1. Motivations: The Computationalist Program, Artificial Intelligence, Pancomputationalism

Given that the ontology of digital states is hardly an established philosophical problem, it will be useful to briefly motivate its discussion. A clarification as to what constitutes a digital state is necessary primarily in the context where digital states are part of a certain kind of digital systems, namely digital computers. There is a significant confusion over which objects in the world are computers because there is no agreement on the criteria; Shagrir calls this the “problem of physical computation” (Shagrir 2006, 394ff). For example, on the one hand there are the proponents of a computational representational theory of mind (CRM or “computationalism”) who believe that the human mind is a functional computational mechanism operating over representations. These representational abilities are then to be explained naturalistically, either as a result of information-theoretical processes (Dretske 1981; 1995), or as the result of biological function in a “teleosemantics” (Millikan 2005; Macdonald and Papineau 2006).

On the other hand, the opponents of computationalism divide into two camps: those who think that some natural mechanisms may be computers, but the human mind is not one of these, and those who think that all systems can be interpreted as computers and so the human mind is just a computer like everything else: “every natural process is computation in a computing universe” (Dodig-Crnkovic 2007, 10) – this position is now often called “pancomputationalism”. Finally, the question to what extent artificial intelligence (AI) is possible, requires an explanation what kinds of machines computers are and what they can do in principle – given that digital computers are currently the main kind of mechanism that is used for AI.

Several further problems for a computational theory of the mind would benefit from a resolution of what constitutes a digital state. Within the context of the discussion of the computationalism mental processes are traditionally understood as information processing through computational operations over representations. Is representation a necessary feature of computing? If yes, perhaps something can be called a digital state only on presupposing mental processes in the system, so there is a threat of a circle here (unless we are looking at a feedback circle). Another is the problem of “grounding” for computational systems: “How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their (arbitrary) shapes, be grounded in anything but other meaningless symbols?” (Harnad 1990, 335). We have argued in recent papers (Raftopoulos and Müller 2006a; 2006b) that a nonconceptual phenomenal content should be at the base of such grounding. If it were to turn out that such content is necessary but is analogue and cannot be present in purely digital systems, this would show that human cognition is not purely digital – and that AI on purely digital computers is impossible. In separate work, we argue that nonconceptual content is precisely non-digital content.

I will argue in the following that being a digital state is to be a state of a type or category, but that we should not conclude from this that being a digital state is “description-dependent”. In particular, a state can be digital if it fulfills a particular function in a system of which it is a part – e.g. a representational function.

2.   Discrete vs. Continuous

In a first approximation, being digital means being in a discrete state, a state that is strictly separated from another, not on a continuum. Prime examples of digital states are the states of a digital speedometer or watch (with numbers as opposed to an analog hand moving over a dial), the digital (binary) states in a conventional computer, the states of a warning light, or the states in a game of chess. Some digital states are binary, they have only two possible states, but some have many more discrete states, such as the 10 numbers of a digital counter or the 26 letters of the standard English alphabet.

Goodman had pointed out in his early theory of representation that digital “marks” (physical entities) are “differentiated”, as he called it, precisely if they can have an exact replica: one can write the same letter “A” twice, since “A” is differentiated from any other letter. Analog marks, in contrast, are “dense”, meaning that for any pair of similar but non-identical marks, there is space for another mark in between (Goodman 1968; cf. Lewis 1971). So, the states of an analog speedometer with a hand moving in analogy to the speed of the vehicle are continuous, just as the speed it represents, and for any two places where the hand can be, there is a third in between. But which of the two characteristics is crucial for an analog state, the analogy to the represented, or the continuous movement?

