There are three classes of meta-analyses concerning the problems of whether human thinking can be formalized and/or whether machines can think in a human sense. The first class, the “mysterian”, denies that either of these is possible because of mysterious properties of mind or consciousness which we cannot analyze or duplicate physically. The second class denies that these are possible on the grounds that our conceptual repertoire is insufficient, perhaps intrinsically insufficient, to the task, i.e., that the questions may be answerable, but not by human beings, or at least not by humans at our present level. This claim, at its strongest, relates to conceptualizing in a deep sense, involving something like the Kantian categories, and maintains that our fundamental human categories of understanding are inadequate to the task, perhaps irredeemably so; at its weakest, it asserts that our theories and understanding of the world are at present inadequate in some fundamental sense. The third class is basically that of present-day scientific materialism, which argues that the lack of such solutions is a result of our lack of knowledge and theory, and that this lack can be remedied through further research and theoretical insight. In considering some of the arguments for the inability of the digital computer to realize mind, then, I will immediately dismiss the first and second positions, not on the grounds of agreement or disagreement, but rather on the grounds that, given either of those positions, it is clearly the case that the answer is negative to both questions. It is the third position which makes for perhaps the most heated arguments, and it is this position that I will assume in this essay.

We are currently attempting to emulate or realize mind through our artifacts, with some limited success. Engineers and computer scientists are pursuing this goal with no regard for the arguments of philosophers; yet those arguments, while largely irrelevant to the details of applications involved, might have great impact, if clearly enough formulated, on the general directions of research. Dreyfus, for example, in What Computers Can’t Do (Dreyfus, 1972), sparked numerous debates within the AI community. I will concern myself here with two other critics of AI. John Searle is a modern critic of the AI position; his arguments are more analytically oriented than those of Dreyfus and thus perhaps more relevant to the reductive approach underlying most of AI. Charles Peirce was present at the inception of the field of AI, and his analyses of mind and of logic are in part directed toward its conceptual underpinnings. In addition, I will present an inductive argument against finite-state devices and AI toward the end of this essay. I will suggest that consideration of the relationships between these various positions might update this dispute and indicate a direction which might prove fruitful in resolving the issue as to what type of machine might ultimately demonstrate “mindedness”.

Searle’s argument (Searle, 1990), as we will see, is based on an analysis of language and formal systems that assumes a clear distinction between syntax, i.e., rule-based operations on symbols which proceed independently of the symbols’ meaning, and semantics, i.e., operations based on the meanings of symbols. He maintains that computers are devices that exclusively employ syntactical operations. Given this point of view, Searle concludes that computers cannot think in the sense that a human being can; since computers cannot assign meanings, but only apply syntactical rules, they cannot possess understanding or mind. as we shall see below. Peirce, on the other hand, who was fascinated by the possibility of machine intelligence[1], explicitly repudiates such a distinction. Peirce's analysis of thought is radically different from Searle’s, in that he differentiates between three types of thought, all describable as variants of a basic syllogism; but maintains that only one is simple enough to be realized by computers. Although some machines, for Peirce, are extensions of people’s thought processes, and some are literally thinking machines, he concludes that the computer will never be able to think in a fully human manner, i.e., employing the full range of human capacities.

Peirce (Peirce, 1992c) offers detailed speculations and arguments (pp. 15-16) concerning the biology and physiology of thinking; these are based on some knowledge of neurophysiology and on speculation about the processes of the central nervous system (CNS). He argues that, starting with extremely complex combinations of very simple sensations, no more than the “excitation of a nerve” (p. 16), and continuing through various processes of inference, the mind creates conceptions of “mediate simplicity” (p. 16) which reduce the “inconceivably complicated” sets of sensations to simpler, abstract, concepts. These concepts are the bases and the components of our understanding of the world. To summarize one of his examples (p. 16), the motion of an image over the retina produces, through such inferential processes, the conception of space.

