Imagine a computer so powerful that it computes not just weather forecasts or language models, but the entire universe – galaxies, atoms, brains, and all. Now imagine that this computer is not a machine, but consciousness itself. This is not science fiction. It is a serious metaphysical hypothesis, with quite a number of philosophical and scientific arguments going for it.
In particlar, absolute idealism holds that everything exists because it is perceived or thought by an "absolute consciousness", which (consequently) in turn exists because it perceives or thinks itself. Thus it is through self-consciousness that the absolute brings itself into existence – a point that the German idealist Fichte in particular developed as the "self-positing" (Selbstsetzung) of the "absolute I" (though the basic idea can already be found in the Neo-Platonist Plotinus; see Gerson, 2011: 34). Absolute idealism is therefore standardly associated with the tradition that runs from Fichte to Schelling and Hegel, and from them to British idealists such as Green, Bradley, McTaggart, and the American idealist Royce.
So absolute idealism as such is not new. What is relatively new, however, is the link with modern computational science. In the following I will introduce a theory that I like to call – for lack of a better term – absolute idealism 2.0. As the term suggests, it concerns a digital elaboration of absolute idealism, in which the absolute consciousness – which underlies reality-as-a-whole – is specifically understood as a "cosmic computer", i.e., as the underlying "hardware" on which the "software" of our universe runs. Absolute idealism 2.0 thus combines the old absolute idealism – from Plotinus to Hegel and Royce – with the latest developments in digital physics, where the computational aspects of physical nature are investigated. In particular, I will argue that the popular hypothesis of the universe-as-a-computer, which emerged from digital physics, can only be understood consistently on the basis of absolute idealism.
Return of Idealism?
But let us first ask whether absolute idealism is still viable at all. After all, the ambitious systems of German and British idealism are among the great ‘losers’ of modern philosophy. Idealism was traded for physicalist materialism, according to which reality does not primarily consist of mind or consciousness, but of material particles such as molecules, atoms, and quarks; consciousness would be merely a secondary product, emerging from matter once it has reached a critical degree of organization through Darwinian evolution, as in the human brain.
Yet the victory of materialism has never been complete. As early as the first decades of the 20th century, cracks began to appear in the materialist worldview – ironically, due to the development of physics itself. The newly developed quantum mechanics seemed to assign a constitutive role to observation (and thus to consciousness) in the "collapse of the wave function", which has given rise to various (quasi-)idealist interpretations of quantum mechanics (e.g., Bohr, Von Neumann, Wheeler, Wigner, and Stapp).
In philosophy as well – particularly in analytic philosophy – a notable return to idealist positions can be discerned (e.g., McDowell and Brandom). In the philosophy of mind, we see that materialism is increasingly being questioned and a reorientation is taking place regarding the status of consciousness in the material world. As in the surprisingly popular panpsychism, in which consciousness is seen as an inherent property of all matter, including seemingly lifeless objects.
Take the experience of seeing the color red. Science can tell you which wavelengths of light hit your retina, which neurons fire in your visual cortex, and which brain regions become active. But none of that explains what it is like to see red – the vivid, subjective quality that philosophers call "qualia". This gap between objective description and subjective experience is the Hard Problem. And it remains as hard as ever.
But if
consciousness is not an effect of matter, what ontological status does it have?
Should we then, perhaps, reverse the dependency relationship and say, with
idealism: matter is an effect of / appearance in consciousness (see Hoffman,
2019)?
The Universe-as-a-Computer Hypothesis
A second physical development that – in addition to quantum mechanics – points in the direction of idealism is the rise of digital physics. In particular, the hypothesis of the universe-as-a-computer is difficult to reconcile with materialism, as we shall see. Originally developed by physicists and computer scientists such as Fredkin, Wolfram, Toffoli, Lloyd, and (albeit with reservations) Deutsch, this hypothesis has also inspired various philosophers (such as Bostrom and Chalmers) and has, of course, captured the imagination of various science fiction books and films. The Matrix (1999), in which humanity is held captive in a virtual illusory world created by malevolent robots, in particular brought public awareness to the theoretical possibility that our world is a computer simulation.
It is a dizzying thought: every rock, every raindrop, every thought you are having right now is a computational process. The laws of physics are code. The universe is running a program. Your brain is a subroutine in that program. Who wrote it? That is the question.
However, if the universe is one vast computation, then the universe might as well be described as a computer, on which the laws of nature run as software. Quantum theorist Deutsch, although critical of the universe-as-a-computer hypothesis, nevertheless points to its explanatory power: "At first sight this seems a promising strategy for explaining the connections between physics and computation: perhaps the laws of physics are formulable in terms of computer programs because they actually are computer programs" (Deutsch, 2011: 190). Various other arguments then support this conclusion.
