If consciousness cannot be explained by algorithms, then, by default, would you have to rely on a supernatural explanation?
Answer by Lev Lafayette:
The following is copy-paste, but dammit, I wrote it in the first place and it's (exhaustively) on-topic.
tl;dr. The foundation of consciousness is having shared symbolic values. Whilst consciousness cannot be reduced to physical phenomena, this doesn't mean it doesn't arise from physical phenomena in a social setting (supervenience).
Mary, the Swampy Philosophical Zombie, Is In Your Chinese Room! Problems With Reductionist Theories of Consciousness
(I intend to use this title for a journal article on the subject)
1.0 What Is Consciousness?
"Consciousness is a fascinating but elusive phenomenon. Nothing worth reading has been written about it."
Stuart Sutherland in the 1989 International Dictionary of Psychology
1.1 Consciousness is variously defined along with sentience (from the Latin “to feel”) and sapience (Latin “to know”, or “to be wise”). "Consciousness" derives from Latin conscientia which primarily means moral conscience (knowledge-with, shared knowledge). Descartes was the first to use it in the sense of the individual ego, but which was expanded by Locke to include moral responsibility. Consciousness is typically described in terms of phenomenological subjectivity; awareness, a sense of self, which is also applied in contemporary medicine as a continuum (from being fully alert and cognisant to being disorientated, to delerious, to being unconscious and unresponsive). The historical definition suggested social co-knowledge (con- "together" + scire "to know") suggesting moral reasoning (conscientia, conscience) and language. This original use is still applied in law with the concept of legal responsibility with consciousness.
1.2 Consciousness is distinguished by Ned Block between “phenomenal consciousness” (P-consciousness) of pure experience, sounds, emotions etc., and “access consciouness” (A-awareness) of introspection, memory etc. The exploration of consciouness as experience and memory is in the philosophical school and psychology of phenomenology. There is also a theoretical distinction between the "easy problem of consciousness", such as functional responses, perceptual discrimination etc, and the the "hard problems of consciousness" (qualia, such as colours, tastes). The hard problem is answering why physical processing gives rise to an inner life at all (Chalmers, 1995).
1.3 The philosophical concept of consciousness has been criticised from sources as varied as Marx, Nietzsche and Foucault. Marx considered that social relations preceeded consciousness (“It is not the consciousness of men that determines their existence, but their social existence that determines their consciousness.”), whereas Nietzsche reversed the conception of free will and moral action ("they give you free will only to later blame yourself"). Some philosophers, elimintavist physical monists, deny the extistence of consciousness at all.
1.4 There is a strong tie between consciousness and language (in its broadest sense). Medical and legal opinion both agree that assessments of consciousness must include the capacity to engage in communication. A concept of 'self' that is beyond the instinctual is only formulated through language and culture with the handful of 'feral children' (e.g., the Genie experience) serving as evidence. Descartes also argued that the lack of language in animals indicated a lack of lack of access to res cogitans, the realm of thought (although many animals have since been shown to engage in fairly sophisticated communication).
"The limits of my language mean the limits of my world.", Ludwig Wittgenstein, Tractatus Logico-Philosophicus (1922), Section 5.6
2.0 Models of Consciousness
2.1 There are two broad models of consciousness as they relate to the mind-body problem (and related subjects such as materialism and idealism). Monism argues that the mind and the body are the same; dualism argues that they are separate. Within monism is there is essentially two types; idealistic monism and physicalist monism; they have a perhaps surprisingly degree of similarity.
2.2 The former, particularly common in some branches of religion, consider that all is consciousness. A particularly strong example is that of Bishop George Berkeley, who argued for "empirical idealism", who argued (effectively) that the universe, and all that is experienced, is a figment of God's imagination. This is very similar to the Hindu notion of Brahman ("non-dual pure consciousness, indivisible, incorporeal, infinite, and all-pervading"), but distinct from the Buddhist dharmic samara/nirvana dichotomy.