For Peirce, then, the elements of thought he termed “cognitions” were, roughly speaking, the operational building blocks of mind. Thus, in that same essay, he argues that cognitions, which he uses to refer to the contents (and, eventually, the objects) of thinking, are allied to sensation, and that there is no independent faculty of intuition. This latter faculty would involve the “determination” (p. 12) of a cognition “directly by the transcendental object” (p. 12). Peirce will argue that the interactions of these cognitions— our mental operations, constituting the basis for our inferences about the world and about our thinking — may be described in terms of one of several types of logical processes (Peirce, 1992d, pp. 28-55).

At this point, Peirce seems to have concluded that mind can result from formalizable operations on arbitrary symbols. That is, if a description of thinking may be couched in terms of logical processes (for further explication of these terms, see the next section), might these same processes be the equivalents of formal logical or algebraic procedures? If Peirce can relate thinking, in general, to cognitions whose interactions are describable in terms of formally manipulable inferential processes, the conclusion seems to be that this same cognition is based on a brain physiology describable by, perhaps even employing, formalizable operations. At first glance, then, his argument seems to start similarly to Searle’s Chinese Room argument (e.g., Searle, 1990), but to come to the opposite conclusion.

However, as will become clear, the above analysis is too superficial. Although Peirce’s position on the logic of thought and language differs radically from Searle’s, he arrives, in fact, at very similar conclusions.

The Chinese Room argument

A digital computer is a device that carries out processes by changing the values and spatial distributions of some physical entity, such as the voltages in various elements of semiconductor circuitry, in discontinuous steps in accordance with a finite set of well-defined (but not necessarily consistent) rules (in the case of modern computers, those rules are related to - but not identical with - Boolean algebra, a logical calculus devised by the mathematician George Boole [Boole, 1958]). When numbers are represented in these devices, they are done so by a placeholder (digital) symbolism rather than by a quantitative (analog; see note 4) symbolism.

Searle, in his Chinese Room argument (Searle, 1994, pp. 200-220), argues that while the symbols' manipulations must be driven and instantiated by physical substances and processes, those physical processes have no relationship except the most abstract to the symbolic processes that they realize. His argument is twofold: first, that in these systems, since they employ abstract logic, the meanings of the symbols are entirely arbitrary: syntax is independent of semantics, and these systems’ rules are exclusively syntactical. Second, in the instantiation of this logic through the above physical processes, the relationship between any given physical quantity and the symbolic element it represents is also entirely arbitrary. In other words, the physical entities — the voltages, in this example — which comprise the functional elements of the device are, qua physical entities, irrelevant to the computer's function as a symbolic manipulator. In fact, it is quite possible, as Searle points out, to construct computers out of "cats and mice and cheese or levers or water…" (Searle, 1994, p. 207). As long as the dynamics of their relationships are constrained to correspond, at some level, to the syntactic relationships of symbolic logic, the actual physical realizations are irrelevant. In digital computers, he claims, all that is happening is the creation and alteration of strings of symbols that must be subsequently interpreted by a "minded" human being.

The Chinese Room argument, then, proceeds as follows: a person totally ignorant of Chinese sits in a closed room, and receives, through a slot in the wall, cards with Chinese characters on them. The person goes to a rulebook and finds some rule (or set of rules) relevant to the character (or the last few characters) just presented, and as a result of those rule-determined operations, picks some other Chinese character(s) from a pile, and passes it out through the wall. According to what Searle calls the "strong AI" position, "thinking is merely the manipulation of formal symbols" (Searle, 1990, p. 26). Thus, if the rules are complete, according to that position, a Chinese speaker will be able to hold intelligent conversation with the “room”: the totality of the operator, rules, and symbols. But Searle argues that there is no thing or person in the room that understands Chinese (nor does the room as a whole). Therefore, Searle concludes, even if that room could intelligently converse in Chinese it does so mindlessly, with no possible basis for understanding the symbols. Since, Searle argues, computers operate in this same fashion, solely on the basis of syntactic operations, they too are and must always be mindless. Thus, since "a physical state of a system is a computational state only relative to the assignment to that state of some computational… interpretation" (p. 210), one cannot generate mind from these arbitrarily instantiated formal processes. Searle notes that an observer who did not recognize Chinese characters, looking through a one-way window into the room, might understand the symbolic manipulations as stock-market formulas, and apply them consistently according to that interpretation (Searle, 1990, p. 31).

