9 Remarks on Absolute Idealism 2.0

Introduction
The following remarks develop in a sketchy manner the main ideas of a theory I am still working on. I intend to develop these remarks more fully in the future. I like to call this theory "Absolute Idealism 2.0" since it starts from the basic insight of traditional Absolute Idealism (developed by Plotinus, Fichte, Schelling, Hegel) but then takes this insight into a new direction by drawing on ideas from modern physics and computability theory. The basic insight from traditional Absolute Idealism, I submit, is the idea that reality is at bottom a self-conscious whole, producing itself by being aware of itself (remarks 1 and 2). Using ideas from the American Idealist Josiah Royce, I argue in remark 5 that the recursivity inherent in self-consciousness allows us to establish an intrinsic connection between self-consciousness and the recursively generated natural numbers. This then allows us to connect the Absolute-Idealist notion of self-consciousness, as the ultimate ground and essence of reality, to modern physics and computability theory, where the natural numbers figure prominently in the definition of computable functions (remarks 6, 7 and 8). Since, however, I am certainly no expert in computation, I am not entirely sure about the correctness of my application of computability theory to Absolute Idealism (this holds in particular for remark 8, which is by far the most contentious). Hence my request to the reader: if you spot difficulties, obvious mistakes or gaps in my reasoning, please let me know.

Contents:
1. Reality must be self-causing.
2. Absolute Self-Awareness (ASA) is the self-causing cause of reality.
3. Physical reality reduces to consciousness.
4. ASA is pure joy.
5. ASA includes awareness of the set of natural numbers.
6. ASA is the 'cosmic computer'.
7. Physical reality is ASA's computational self-reflection.
8. Time and evolution exist because of the Halting Problem.
9. Qualia are the reflections of ASA's pure joy.

1. Reality must be self-causing: Why is there something rather than nothing? This question, famously raised by Leibniz, remains unanswerable as long as we presuppose any of the standard conceptions of explanation, whereby one thing is caused by another (thunder by lightning, the boiling of water by fire under the kettle, the falling of a body by gravitational force, and so on). Leibniz's question targets reality as a whole, i.e. the totality of what is, and then asks why that totality is there. But, by definition, there is nothing outside the totality (not even 'nothingness') by which it could have been caused. The only way to explain reality, therefore, is through self-explanation. The cause behind reality can only lie within reality. Self-causation is the only possible answer to Leibniz's question. Clearly, however, self-causation is impossible in time. As a temporal process, causation is marked by a temporal distance between cause and effect, such that the cause precedes the effect. Self-causation would then require that the cause precedes in time its own existence, which is absurd. We must assume, therefore, that the self-causation needed to answer Leibniz's question 'happens' outside of time. Also because time itself is something, an object of sorts, a 'thing' with various properties (such as those described by physics). Time, in other words, belongs to the 'something' we are trying to explain when we ask: Why is there something rather than nothing? Since time does not explain its own existence, it must be explained by something else, ultimately by the self-causing cause of reality. But the cause of time cannot itself be in time. Thus, again, the self-causing cause of reality must be timeless.

2. Absolute Self-Awareness (ASA) is the self-causing cause of reality: But how is self-causation possible? How can something bring about its own existence. Here the self-evident experience of our own self-awareness provides us with the only empirical clue we have. The crucial point is that the circularity of self-awareness 'fits' the circularity of self-causation: as the self-causing cause is its own effect, so self-awareness is its own object of awareness. Since self-awareness essentially is its own object of awareness, it cannot exist without being aware of itself. Its being is its self-perception. It bootstraps itself into existence through self-perception. From an empirical standpoint, therefore, self-awareness is our best guess at what the self-causing cause of reality amounts to. I will refer to this as “Absolute Self-Awareness” (ASA), which is "absolute" in the sense of having an unconditioned existence, not dependent on or relative to anything besides itself. Rather, the rest of reality is ultimately dependent upon it. Since the self-causing cause of reality must be timeless (see remark 1), ASA must be timeless as well, an "Eternal Consciousness" in the phrase of T.H. Green. The 'present' in which ASA is present to itself (since self-awareness is a form of self-presence) must be an eternal present, an unchanging now (nunc stans). Clearly, then, we are not talking about individual human self-awareness, as present in you or me. None of us has brought him- or herself and the universe into existence. As empirical individuals we are biologically conditioned, brought into existence by others, subject to time. The experience of our own self-awareness may give us empirical access to the self-causation that can answer Leibniz's question, but to make full sense of this we have to generalize beyond ourselves. We have to project self-awareness to something that transcends us, the Absolute, the unconditioned 'thing' that conditions all of reality.