One consideration extrapolates from the exponential growth of computing power (Moore's law) and the consequently growing possibility of generating computer simulations: at some point, computer simulations will become so realistic that they are hardly distinguishable from 'real'. In that case, physical reality might as well be understood as a virtual reality – in accordance with the principle: if it looks like a duck, quacks like a duck, walks like a duck, then it probably is a duck (see Steinhart, 2014: 78).
According to some
scientists, the universe-as-a-computer hypothesis is furthermore empirically
confirmed by certain physical properties of the universe that point to data
compression, which is a well-known technique among computer scientists and
programmers to optimize the functioning of computers (see Vopson, 2023). We
might then ask rhetorically: why would the universe use data compression if it
were not itself a computer?
The Problem of Cosmic Hardware
However, once we assume the hypothesis of the universe-as-a-computer, we also assume the distinction between software and hardware, i.e., on the one hand the algorithms of the laws of nature and on the other hand the underlying 'machine' on which these algorithms run. But what then is that cosmic hardware? It is precisely this problem that calls for an absolute-idealist solution.
The cosmic hardware cannot itself be understood in physical terms. Physical reality is precisely that reality which is described by the laws of nature; so if the laws of nature together constitute the software, then the hardware must logically precede it. The hardware constitutes a more fundamental reality, which underlies the 'virtual reality' of the physical: "According to digital physics, our universe is a software process running on a computer. Our universe is virtual. Of course virtuality does not imply that our universe is unreal. It just implies that it is not ultimately real. Just as a wave supervenes on water, so all physical things in our universe supervene on a computer" (Steinhart, 2014: 78). Ultimately real is only the underlying computer, which must then be non-physical or – as Steinhart (ibid.) puts it – "sub-physical".
Imagine playing a video game and asking yourself about the 'real world' behind the pixels. You open the game's code, but that code runs on an operating system. You open the operating system, but that runs on transistors. Eventually you hit the physical hardware – silicon chips. But if the universe itself is a simulation, what are the silicon chips made of? Looking for the 'real world' behind the video game, you never get out of the simulation...
Note, however,
that Deutsch here tacitly assumes that the cosmic hardware must itself be
physical; but it is precisely that assumption that leads to the regress. There
is thus nothing wrong with the universe-as-a-computer hypothesis as such – as
long as we assume the hardware to be non-physical.
Royce's Absolute Idealism
But then what is this 'sub-physical' substrate that constitutes the cosmic hardware? Given the fact that consciousness cannot be reduced to matter (as the "hard problem of consciousness" shows), we have only consciousness available as a possible candidate for the cosmic hardware.
Of course, the consciousness through which our universe is computed cannot be individual human consciousness, since our consciousness is functionally dependent on the brain (and thus on the physical universe in which those brains evolved). It must therefore be an "absolute consciousness" that ontologically precedes the physical universe, and hence space and time. The question now is: how can we understand the absolute consciousness from the tradition of absolute idealism as a 'cosmic computer'?
Here, the American idealist Josiah Royce is particularly important. Royce is unique among absolute idealists because he traded the Hegelian dialectic – hitherto dominant in German and British idealism – for modern mathematics as the central logic of absolute-idealist thought.
Royce wanted to elevate absolute idealism to a higher level and align it with modern scientific developments. He was bothered by the disdain with which Hegel and Bradley in particular spoke of mathematics. According to Royce, this had resulted in an unfortunate and completely unnecessary unscientific character in absolute idealism: "The contempt of the older idealism for the precise analysis of mathematical forms – its characteristic unwillingness to attend to the dry details of the seemingly lifeless realm of mathematically pure abstractions – is largely responsible for the imperfect and relatively vague character of the idealistic conception of the Absolute" (Royce, 1959: I, 526).
To remedy this weakness of absolute idealism, Royce – drawing mainly on the mathematician Dedekind – developed a fascinating theory about the mathematical structure of absolute self-consciousness, which since Fichte had formed the ontological foundation of most absolute-idealist systems. Royce also starts from Fichte's theory of the ontological 'self-production' of the "absolute I", which exists only because it perceives or knows itself. Thus, absolute self-consciousness brings itself into existence and thereby forms the ontological ground of reality-as-a-whole (see Sas, 2015).
Thus Royce:
"If all that exists exists only as known, then the existence of knowledge
must also be a known existence, which can ultimately be known only by the
ultimate knower, who as such [...] must be defined in terms of absolute
self-knowledge" (Royce, 1959: I, 400). This is the core of Royce's
absolute idealism: reality exists only as known by an "absolute
Knower" who in turn exists through "absolute self-knowledge":
"What exists, is present to the insight of a single self-conscious Knower,
whose life includes all that he knows [...] and whose self-consciousness is
complete" (ibid.).