Peirce, logic, and thought

Several important issues raised by the above argument concern the nature of formalizability, of manipulations of symbols, and of the various types of formal logic. Peirce wrote voluminously on these subjects. Roughly speaking, according to Peirce (e.g., Peirce, 1992a), there are three basic types of logic, derived from the three-part syllogism. This syllogism consists of

R, a rule: (the beans in this bag are white),

C, a case of the rule: (these beans are from the bag),

E, a result: (these beans are white)

(Peirce, 1992a, p. 188).

By altering the order of the elements in this expression, Peirce realized that one could symbolize entirely different types of thinking. Thus, deduction consists of statements in the above order: (1) R, C, E; induction in the order (2) C, E, R; and hypothesis construction (also termed "abduction" (e.g., Houser & Kloesel, 1991, p. xxxviii; also Peirce, 1998b, p. 95), the order (3) R, E, C (Peirce, 1992a, pp. 188-189).

Before proceeding further, it is necessary to elaborate on Peirce's classification of types of thinking. "Firstness" has to do with "immediate feeling" (Peirce, 1992b, p. 260), a thinking involving only the "fleeting instant," which once past, is "totally and absolutely gone" (p. 259). These instants run in a “continuous stream through our lives” (p. 42). "Secondness" is type of thought in which the will appears, consisting "of something more than can be contained in an instant" (p. 260); the continuous stream of instants of thought begin to be combined by an “effective force behind consciousness” (p. 42). "Thirdness… is the consciousness of process, and this in the form of the sense of learning, of acquiring… the consciousness of synthesis" (p. 260).

Peirce then goes on to speak of three different senses of thirdness. The first is "accidental," and corresponds to "association by contiguity." This is interesting in its relation to behaviorism, to deductive logic, and also to our perception of space, for Peirce states that "we cannot choose how we will arrange our ideas in reference to time and space, but are compelled… [by an] exterior compulsion" (p. 261). The second type of thirdness is "where we think different things to be alike or different" (p. 261); a thinking in which "we are internally compelled to synthetise them or sunder them… association by resemblance" (p. 261). One is reminded of associational psychology, some aspects of cognitive psychology, and of inductive logic. The third type of thirdness is the highest, which the mind makes "in the interest of intelligibility… by introducing an idea not contained in the data" (p. 261). Here we have the kind of thinking involved with hypothesis construction and testing, with science in general, and with art. Peirce states, "The great difference between induction and hypothesis is, that the former infers the existence of phenomena such as we have observed in cases which are similar, while hypothesis supposes something of a different kind from what we have directly observed" (p. 197).[2] Peirce further states, "the work of the poet or novelist is not so utterly different from that of the scientific man" (p. 261). Habermas, commenting on abduction, states that, "what Peirce called 'percepts'… depend upon those limiting cases of abductive inference which strike us in the form of lightning insights" (Habermas, 1995, p. 254). Peirce held that the most important and creative aspect of the mind, i.e., "synthetic consciousness, or the sense of the process of learning" (Peirce, 1992b, p. 264), related to "thirdness" (p. 260) operates through a combination of habit and chance. It "has its physiological basis… in the power of taking habits" (p. 264). In addition, however, he maintains that "it is essential that there should be an element of chance… and that this chance or uncertainty shall not be entirely obliterated by the principle of habit" (p. 265). For Peirce there seems to be a kind of balance between habit: fixed thinking and behavior, and chance or uncertainty: fluctuations in thought and behavior, producing variants in fixed habitual patterns.

Peirce's stance on formal deductive logic is thus clearly delineated. He states that "formal logic centers its whole attention on the least important part of reasoning, a part so mechanical that it may be performed by a machine" (Ketner, 1988, p. 44). And we can now appreciate that this results from either or both of “firstness”, and thirdness of the first type, where nothing external to the given data is required or arrived at, and the sequence of association is "externally compelled." To put this explicitly in terms of the computer, this external compulsion is the equivalent of an algorithmic procedure, in which every step is determined in advance, i.e., every process realized by the physical machine is “compelled” through its programming.