This question becomes relevant in the case of analogous representations that proceed in steps, e.g. a clock the hands of which jump from one discrete state to another. Zenon Pylyshyn argues that the underlying process is analog, and this is what matters: “an analog watch does not cease to be analog even if its hands move in discrete steps” (Pylyshyn 1984, 200; Shagrir 1997, 332 agrees). James Blachowicz also thinks that being on a continuum is sufficient for being analog, taking the view that “differentiated representations may also be analog – as long as they remain serial”, his example is a slide rule with “clicks” for positions (Blachowicz 1997, 71). (Note how these authors assume a functional description, an issue to which we shall return later.)

These views ultimately fail to differentiate between analogue and digital representations. Note that the very same underlying mechanism could give a signal to a hand to move one step and to a digit to go one up (this is actually how clocks are controlled in centralized systems, e. g. at railway stations). In any case, some classic examples of digital states are clearly in a series, indeed a series of infinitely many steps: the series of the natural numbers. These two points rule out Blachowicz’ proposal to take being serial as a criterion. Pylyshyn, on the other hand, would presumably say that the underlying mechanism is already digital, so the clock is digital in this case – but surely there are systems where a digital signal is converted into an analogue one (the speedometer in most modern cars) and where an analogue signal is converted into a digital one (an analogue central clock that controls several digital clocks), so we should then say that the system has digital and analog parts. I conclude that the first crucial feature of a digital state is indeed that of being a discrete state – not excluding that of being in a series, even in a series that is analogue to what is represented.

3. Multiple Realization

As we already pointed out with reference to Goodman, it is characteristic of a digital mark that it can be realized several times. So, one can write the same word twice, even if one cannot make exactly the same mark on paper twice. John Haugeland usefully explains this phenomenon with games: chess is a digital game because we can reproduce an earlier position precisely, and we can resume the same game with different pieces. Billiards, on the other hand, is analogue, because we can reproduce an earlier position only to a certain degree of precision, and if we were to reproduce the same position with different physical objects, it would not be the same position (Haugeland 1985, 57; earlier in Haugeland 1981). The possibility of multiple realization is a result of the discrete states: since a white pawn in chess can be precisely on field C3, we can put it back on C3, or replace it with a different pawn; it does not matter that it is not identical to the earlier one, provided it is clearly a white pawn on C3.

4.   Everything Is Analogue – and Digital, too?

A given blob of ink on a piece of paper might be in a particular digital state but it has several analogue properties, too, such as a color, a shape, a history, a value, etc. In fact, all digital states we have seen so far are states of physical entities, and thus have analogue properties as well. (For our purposes, we can leave aside the question whether abstract objects can be digital.) Being digital is a property of certain physical entities that are also analogue – though they might not be analogue representations. But of which entities? Negroponte puts it nicely: “A bit has no color, size or weight, … It is a state of being: on or off, true or false, up or down, in or out, black or white.” (Negroponte 1995, 14) But, which of the black things are bits? What determines whether something is a bit?

It may seem that we can just define what counts as digital as we please, so everything is digital. Say, for example, the two of us agree that if I light a fire on a particular hill that means “the King is out of town”. Is the hill henceforth in a binary digital state? Is anything not in any number of digital states, then?

For a given physical thing (say, my desk lamp), there are descriptions as continuous (where is the light, what is its shape, what its color?) and as digital (is it on/off?), so a natural response is to say that being a digital state is relative to a particular description: Under one description the light is digital, under another it is not, so we have at least a “relativity of descriptions” (Boghossian 2006, 29).

This consequence is very tempting for digital computation and its algorithmic procedures. Alan Turing already seems to have already gone in this direction: “The digital computers […] may be classified amongst the ‘discrete state machines’, these are the machines which move by sudden jumps or clicks from one quite definite state to another. […] Strictly speaking there are no such machines. Everything really moves continuously. But there are many kinds of machine, which can profitably be thought of as being discrete state machines.” (Turing 1950, 439).