Royce and Dedekind's Gedankenwelt Argument
How does Royce arrive at his insight into the mathematical structure of absolute self-consciousness? As mentioned, he draws on the mathematician Dedekind, known for his definition of real numbers ("Dedekind cuts"). For Royce, however, it is especially the notorious Gedankenwelt argument that is important, with which Dedekind (1888: §66) supports his mathematical views on infinity with a strikingly mentalist model.
Unlike his
definition of real numbers and his specific conception of infinity, Dedekind's Gedankenwelt
argument found little resonance among mathematicians: the concepts used – such
as the I and the reflexive structure of thought – were considered far too vague
for exact mathematics. Dedekind's assumption that human thought is capable of
infinite self-reflection (i.e., the sequence I, G, G', G'', ...) also sounded
implausible to many of his contemporaries. According to Bertrand Russell, for
example, all these reflection levels have no "actual empirical
existence" in the human mind: "Beyond the third or fourth level they
become mythical" (Russell, 1970: 139).
The Mathematical Structure of Absolute Self-Consciousness in Royce
That Royce, as an absolute-idealist thinker, was fascinated by the Gedankenwelt argument is understandable: in effect, Dedekind provides an abstract model of what Royce calls "complete self-consciousness". The set {I, G, G', G'', ...} models a fully crystallized self-consciousness, in the sense that the I not only has consciousness of itself (G), but also a consciousness of that consciousness (G'), and a consciousness of its consciousness of that consciousness (G''), ad infinitum.
In plain language: you are conscious of yourself. But you are also conscious of being conscious of yourself. And you can be conscious of that too – and so on, without end. Now, this infinite regress may be humanly impossible, but it is not a problem for absolute consciousness; it is the very engine of its existence. The absolute is not a mind that runs out of reflective levels. It is the whole infinite stack. For Royce, this infinity is precisely what makes this self-consciousness "complete": "complete self-consciousness means consciousness of an infinite series as one whole" (Royce, 1959: II, 18).
According to Royce, absolute self-consciousness cannot be understood otherwise than as infinite in this sense. In fact, this absolute-idealist context is a much more natural 'habitat' for Dedekind's Gedankenwelt proof than his psychologism, with its focus on the human thought process. Infinite self-reflection may be problematic for human consciousness, as Russell argues, but of absolute self-consciousness – which, as self-producing, underlies all of reality – one might surely expect infinity?
What particularly interested Royce (1959: I, 494-501) here was the striking parallel between, on the one hand, the recursive structure of self-reflection and, on the other hand, the recursive successor function S(n)=n+1 which, starting with n=0, generates all natural numbers. Both are recursive in the sense that they take their output as input and thereby generate an infinite series. Thus, the series S(0)=1, S(1)=2, S(2)=3, ... is structurally equivalent to the series generated by self-reflection: G, G', G'', etc. If we adopt a structuralist view of mathematics (such that mathematical objects are identical if they are structurally equivalent), then we can say that the series G, G', G'', ... is identical to the set of natural numbers ℕ.
Royce thus
interprets the Gedankenwelt argument in a way that diametrically opposes
Dedekind's psychologistic orientation, in which natural numbers – and, by
extension, all mathematical objects and relations – are conceived as "free
creations of the human mind" (Dedekind, 1888: vii-viii). For Royce,
natural numbers are rather 'creations of the absolute mind', namely through the
recursive structure of its complete self-consciousness. The timelessness of
absolute self-consciousness (which precedes the physical universe) then
guarantees the timeless 'Platonist' existence of natural numbers.
Can Absolute Self-Consciousness Be a Computer?
How can we use Royce's mathematical vision of absolute self-consciousness to formulate an idealist solution to the cosmic hardware problem in digital physics? Can we understand absolute self-consciousness in Royce's vision as a computer? With Royce's explanation of natural numbers, we have in any case taken an important step, since all computational processes can be understood in terms of computations on natural numbers (or, as digital computers do, on their binary representations).
Royce himself describes the "absolute thinking" – as it follows from the "complete self-consciousness" of the absolute – as "wandering from number to number" (Royce, 1959: I, 575), which we can interpret as a primitive conception of computation. In his explanation, however, Royce remains completely bound to the outdated work of Dedekind (see Steinhart, 2012). Royce still lacks insight into the difference between computable and non-computable functions, as well as the modern concept of an algorithm. This is not surprising given his death in 1916, while modern computer science only emerged in the 1930s with Gödel, Turing, and Church.