We thus can relate the three types of syllogism above to the different kinds of thirdness. Deduction is related to the lowest kind, the association by contiguity, since it can proceed solely through habit, without choice, and can, in addition, be performed by machines. Induction, since it involves ideas of similarity and difference, and association by resemblance, would seem to employ the second type of thirdness; whereas abduction must employ the last type. This is a much richer classification of logic and thought than Searle's, insofar as the Chinese Room argument is concerned, and it opens several questions about the relationship between the two positions.

But Searle's question remains: despite its algorithmic nature, is this kind of thought "minded"? Does it require, or may it possess, understanding? Searle regards syntax and semantics as inherently separable in formal languages, and thus the difference between purely formal operations on symbols with arbitrary meaning is clearly differentiated from operations on symbols possessing meaning, i.e., semantic operations. In addition, while understanding may involve neural processes which are entirely unconscious but that may cause "conscious phenomena" (Searle, 1994, pp. 239-241), those neural processes are not mental processes. Unconscious neural processes can however correspond to, i.e., produce the same effects, as syntactic rules. Thus for Searle, only unconscious neural processes may be algorithmic; consciousness, dependent on but not identical with those neural processes, intrinsically involves meaning, and thus transcends algorithmic processes.

Peirce, on the other hand, regards all sensation as conscious. Thus, the entities he calls “sensations” at the lowest level seem to be mental entities that, although we may be aware of them in the instant in which they are present to us, we are not aware of as individuals over time. In fact, he claims (Peirce, 1992d, pp. 42-44) that those sensations are claimed to be “unanalyzable,” and “something which we cannot reflectively know” (Peirce, 1992d, p. 42).[3] However, as this quote indicates, although these sensations are immediate, fleeting, and gone "absolutely" when their instant of perception has passed, during the instant that they are present, they are mental contents. There is, in addition, “a real effective force behind consciousness” (my Italics; p. 42) — and note that this “force,” which works on the sensations, while it seems unconscious, is still, for Peirce, mental — which unites the individual sensations in their “continuous stream” into those mental events and contents of which we are continuously aware. Peirce, then, seems to have as his starting point a class of entities which correspond, roughly, to nerve signals which have something like the status of pre-qualia mental contents, a type of entity that Searle denies, if I understand him correctly.

Peirce's position on symbols derives from his analysis of mental contents. In contrast to Searle, he recognizes no symbols without meaning, i.e., related solely by syntactical rules. His extensive classification of types of signs — there are up to sixty-six types (Houser & Kloesel, 1991, p. xxxvii) — includes pictorial or analog symbols: icons which correspond structurally in some relevant manner to that which they symbolize.[4] Those icons, according to Peirce, are necessary for all thinking, including deductive logic. In addition, according to Ketner, Peirce uses the term "diagram" much more generally than to refer to pictures or pictograms, and instead refers to virtually all models — verbal, pictorial, or mathematical — as diagrams: "Indeed, 'diagram' for Peirce is roughly equivalent to a generalized notion of 'model'." (Ketner, 1988, p. 47). Thus, in speaking of errors which are made about the nature of logic, he states, "one such error is [in thinking] that demonstrative reasoning is something altogether unlike observation… [iconic representations] represent relations in the fact by analogous relation in the representation… it is by observation of diagrams that the [deductive] reasoning proceeds" (Ketner, 1988, p. 41).

The above serves to further explicate the differences between Peirce and Searle. Peirce was explicitly stating that deductive reasoning, as performed by mathematicians, involves much more than syntactical operations, in fact, that the representations necessary for deductive reasoning are, in part at least, not, as icons, arbitrary symbols. Even though we have seen that for him deductive reasoning is in part algorithmic, i.e., capable to some extent of being performed by machines, it necessitates, in toto, the highest levels of thought (e.g., "every kind of consciousness enters into cognition" [Peirce, 1992b, p. 260]). It is, then, not as a consequence of a fundamental difference in types of symbols and/or symbolic operations, with or without semantic content, but as a consequence of different levels of thought that Peirce argues for the non-computability of non-algorithmic logic.