John Searle takes it one step further: “The electrical state transitions are intrinsic to the machine, but the computation is in the eye of the beholder.” (Searle 2004, 64). Oron Shagrir concurs: “… to be a computer is not a matter of fact or discovery, but a matter of perspective” (Shagrir 2006, 393), and about algorithms: “… whether a process is algorithmic depends on the way we describe the process.” “… processes are not really step-satisfaction [algorithmic]. It is simply useful to describe them this way.” “Whether a system is digital depends not only on its natural properties, but chiefly on the context in which it is described.” (Shagrir 1997, 321, 331, 335).

It now seems that not only do we have a relativity of descriptions, but that a description dependence of facts: it would then be constitutive of being a digital state that its existence is dependent on contingent social interests, namely the interest in a particular feature that makes a digital state. To illustrate this with a classical example: Being ‘digital’ is more like the word ‘constellation’ than the word ‘star’. What is part of a stellar constellation depends on what we make part of it. What is a star depends on the world and is a matter of astronomic discovery (cf. Boghossian 2006, 18, 28; McCormack 1996)

5.   Clarification I: Type/Token

Understanding the true nature of relativity here requires some further clarifications. Haugeland defines as follows: “A digital system is a set of positive and reliable techniques (methods, devices) for producing and reidentifying tokens, or configurations of tokens, from some prespecified set of types … A positive technique is one that can succeed absolutely, totally, and without qualification; … Many techniques are positive and reliable. Shooting a basketball at the basket is a positive method (for it getting through), for it can succeed absolutely and without qualification;” (Haugeland 1985, 53f) Demopoulos thus calls being a digital mechanism of a certain type being a member of an “equivalence class” (Demopoulos 1987). Harnad talks about “symbol tokens” – but not of types (Harnad 1990, 1.2). The characteristic of “multiple realization” (see above 3) is crucial, so there must be a  “positive technique” to produce perfect realizations that are clearly of this digital state.

Multiple realization, however, this is not a feature of certain types, it is a feature of types, quite generally. For example, a transistor can be in a voltage state that is clearly of type “on” or “off”, but it can also be on the borderline between the two – it just so happens that our computing machines are made with systems that do not usually get stuck in intermediate states. Every digital state is also on a continuum: the digital speedometer might change quickly from one number to another, but it does have intermediate states – just that these are not states of numbers, not states of these types, of these descriptions. What is crucial here, therefore, is that a digital state is of a type. If it is of a type, then there can be multiple perfect realizations of it: No matter how many borderline cases a type happens to have (some have many, some have none), there is always the possibility of clear cases, and that is what is needed for being a digital state; we need to fulfill the implied semantic normativity of the “token of a type”. So, we require in a first instance that a digital state is a state that is a token of a type. What we need to see now is which tokens of a type are the digital states.

6.  Clarification II: Levels of Description

In a next step, it is helpful to differentiate at least three levels of description of a proposed candidate for being in digital or digital computational states: (a) physical, (b) syntactic and (c) semantic levels – something only very few people do, despite the tradition of functionalism (Pylyshyn 1989, 57; Harnish 2002, 402f).

The physical level (a) is that of the physical ‘realization’ of the computation – this is presumably what Searle had in mind with his “electrical state transitions” (above).

That physical state is in (b) a particular digital state on the syntactic level (a binary state, or a number, a letter, a word). It is at this level that a particular mathematical function is computed, it is fully specified by specifying it on this level.

(c) That digital state in turn may represent something else, e.g. a truth value, a time, or a color, let us call this the semantic level. What is represented at this level may, again, have representational functions on several levels (the color can represent a political opinion, etc.).

A digital computer works because it is constructed in such a fashion that its physical states cause other physical states in a systematic way, and these physical states are also digital states on the syntactic level. The semantic level is not necessarily present and is not necessary for the digital system or digital mechanism. Contrary to popular belief, a computer does not require semantic content to function, (e.g. Boden 1990; 2006, 1414ff) and (Haugeland 1985, 66; 2002, 385).