By thinking creatively on the basis of Royce, however, we can get quite far. To begin with, we take over Royce's idea that natural numbers are successive levels of reflection in the recursive development of absolute self-consciousness. What we can then show, in a relatively simple manner, is that the absolute is thereby also conscious of all functions on natural numbers f:ℕ→ℕ (or that it at least performs those functions). This follows in a sense from Royce's principle that the absolute has "complete self-consciousness", that it knows everything about itself that there is to know.
From this follows a specific principle that we might call inter-level self-awareness. That is: a constant self-awareness that the absolute has at all reflection levels – thereby it knows, for example, that at reflection level 4 it is the same entity as at level 9. We can then interpret this specific instance of inter-level self-awareness as a functional mapping from 4 to 9, i.e., f(4)=9. Generally speaking: the awareness of one's own identity at different reflection levels n and m amounts to a mapping from n to m, i.e., a function f such that f(n)=m. And since this, as indicated, holds for all reflection levels n and m in ℕ, it follows that the absolute performs all functions f:ℕ→ℕ.
Now, the set of
all f:ℕ→ℕ includes, as a subset, all computable functions. By performing all
f:ℕ→ℕ, then, the absolute thus also performs all possible computations. In that
sense, absolute self-consciousness is a computer. But what does it compute?
Given the essence of absolute self-consciousness, only one answer is possible:
it computes itself. This is the ultimate bootstrap: the absolute is the
hardware, the software, the programmer, and the program.
A Speculative Step: Algorithmic Information Theory and Computational Self-Recognition
But when we say that the absolute – through its consciousness of all computable functions – is also conscious of all computations, we are cheating a little bit. The concept of "computable function" does not simply coincide with the concept of "computation" in the sense of an algorithm, i.e., an effective procedure that mechanically relates an input to an output.
A computable function is merely a mapping from ℕ to ℕ for which an algorithm is in principle available. But with a computable function, the associated algorithm is not automatically included; it has to be additionally specified (and sometimes there are multiple algorithms possible for the same computable function). So how does the absolute know which functions are computable and which are not? In other words: how does the absolute obtain the algorithms that distinguish computable functions from non-computable ones?
How can we use this to solve the above problem? We must bear in mind that every f:ℕ→ℕ forms an infinite sequence of numbers, namely f(0), f(1), f(2), etc. (To be precise, each f generates the decimal expansion of a real number, such that the set of all f:ℕ→ℕ equals the set of all real numbers; see Burrill, 1967.) So by being conscious of all f:ℕ→ℕ, the absolute is also conscious of all number sequences (and thus of all real numbers).
Now it follows from algorithmic information theory that some of these sequences are ordered because they can be generated by algorithms; these are of course precisely the algorithms that execute the computable functions. The vast majority of number sequences, however, are random; they constitute the output of non-computable functions, which are vastly in the majority. The difference between computable and non-computable functions thus amounts to the difference between ordered and unordered number sequences.
The next step is more speculative, but not unreasonable: we can say that the absolute recognizes itself in the patterns of ordered number sequences, as opposed to unordered sequences where any self-recognition is absent. This is how the absolute can distinguish between computable and non-computable functions. The crux is that some ordered number sequences contain the same information content as algorithms that simulate self-conscious and intelligent life – for example, the algorithms that describe the functioning of the human brain. In short: some ordered number sequences 'embody' the algorithmic structure of the human brain. It is plausible that the absolute recognizes itself in them, i.e., that it 'sees' its own essence of infinite self-consciousness and intelligence reflected in the algorithmic structure of the human brain, as well as in other algorithms that simulate self-conscious intelligent life.
We can derive this as a principle of self-recognition or self-reflection from Royce's more general principle that the absolute has "complete self-consciousness", such that it knows everything about itself that there is to know. One of the things it can know is that some algorithms reflect its own essence. By recognizing itself in them, absolute self-consciousness becomes even "more complete".
So what does it all mean?
In short, in the mathematical unfolding of its infinite self-consciousness, the absolute discovers specific computational structures in which it sees its own essence reflected. We can then understand the physical universe as that all-encompassing supercomputation in which the absolute optimally recognizes itself. The algorithmic structures of our brains are, after all, subroutines in the supercomputation of the universe. From the perspective of absolute idealism 2.0, then, it is no accident that the laws of nature of our universe – according to the anthropic principle in cosmology – are eminently suited for the evolution of life. For in that sense, the universe is also eminently suited as a computational mirror of absolute self-consciousness.
We are used to thinking of consciousness as something that happens inside our heads. But if absolute idealism 2.0 is correct, the opposite is true: our heads – and our brains, and our universe – happen inside an infinite, mathematically structured (self-)consciousness. The algorithms that describe our thoughts are not causes of consciousness. They are mirrors. And in those mirrors, the absolute sees itself. We are not the spectators of this cosmic self-reflection. We are its most intricate, most self-aware, most breathtaking reflection.
Literature
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