belief begins with “impressions”, i.e. sensations, passions, emotions, which are the primitive imprints of external objects on our passive sensibility. We then form “ideas” which are the recollections of these impressions, their “faint images” or “copies” in memory. Hume argued that what guides us in these recollections of impressions, and thus in the formation of ideas, is the associative law of similarity: impressions which are sufficiently similar to each other get mutually associated, and thus form an idea. For example, our sense impressions of particular fires start over time to evoke recollections of each other due to mutual association, and this gives us the general idea of fire. Finally, beliefs emerge because these ideas, too, get linked to each other on the basis of association. To give an obvious example: in the past we have often experienced one sort of impression, e.g. of smoke, as immediately following upon another kind of impression, e.g. of fire, and this causes the general idea of smoke to become associated with the general idea of fire. This, according to Hume, is the full extent of what we mean when we say “fire causes smoke”. There is nothing more to our concept of causality, according to Hume, than this regular, inductively based association of one idea with another:

“We have no other notion of cause and effect, but that of certain objects, which have been always conjoin’d together, and which in all past instances have been found inseparable. We cannot penetrate into the reason of the conjunction. We only observe the thing itself, and always find that from the constant conjunction the objects acquire an union in the imagination. When the impression of one becomes present to us, we immediately form an idea of its usual attendant […].” (Hume 2003 [1739-40]: 67)

For Hume, then, the necessity we associate with the laws of causality, i.e. the idea that if one thing happens then another thing must happen, is nothing but the strength of this association, the power exerted by habit over the workings of our minds. We project this feeling of necessity onto the world, seeing the connection between one object and another as a necessary link between cause and effect. But, according to Hume, this is just an illusion, albeit a very powerful one. If we analyse our ideas more closely, Hume argued, we find no intrinsic connection between them that could substantiate a causal claim, such as that fire causes smoke. Imprisoned as we are within the circle of consciousness, we cannot know the real causal connections between external objects, if there are any at all. All we can know, Hume concludes, are the impressions and ideas of those objects within consciousness, and the merely associative connections between those impressions and ideas. Thus the causal laws of natural science evaporate into subjective feelings of necessity as we have been habituated to associate one idea with another.

The Mind-Body Problem and the Crisis of the Causal Theory of Perception
In sum, the Way of Ideas fostered epistemological skepticism by imprisoning the knowing subject with the circle of consciousness, hiding external reality behind a veil of perception. But it fostered such skepticism also in another (though closely related) way, namely, by inviting the mind-body problem. For how can mind interact with the external and supposedly material world if they are so very different, as the Way of Ideas suggests? The external world, after all, insofar as we can know it, is knowable only through its primary qualities, such as solidity, spatial position, and motion. For all we know, therefore, external reality is nothing but solid bodies interacting mechanically in space. Hence, of course, Descartes’ definition of the external world in terms of “res extensa”. But consciousness is very different from this world of extension, since ideas appear to have no solidity, no weight, no well-defined spatial position (if ideas can be said to be in space at all, they must be somewhere in my head, but where exactly?), and they do not interact by bumping into each other as material bodies do. Moreover, the conscious subject appears to have the capacity for free will, but free will seems impossible in a material world governed by causal determinism (pace Hume). Thus, consciousness appears to be in an entirely different realm of being, the immaterial realm of “res cogitans” as Descartes put it. Locke, too, drew the conclusion that mind must be immaterial, and thus categorically different from the material world which we can know through its primary qualities.

But, to repeat, if mind and matter belong to ontologically distinct realms, how can they possibly interact? Descartes wavered on this question, sometimes allowing mind-body interaction in the pineal gland, at other times doubting the possibility of such interaction; to Princes Elisabeth of Bohemia, with whom Descartes corresponded extensively, he admitted that this problem vexed him greatly and that he had no good solution to it. Locke was more resolute in that he openly declared the problem insoluble, there being no possibility for mind and matter to interact, except through divine intervention. As Locke argued, all you can get from spatial form and motion are other spatial forms and motions, and since the contents of consciousness are neither spatial forms nor motions, they cannot be caused by matter; nor can they exert causal influence on matter. However, since mind and matter obviously do interact, Locke felt compelled – much like Descartes in his solution to the problem of skepticism – to invoke God, who must have “superadded” mysterious properties to material objects, over and above their essential primary qualities, rendering them capable to cause sensations and ideas. Thus in his Essay Concerning Human Understanding, Locke writes:

“[B]ody as far as we can conceive being only able to strike and affect body; and Motion according to the utmost reach of our Ideas, being able to produce nothing but Motion, so that when we allow it to produce pleasure or pain, or the Idea of a Colour, or Sound, we are fain to quit our Reason, go beyond our Ideas and attribute it wholly to the good pleasure of our Maker.” (Locke 1996 [1989]: 237)

Obviously, no skeptic will be persuaded by this appeal to God in order to explain mind-body interaction. That Locke feels compelled to invoke divine intervention in this context only goes to show the deepness of the problem. And apart from being an ontological problem concerning the place of mind in the material world, it is also an epistemological problem, and one that aggravates the skepticism already induced by the Way of Ideas. For insofar as the causal interaction between matter and mind becomes mysterious, it becomes equally mysterious how perceptions can convey information about external objects. For here the only possible theory seems to be some version of the causal theory of perception, such that perceptions carry information about external objects because they have been caused by these objects, i.e. by the impingements of material objects on our external sense organs. Locke accepted a causal theory of perception, and he used it to explain how we can know external objects. Although the secondary qualities caused in our minds by external objects do in no way resemble those objects, as Locke admits, the situation is different with the primary qualities, i.e. with our perceptions of solidity, spatial position, figure, motion, etc. Here, according to Locke, our perceptions do resemble the objects by which they have been caused. By causing perceptions in us, then, external objects convey to us information about their primary qualities. And, for Locke, this is the only way we can know external objects, since according to him all knowledge starts with sensory impressions, the mind being a tabula rasa prior to experience. Hence the dire consequences of the mind-body problem. If the causal interaction between mind and matter becomes mysterious, to such an extent even that we need to invoke divine interaction to explain it, then clearly the causal theory of perception is of little help in explaining the veracity of our perceptions. Due to the mind-body problem, then, the epistemic position of the subject under the Way of Ideas deteriorates even further: not only is the subject shielded from external objects by a veil of perception, imprisoned in the circle of consciousness; the only way for external objects to pierce through that veil – by causing perceptions in us that resemble their primary qualities – falls away by being a complete mystery. And even if we accept mind-body interaction as an unexplainable yet undeniable given, we still have the problem raised by Berkeley (following Democritus) that we really have no perception of primary qualities apart from secondary qualities… 

References
-Arnauld, A. (1964 [1662]), The Art of Thinking. Indianapolis: Bobbs-Merrill.
-Bennett, J. (1971), Locke, Berkeley, Hume: Central Themes. Oxford: Oxford University Press.
-Berkeley, G. (2003 [1710]), A Treatise Concerning the Principles of Human Knowledge. Mineola: Dover Publications.
-Descartes, R. (1996 [1641]), Meditations on First Philosophy. Cambridge: Cambridge University Press.
-Hume, D. (2003 [1739-40]), A Treatise of Human Nature. Mineola: Dover Publications.
-Locke, J. (1996 [1689]), An Essay Concerning Human Understanding. Indianapolis: Hackett Publishing Company.
-Stroud, B. (1984), The Significance of Philosophical Scepticism. Oxford: Oxford University Press.