Thus Peirce, in contrast to Searle, would not, I believe, allow any separation between syntax and semantics, in the following respect. He would claim that what Searle is terming "syntactic rules" partake of what Searle would consider semantic characteristics, and, generally, that such rules must so partake. However, if those rules were simple enough so that pure deduction, i.e., thinking of the first type of thirdness, was all that was required, then a machine could indeed duplicate such "routine operations" (Peirce, 1992d, p. 43). In this simple sense, for Peirce, a digital computer has "mind" or "understanding." However, for Peirce, the crucial difference between man and machine lies in the use of "fixed methods" of thought, in contrast to "self-critical… formations of representations" (p. 46). "If a machine works according to a fixed principle… unless it is so contrived that… it would improve itself… it would not be, strictly speaking a reasoning-machine" (p. 46). The difference for Peirce, then, was not in a syntax/semantics difference, but in a difference in "self-control": "routine operations call for no self-control" (p. 43; also see below). That is, routine operations, which we now might term algorithmic procedures, while they may entail self-critical modifications and learning from error, nonetheless perform no hypothesis testing in the sense explicated above (the third sense of thirdness). In fact, Peirce states, referring to the difference between mental modeling in reasoning and laboratory experimentation with apparatus, that "every machine is a reasoning machine, in so much as there are certain relations between its parts… that were not expressly intended. A piece of apparatus for performing a physical or chemical experiment is also a reasoning machine… [they are] instruments of thought, or logical machines" (p. 52). A position similar to this, perhaps, is held today by Clark (Clark, 1998).

Difficulties

Each of these positions has its own problems. Searle's is very compelling, but it is based on a notion of symbol manipulation which is foreign to Peirce's conception, and in addition, a notion of understanding or meaningfulness which, while seeming plausible, even obvious, becomes upon investigation, if not problematic, at least extremely complex. That is, in the Chinese Room argument, Searle maintains that "like a computer, I manipulate symbols, but I attach no meaning to the symbols" (Searle, 1990, p. 26), and that in a computer, "symbols are manipulated without reference to any meanings" (p. 27). To maintain this, as I have mentioned, presupposes the clear separation of rule-governed operations, i.e., syntax, and meaning-governed operations, i.e., semantics. This partitioning has been disputed by theories in cognitive linguistics in which all linguistic operations encompass both semantic and syntactic components (e.g., Johnson, 1993; Lakoff, 1990). Natural language operations, in these theories, cannot be categorized in this manner, and neither, by extension, can operations in formal languages (see especially Lakoff & Núñez, 2000). Thus, for these theories, as for Peirce’s, even the simplest symbolic manipulation is, in some primitive sense, a manifestation of understanding.

In addition, one must note that the interpretation of the Chinese room “rulebook” is not actually arbitrary. That is, although Searle argues that the Chinese room might be interpreted as modeling the stock market (Searle, 1990), we must ask whether this argument actually holds. It sounds plausible, until one reflects that there must be some structural similarities between a symbolism and what it symbolizes. That is, all possible structures cannot be symbolized by the Chinese room’s syntactical operations. Thus, by inspecting sets of truth-tables corresponding to those operations, it is clear that some physical events simply will not fit their conditions, even though many, perhaps even an infinite number, will. One might then ask what subset of all possible structures are symbolized by some complex set of syntactical operations, and more importantly, what the implications of that limitation are. Once the door is opened to some limitation as to what a particular structure can symbolize, it seems to me that this particular argument of Searle’s has been, if not refuted, at least weakened: the interpretation of the symbolic operations in the Chinese Room is not arbitrary.