2.3 Physicalist monism argues that there is no distinct mental states from physical brain and nervous-system states. Eliminativism, for example, argues that like astrology and alchemy eventually eliminated false folkloric notions from the sciences of astronomy and chemistry, so to will the mental states of everyday discourse (e.g., intent, belief, desire, love, pain) will be shown to be false, as will the study of psychology. The proposition is argued by philosophers such as Wilfrid Sellars, Richard Rorty, Paul and Patricia Churchland and Daniel Dennett. Some eliminativists, such as Frank Jackson, claim that consciousness does not exist except as an epiphenomenon of brain function; others, such as Georges Rey, claim that the concept will eventually be eliminated as neuroscience progresses.
2.4 A related form of physical monism is reductive materialism, also known "Type Physicalism", argues that that mental events can be grouped into types, and can then be correlated with types of physical events in the brain. Its origins are with the psychologist Edwin Boring (The Physical Dimensions of Consciousness, 1933) and further developed by Ullin Place, Herbert Feigl, and Jack Smart. One conflict that arises in type physicalism is the possibility of the type-token distinction. If type physicalism is true, then mental state M1 would be identical to brain state B1. However token-physicalism, such as argued by Hilary Putnam and Jerry Fodor, argues for "multiple realisability"; the same mental state can be produced from many different physical brain states. Experiments with colour recognistion seem to support multiple realisability.
3.0 Chinese Rooms, Mary The Scientist, Swamp-men and Philosophical Zombies
3.1 Reductive monism, whether physical or ideal, can be challenged by four related thought experiments; the Chinese Room by John Searle (1980), Frank Jackson (1982), Swampman (1987) by Donald Davidson, and Philosophical Zombies by David Chalmers (1996). All three are examples of arguments that emphasise not just the importance of subjectivity and qualia, but also introduce issues relating to understanding, meaning, and language.
3.2 The Chinese Room article is specifically presented as an argument against artificial consciousness, however it is particularly important as a challenge to physicalist monism which, like the AI advocates of computationalism, argue that the mind is a information processing system operating on symbols (c.f., Alan Turing Test). "The Chinese Room" takes Chinese characters as input and, by following the instructions of a computer program, produces other Chinese characters, which it presents as output. Whilst it (being the system, or the individual processing the data) can carry on a conversation, at no point does it understand the characters. As Searle (1999) argues: "The program enables the person in the room to pass the Turing Test for understanding Chinese but he does not understand a word of Chinese".
3.3 One strong response to the Chinese Room argument concedes the example, but challenges it with a robot that has extended sensory system and therefore attaches semantic correlations from sensory input to symbols. The "Robot Reply" has been endorsed at different points by Margaret Boden, Daniel Dennett, Jerry Fodor, Hans Moravec et al. For Searle, this is just additional input, and whilst it may strengthen the rule-based system, still doesn't provide understanding. Tim Crane eventually ties this criticism with social interaction, something which Searle neglected to make sufficiently explicit – and therefore was prone to accusations that he was begging the question; "… if Searle had not just memorized the rules and the data, but also started acting in the world of Chinese people, then it is plausible that he would before too long come to realize what these symbols mean" (The Mechanical Mind, 1996)
3.4 Frank Jackson's "Mary's Room" is a thought experiment that is aimed against physicalism in particular. Mary is a scientist of the neurophysiology of vision, but who has done all their work in a black-and-white environment. She knows all about the physical properties of colour, wavelengths, the effects on the retina and brain etc., but has never experienced color. Once she experiences color, does she learn anything new? If she does, then not all knowledge is physical knowledge; Mary has learned about qualia; subjective, qualitative properties of experiences. Arguably, Mary has gained an acquantaince to facts or abilities that she already had.
3.5 In the Swampman argument Donald Davidson explores the mind of a replicant: "Suppose Davidson goes hiking in the swamp and is struck and killed by a lightning bolt. At the same time, nearby in the swamp another lightning bolt spontaneously rearranges a bunch of molecules such that, entirely by coincidence, they take on exactly the same form that Davidson's body had at the moment of his untimely death." Swampman would make noises that his friends and family would interpret as language, but, according to teleological theories (and Davidson's own theory of content) Swampman has no ideas about philosophy, no perceptions of his surroundings and no beliefs or desires about anything at all; Swampman has no intentional states.