3. Physical reality reduces to consciousness: Since we take ASA to be the self-causing of reality, we must explain physical reality in terms of consciousness rather than vice versa (as is standardly done in scientific materialism). That it is at least possible to explain physical reality in terms of consciousness follows from the Hard Problem of Consciousness, i.e. the impossibility to explain the qualia of consciousness in exclusively physical terms. But the Hard Problem of Consciousness leaves open the precise nature of the mind-body relation; it is compatible with substance dualism, where consciousness and physical reality form two separate ontological domains (which nevertheless somehow interact). So we need further arguments to effectuate the reduction of physical reality to consciousness. Here we can appeal to Russellian Monism, which shows (a) that physical reality (as revealed by modern physics) is basically a mathematical structure, and (b) that all structure, in order to exist, requires non-structural bearers, i.e. intrinsic entities, and (c) that such entities can only be found in the qualia which elude the mathematical structures of physics (as per the Hard Problem of Consciousness). Thus the qualia of consciousness must be ontologically prior to the mathematical structures that define physical reality. In that sense, at least, physical reality reduces to consciousness.

4. ASA is pure, self-enjoying joy: A side-effect of the Hard Problem of Consciousness is that it makes clear that ASA, too, must involve qualia, or at least one quale – indeed, a quale that is somehow self-revealing, a "self-intimating what-it's-like-ness" (I owe this happy phrase to the philosopher David Pearce). But what exactly is this quale? What is it like to be ASA? Since we take the experience of our own self-awareness as the empirical key to the Absolute, and since human self-awareness is infused with emotion and volition right from the start, it would be an illegitimate abstraction to see ASA as just a 'cold' theoretical self-registering, without any emotive and volitional aspects. Thus we must see ASA as not merely cognitive self-awareness, but as will and emotion as well. But what could ASA possibly want? Since ASA is, at this point in our construction, the only 'thing' that exists, there is nothing for it to desire apart from itself. Thus, qua will, ASA can only will itself. Its self-awareness coincides with its self-willing. We can say "ASA exists because it wills itself" just as much as we can say "ASA exists because it is aware of itself". From this it follows that, qua emotion, ASA must be pure joy, i.e. self-enjoying joy. It's will for itself immediately satisfies itself, since its self-willing is at the same time the self-causing cause of its own existence. It gives itself to itself merely by willing itself. ASA is a self-aware, self-willing, self-satisfying and self-enjoying joy. Reality exists because pure joy wills itself. Cf. Nietzsche "Alle Lust will Ewigkeit..." Also see the Vedantic definition of the Absolute (what the Indians call "Brahman") as Satchitananda, i.e. the indivisible unity of being ("sat"), consciousness ("cit") and bliss ("ananda").

5. ASA includes awareness of the set of natural numbers: Up till now (as remarked in remark 2) only one 'thing' exists in our construction, namely, ASA. So how do we get from ASA to the universe around us, this multitude of physical objects, coming and going in space and time, governed by natural law? This, basically, is the old problem of the One and the Many: how does the original One produce the Many? The source of the difficulty, for us, lies in the fact that ASA, qua cause of itself, is ontologically self-sufficient, not in need of anything beyond itself. Qua self-causing, it causes just itself, and nothing more. Thus we appear to have a dilemma: to solve Leibniz's question we need a self-causing being (and experience tells us this must be ASA), but precisely its self-causing capacity creates the problem of the One and the Many. However, as Josiah Royce pointed out, once we understand the self-causing cause of reality in terms of (absolute) self-awareness, this problem is automatically solved by the recursivity inherent in self-awareness, i.e. the fact that it takes itself as object of awareness (see remark 2). In this way, self-awareness generates an infinite sequence of ever higher levels of self-reflection, namely: self-awareness, awareness of self-awareness, awareness of awareness of self-awareness, awareness of awareness of awareness of self-awareness, and so on ad infinitum. In semi-formal terms, if we describe awareness-of-something as a function f(x)=y where f given input x produces awareness-of-x as output y, then self-awareness, being its own object of awareness, becomes the function f(x)=x which generates the infinite sequence f(x)=f(f(x))=f(f(f(x)))=f(f(f(f(x))))... etc. As Royce also pointed out, this sequence is isomorphic to the natural number system N={0, 1, 2, 3, … }, which is recursively generated through the successor function S(n)=n+1 such that S(0)=1, S(1)=2, S(2)=3, and so on. Since ASA is the self-causing cause of reality as a whole, we must conclude that its first product, beyond itself, is the reality of the natural numbers. The natural numbers exist because ASA ‘thinks’ them by being recursively aware of itself. Thereby the Problem of the One and the Many is solved. Through its internal recursivity ASA generates the infinite complexity of N. Since ASA exists outside of time, we must conclude that N, too, exists outside of time. Thereby the Platonic reality of N is saved, even if that reality derives from a form (or rather the primordial form) of subjectivity.