In yet another facet of this argument, Searle maintains that the “biological nature” (Searle, 1990) of the brain enables it to realize or generate meaning. However, we are (I will assume) material information-processors ourselves. As far as is known, if we view the central nervous system (CNS) microscopically we find only physical, mindless components: neural structures, various chemicals, and so forth, like the gears in Leibnitz’s mill. What assigns meaning to our internal operations (for more on this, see also Harnad, 1990 and the “symbolic anchoring” problem; Pattee, 1997, Cariani, 1989, and Cariani, 2001)? Searle argues that, unlike a computer, a biological system such as a real stomach digests real food. But this analogy does not carry through for the mind. We do not “digest” ideas, as entities, as our stomachs process food; we do not pump ideas, as entities, as our heart pumps blood. That is, ideas are simply not entities “floating around” to be snatched by mental forces, and then, by mental “chemicals”, somehow processed. We might use these expressions metaphorically, but not literally. But in that case, ideas or concepts are just as much abstractions for us as they are for the computer. A real robot, controlled by a computer, picks up a real block. If one maintains that the remote programmer is the ultimate interpreter in that situation, then one would have to say the same for the Chinese room, and that argument could not get started.

Peirce’s response, I believe, would be similar, and would include the point that the analog components of deductive symbolisms, the “diagrams,” do instantiate or imply a structuring analogous to the neuron’s physical structure (see note 4).

Peirce's ideas, however, also have their problems. There are systems with internal controls which cannot by any reasonable criteria be “minded”: thermostats, to take an extreme example, are such self-correcting machines. Their behavior, although it involves negative feedback — self-correction, in a sense — is, nonetheless, “externally compelled”: completely repetitive and determined, in the sense that it can never originate new states and merely repeats old ones. If a simple example like the thermostat clearly refutes Peirce’s general point, then it would seem that some other criteria, in addition to self-correction, are necessary. Precisely what, therefore, must "self-criticality" entail in a machine for it to think in any interesting way? Feedback and recursive processes in computers have been implemented for decades; computers now learn, in some sense of the term. Peirce might answer that computer learning proceeds through algorithms; that is, that the determinants of the changes in the computer's programming are themselves fixed, and thus at this level the machine is not self-critical, i.e., it cannot originate its own programming. The AI argument, in turn, might be that biological systems themselves are constrained by physiological parameters. Peirce's response, I believe, would be to invoke his principle of chance: "it is essential that there should be an element of chance in some sense as to how the cell shall discharge itself" (Peirce, 1992b, p. 265). A proponent of AI, however, might respond that in fact computers can and do use random number generators, for example, to produce just such an effect.

However, Peirce’s later writings (e.g., Peirce, 1998c, pp. 245-248) seem to indicate that the relationship between what he termed “self-control” and the behavior of particular cellular structures is tentative, at best. The term “self-control” in this and similar essays refers to one’s willed actions and decisions. This is indeed a common meaning of the term, but its reference to the earlier analysis, in the context of biological structures, is not explicated. Given such an abstract meaning, it is fairly straightforward to claim that computers cannot act through the will, unless that faculty is equated, as I mention above, with mere random choice. But Peirce (especially the Peirce of this essay) would deny that latter option. Peirce stated, in fact, that in order to create a machine that can reason as a human can, it must “be endowed with a genuine power of self-control” (Peirce, 1998a, p. 387), which seems virtually impossible[5] to him.

This latter position, however, because of the lack of an explicit relationship between biological structures and the will (hardly surprising, given the state of physiology at the time), leaves Peirce open, I believe, to claims by AI proponents that they have in fact caused machines to manifest willed action. A Peircian objection would be countered with an accusation of vagueness.

Peirce and Searle: conclusions

What are the implications of these differences between Peirce and Searle? We have seen that for all the initial superficial similarities, there are profound disparities between their attitudes toward symbolic systems and "thinking" machines. While Searle dismisses the possibility of computers which understand in anything like a human sense (unless those machines are "biologically based"), Peirce does not. For Peirce, virtually any machine is, first, an extension of human thought, and second, in the case of calculating machines, already employs some aspects of human thought and thus of human understanding. However, a Peircean “theorematic machine” (Ketner, 1988, p. 52) would require a kind of processing which Searle certainly, and Peirce probably, would regard as beyond the capabilities of the digital computer.

The latter point brings us back to the beginning of this essay, in which I indicated that I would introduce another argument with just that conclusion. Although moving through radically different terrain, both Peirce and Searle would, I think, agree with it.