Given this clarification of levels, we can re-evaluate the understanding of digital states. The semantic level allows for a true relativity of facts, not just of descriptions: The same computer following the same algorithm can be said to compute different things. This is hardly surprising. For example, it may well be that what a computer does with the same binary sequence is to add two numbers or to change one letter to another. Whether we want to regard the binary sequence as the one or the other will depend on the context. So, these binary states can have any content; just like “2 + 2 = 4” can add apples or pears. This, however, does not make the addition itself stand in need for interpretation. Contrary to popular belief, it does not show that there is a relativity of facts on the syntactic level, on the level of digital states.

7.  Clarification III: A Digital State is a Token of a Functional Type

It is useful to note that not all systems that have digital states are digital systems. We can, for example, consider the male and female humans entering and leaving a building as digital states, even as a binary input and output, but in a typical building these humans do not constitute a digital system because a relevant causal interaction is missing. In the typical digital system, there will thus be a digital mechanism, i.e. a causal system with a purpose, with parts that have functions. Digital mechanisms in this sense may be artifacts (computing machines) or natural objects (perhaps the human nervous system). However, it seems clear that not all digital states are parts of computational systems: the words in this paper are digital states, but their function is not computational.

If  being of a type was the criterion for being digital, then everything would be in any number of digital states, depending on how it is described. However, what we really should say is that something is digital because that is its particular function. My desk lamp is always in a digital state, because being on/off is part of its function. The first letter of this sentence is in the digital state of being a “T” because that is its function – it is not an accidental orientation of ink or black pixels. The sun, on the other hand, is not in a digital state at present, though it can be shining or not shining at some place.

We make artifacts where some physical states cause other physical states such that these are physical states of the same set of types, e.g. binary states. (Note that one machine might produce binary states in several different physical ways, e.g. as voltage levels and as magnetic fields.) If someone would fail to recognize that my laptop computer has binary digital states, they would have failed to recognize the proper function of these states for the purpose of the whole system – namely what it was made for. The fact that a logic gate in my laptop is a binary state depends on whether it has that function and is not description dependent. (And the fact that it computes is crucial to its function, but not to that of, say, my shaving brush – so pancomputationalism seems misleading here.)

I conclude that we should say a state is digital if and only if it is a token of a type that serves a particular function.

8.  Which States Are Digital?

At this point, it is clear that the description dependence of being digital depends on that of having a function. Functions are a very large issue, let me just indicate why one might think that there may be some facts here that are not description dependent.

In the case of an artifact, we assume a functional description. If the oil-warning light on a car dashboard is off, is it in a digital state? Yes, if its function is to indicate that nothing is wrong with the oil level. (It may serve all sorts of other accidental functions for certain people, of course.) But if the light has no electricity (the ignition is off), or if it was put there as a decorative item, then the lamp is not in a digital state “off”. It would still be off, but this state would not be digital, would not be a token of the same functional kind.

In the case of a natural object, the allocation of proper function is dependent on teleological and normative description of systems (cf. Krohs 2007, esp. 2.2) – a problematic but commonplace notion. The function of a human’s legs seems to be locomotion (and kicking balls), but we are not tempted to say that the leg is in digital states, while perhaps the muscle cells are – with respect to their function. Whether or not the legs are digital, they can be simulated (to an arbitrary degree of precision) on digital systems – only that the simulation will not walk, it will just “walk in the simulation”.

In the case of the human nervous system, there are the questions whether it is a digital system on the level of mental functions, and whether it is a digital system on the level of cell properties and interactions. Many neuroscientists think of the latter in digital computational terms. Computationalists think that representational function makes the mental level a digital computational system as well. Reproducing it in an AI computer system would thus yield mental properties.

What I have tried to show here is that these are questions that deserve answers, not just decisions.

9.  Acknowledgements

I am grateful for audiences at the universities of Tübingen and Mälardalen for useful comments, especially to Alex Byrne and Kurt Wallnau. My thanks to Gordana Dodig-Crnkovic and Luciano Floridi for comments on an earlier draft. Thanks to Bill Demopoulos also.

Vincent C. Müller

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