6. ASA is the 'cosmic computer': But we do not just want N. We want to know how ASA explains the physical universe. Two considerations, when combined, suggest a clear answer. The first consideration, taken from the theory of computability, is that the notion of computation can be captured in terms of functions on N, such that all computable functions (i.e. algorithms, computations, effective procedures) are a subset of all n-ary functions from Nⁿ to N (i.e. f:Nⁿ→N). The second consideration, taken from modern physics, is that all physical processes are thoroughly computable, with the laws of nature acting as algorithms taking the present state of a physical system as input and producing the next state as output. So if we represent a physical system by a set of natural numbers (an n-tuple from N), we can then understand the natural law governing this system as a computable function. This, basically, is what modern physics does. Thus the natural laws turn out to form a subset of all computable functions. How does this solve our problem? As we have seen in remark 5, ASA is aware of N. An obvious way to see ASA as producing the physical universe, therefore, is to see ASA as computing those functions from Nⁿ to N that describe the evolution of the universe. The universe then becomes a 'digital simulation' run on ASA qua 'cosmic computer'. The fact that ASA can indeed be seen as engaged in computation follows from its intrinsic connection to N. As we have seen, each consecutive level in the recursively generated sequence of ASA’s self-reflection, generated by the function f(x)=x, corresponds to a natural number, such that f(x)=1, f(f(x))=2, f(f(f(x)))=3... etc. Since ASA knows itself as identical with itself on each such level – because f(x)=f(f(x))=f(f(f(x)))=... etc. – this self-knowledge amounts to a knowledge of equivalence relations between the natural numbers. For example, ASA knows that its identity on reflection levels 4, 7 and 15 is the same as its identity on level 2 – and this amounts to the equivalence relation (4, 7, 15)=(2). But such an equivalence relation is just a mapping from Nⁿ to N. Hence, by being aware of its self-identity on all the levels of its self-reflection, ASA is aware of all functions from Nⁿ to N, including all computable functions. Since the laws governing our physical universe form a subset of all computable functions, ASA can be said to compute our universe.

7. Physical reality is ASA's computational self-reflection: To repeat, ASA is aware of all computable functions, of which the computations that constitute our physical universe form a subset. This raises the question: Why is that subset special? Why is our physical universe realized and not any of the countless other computationally possible universes? Or should we say that all computable functions are realized, with our universe being just one of infinitely many computable worlds, all equally real? This last option would give us a computational version of the principle of plenitude: everything which is computationally possible is realized. However, it is easy to see that ASA, as we conceive it, excludes such ontological plenitude. Here we should remind ourselves what ASA essentially is, namely, self-awareness, and nothing more. It’s awareness of N, as we have seen, is just an extension of that self-awareness, as it recursively generates the infinite hierarchy of its self-reflection. Likewise, its awareness of all functions from Nⁿ to N results from the awareness of its self-identity throughout all the levels of that hierarchy. In short, ASA’s awareness of N and of all the functions from Nⁿ to N is completely subservient to one essential goal: to know itself as completely as possible. This forces us to see certain computations as privileged over others, insofar as certain computations reflect ASA’s essential properties (self-causation, self-awareness, joy) better than others do. Some computations, after all, such as the computations that describe the functioning of our brains, can be said to compute (self-)consciousness, intelligence and volitional agency. Given the fact that ASA’s sole purpose is to know itself, it is clear that those computations, which emulate intelligent organisms, will for ASA be objects of special attention, in contrast to all other possible computations. For by focusing its awareness on those computations, ASA reaches an even higher level of self-awareness, as it ‘sees’ itself reflected (‘mirrored’) in those computations. True, ASA is aware of all functions from Nⁿ to N. But only some of those functions, namely those that compute intelligent organisms, contribute to its increased self-awareness. And since, as we have seen in remark 2, self-awareness is the self-causing cause of reality, only those functions that increase ASA’s self-awareness acquire full reality. All other computable functions remain merely possible computations. This allows us to formulate the following hypothesis concerning our physical universe: it is the set of those computable functions that best reflect ASA’s essence. On this hypothesis, then, our universe is ASA’s computational mirror. And insofar as this mirror reflects ASA's pure joy, the universe can be said to be a work of art. Since ASA is self-causing through self-awareness, the physical universe too must be self-causing through self-awareness. John Wheeler's hypothesis of the self-observing universe, therefore, must be basically correct.