3.6 A variant on Swampman is Philosophical Zombies by David Chalmers (although it dates back to Robert Kirk, 1974). It is a being that is physically indistinguishable from a normal human being, even down to neurological effects, however it lacks conscious experience and qualia; "all is silent and dark within" (Iris Murdoch). The strength of the philosophical zombie argument is that (a) we recognise that people have periods without consciousness and (b) that human behaviour to occur automatically (e.g., sleepwalking). Elaborating these to the extreme, philosophical zombies are logically conceivable (even if practically improbable).
3.7 According to the physicalists, everything – including consciousness – is reducible to pure physicality. If physicalism is true, then conscious experience must exist in such all such possible worlds that contain the same physical facts as our world (P). However it is possible to conceive of a possible world (Q) where there is no consciousness (where p-zombies exist), but the physical facts are the same. Therefore, physicalism is false. This is known as modus tollens in predicate logic. If P then Q; not Q, therefore not P.
4.0 Never Mind, It Doesn't Matter; Escaping Monist Reductionism and Avoiding Substance Dualism
4.1 In contrast with monist approaches (whether physicalist or idealist), there are a variety of dualist approaches, which argues that the mind and the brain are ontologically separate categories. There are three basic types; substance dualism, property dualism, and predicate dualism.
4.2 Substance dualism is the argument that the mind and brain are different substances. Originating with Descartes (and famously resulting in "Cartesian dualism" of res cogitans versus res extensa) it argues that the mental universe is not extensible into space, and the material cannot think. It is considered compatible with most theological perspectives that distinguish in substance between the body and the mental "soul". Whilst extremely influential in the history of the mind-body problem, substance dualism is not considered a popular theory due to numerous problems that show that the brain and mind at least have high levels of correlation (e.g., the mental effects of brain damage is indisputable e.g., Phineas Gage).
4.3 Property dualism argues that whilst there is but one type of substance (physical or ideal), but two types of properties that result; physical and mental; non-physical, mental properties (such as beliefs, desires and emotions) correlate in some physical substances (the brain), but are not reducible to these. Examples include emergentism or supervenience, with advocates ranging as far as John Stuart Mill and Jaegwon Kim. In this model mental states emerge or depend on brain states, but cannot be reduced to brain states as they have different properties. Emergence and supervenience is notably popular among biological scientists (e.g. Philip Kitcher, Elliot Sober, Alexander Rosenberg). Property dualist can be further split into epiphenomenalism and interactionism. In the former, physical states can give rise to mental states, but not the reverse. Interactionism, claims that mental states can produce material effects (and vice-versa).
4.5 Predicate dualism, advocated by Donald Davidson and Jerry Fodor, argue that while there is only one ontological category of substances and properties of substances, the predicates that we use to describe mental events cannot be reduced physical predicates of natural languages. Another description of predicate dualism, used by Donald Davidson, is "anomalous monism" (Mental Events, 1970). The theory states that (a) mental events are identical with physical events, (b) the mental events are anomalous, and are not regulated by strict physical laws. Davidson also developed the notion of supervenience to answer critics that noted that this wasn't really a form of physicalism.
4.6 A final argument against reductive physicalism is that its pragmatically impossible. Physicalism can only provides statements of facticity; quantity and spatio-temporal location. It cannot provide any information on moral norms or aesthetic expressions. Although physical facts, moral norms, and aesthetic expressions all depend, or emerge, from empirical foundations, any one approach cannot provide answer to the others; they are pragmatically incommensurable; David Dennet's Consciousness Explained, 1991, is particularly noteworthy for this category error. It is as risible to argue that morals and aesthetics are reducible to facts as it is to suggest that aesthetics or facts are reducible to moral norms etc.