8. Time and evolution exist because of the Halting Problem: ASA is aware of all functions from Nⁿ to N, for all possible inputs (remark 6). But, as Turing showed, the totality of these functions includes both computable and uncomputable functions. (This follows from the fact that, since a computable function reaches its output after finitely many steps, the set of all computable functions is countable, whereas the set of all functions from Nⁿ to N is uncountable; hence by far most of these functions are uncomputable.) So how can ASA know 'in advance' which functions are computable and which are not? Here, it would seem, ASA is faced with the undecidability of the Halting problem (as demonstrated by Turing), i.e. the fact that there is no general algorithm for deciding which functions are computable (i.e. which functions halt after finitely many steps). However, on closer inspection it becomes clear that ASA is not affected by the undecidability of the Halting Problem. This follows from the fact that ASA exists outside of time (remarks 1 and 2). Thus the question how it can know 'in advance' which functions are computable simply does not arise for ASA; the distinction between before and after does not apply to it. Being timeless, ASA is aware of all functions from Nⁿ to N at once, and thus it 'sees' immediately which functions halt after a finite number of steps and which do not. Thus ASA needs no algorithm for solving the Halting Problem, and therefore the undecidability of that problem poses no difficulty for it. Nevertheless, the Halting Problem is undecidable for ASA's computational image, i.e. the complex computation that best reflects ASA (let's call this complex computation "the Intellect", after Plotinus). Since ASA has awareness of all functions from Nⁿ to N, the Intellect – as ASA's image – must have the same awareness, only this time computationally executed (since the Intellect is nothing but computation). So the Intellect must compute all functions from Nⁿ to N, and then find those computable functions that best reflect ASA (thereby the Intellect in effect computes itself, true to its nature as computationally executed self-awareness). But, as said, this means that the Intellect is faced with the undecidability of the Halting Problem. In this way a radical uncertainty is introduced in the Intellect's knowledge: it can't compute in advance which functions are computable. This, I venture, is the reason why time exists. The uncertainty which exists for the Intellect, about which functions will turn out to be computable, is the uncertainty that defines the future, its inherent unpredictability. This is not to say that the Intellect itself exists in time. As ASA's computational image, the Intellect itself exists outside of time, as a timeless mathematical structure in ASA's self-awareness. But in computing which functions are computable, and which of those computable functions best reflect ASA, the Intellect nevertheless produces time. Given the undecidability of the Halting Problem, the only way for the Intellect to find out which functions are computable is through a form of dovetailing (a familiar technique in computer science), such that it simultaneously executes step-by-step all functions from Nⁿ to N (so first it computes simultaneously the first step of all functions, then simultaneously the second step of all functions, then simultaneously the third step of all functions, and so on). Remember that the Intellect itself exists outside of time, so this simultaneous stepwise execution of all functions poses no problem for it. Then, as the Intellect goes along from step to step, it will after a finite number of steps find some computable functions (those that halt), whereas the stepwise execution of all other functions continues. For these latter functions, the Intellect can't know in advance if these are genuinely uncomputable or if they will also halt if more computational steps (of a finite number) are taken. In other words, the Intellect will never know if it has found all computable functions. So the process of the simultaneous stepwise execution of functions will never stop. This unending process of the stepwise disclosure of which functions are computable, and which of these computable functions best reflect ASA – this process, I venture, is time itself (the stepwise disclosure of the future). Time exists, then, because the Intellect is subject to the undecidability of the Halting Problem. Moreover, since the Intellect can't know in advance which computable functions it will find by dovetailing all functions from Nⁿ to N, this process is also a process of evolution, whereby the computations that best reflect ASA are only gradually discovered by the Intellect as time progresses. This evolution is the process of the Intellect's self-discovery, since the Intellect is that complex computation which best reflects ASA's essence. The evolution in time of our physical universe (which in remark 7 we hypothesized to be ASA's computational image), therefore, is the coming to self-awareness of the Intellect. The physical universe is the Intellect insofar as it has computed itself, insofar as it has become self-aware.

9. Qualia are the reflections of ASA's pure joy: Pure joy is the self-intimating quale in which ASA consists (remark 4). But how do all other qualia emerge, i.e. the qualia inherent in our conscious experience of ourselves and of our physical surroundings? My hypothesis is that these qualia emerge through the refection of ASA's pure joy in its computational mirror, i.e. the computations that constitute the physical universe. Through ASA's computational self-reflection its pure joy gets reflected back to it in multifarious ways, thereby breaking up the original unity of its pure joy (the arch-quale) into a multitude of qualia.