That argument is the following:

An argument for the impossibility of mind in any finite-state device (or device in which the states are functionally partitioned into discrete or bounded subsets):

A) Let us assume that an automaton with only one possible behavioral path, i.e., with only one linear set of states, which could be infinitely long, cannot have mind.

B) Let us now add one contingency state: suppose that instead of the one path in A, there are now two paths, activated by two buttons or sensors, such that this device now instantiates a single counterfactual. That is, IF a red light shines on one sensor the device initiates one linear sequence OR IF a green light shines it initiates another. Now clearly either of these can be infinitely long; in addition, either could start at any point after the other has started. It is evident that this second device cannot have mind any more than the first; two mindless devices have merely been added together.

1. If this second sequence is initiated by some internal state change so that the contingency now depends on an internal switch instead of an external one: the number of times, for example, that the device passes through the first state sequence, we have still merely added two mindless devices together.

C) Through induction we can now see that any finite-state device cannot have mind. Further, it would similarly seem that any device with a countably infinite number of states (initial states, i.e., a countably infinite-state device in the sense that a finite-state device is finite) cannot have mind. [6]

One could object to the above argument, however, on the following grounds: that it is valid only if the state-paths do not change dependent on context. That is, when a contingency is added, if the original linear set of states remains the same, clearly we are dealing with a simple additive linear process. However, if the original state sequence changes when a second is added for another contingency, then the additive process is no longer linear. A computer programmed along those lines might refute this argument, if the change took place in both the original and the new sequences. In that case, the interdependence of the sequences might invalidate the linearity criterion.

To put this another way, this counter-argument might be termed a “lemon-meringue” example, i.e., a synergistic or retroductive counter-argument. If the system acted, in effect, as a gestalt, where any change to any part changed all (or virtually all) other parts, then linearity no longer applies. Mind then would be a synergistic property, an interactive property, similar to the emergence of a lemon-meringue pie from lemons, eggs, etc., where the resulting whole has none (or few) of the properties of the original components. That is, if this non-linear case held, an inductive argument would not be appropriate to critique it, since “mind” (or better, perhaps, “the mental”) does not arise - since it is not a property (as in the blackness of all crows) of individuals - from the sharing of a property over a class of individuals, as in classical induction. Thus, the inductive argument would be misapplied to refute a retroductive process (and this is perhaps an interesting comment on the limitations of induction).

The lesson here, however, is that if the above argument is correct, a computer program which does not work synergistically or retroductively, i.e., which does not change its components with context, as does the CNS, will not generate mind.

At this point, there are some indications as to the precise differences between biological systems and digital computers which might enable the latter to embody meaning, but those differences do not hinge on intrinsically biological characteristics; they can be realized by machines.

Let us look more closely at the mechanics of the CNS. I will argue that the well-known analogy between the CNS and the digital computer is, in fact, almost totally incorrect. Roughly speaking, the CNS operates as follows: sensory organs excite neurons such that the frequency of the impulses resulting from stimulation is proportional to the (logarithm of the) magnitude or intensity of the stimulation. Thus an analog property, frequency, encodes magnitude from the most peripheral aspect of the CNS. When these impulses, carried along axons, enter processing areas (the visual cortex, let us say) of the CNS, many inputs converge on single cells. So far, some “processing” has occurred (starting from the initial transduction of light to neural impulses, frequency-coded, through a complex series of procedures on the retina), leading to the transmission of impulses further into the CNS. When a subset of these early impulses arrive at a presynaptic terminal of a cell in a cortical area, they are again transduced into chemical transmitters (except for some few neurons connected directly through electrical fields or ions) which rapidly diffuse across the synaptic gap. These chemicals then depolarize (unless they are inhibitory, then they hyperpolarize) the post-synaptic membrane. This depolarization then spreads rapidly over the surface of the membrane, reaches a maximum in magnitude (an analog property) and area (another analog property) in some short time period (another analog property), then recedes. During this period, if the magnitude of the depolarization is great enough, this neuron will fire (employing, as before, frequency coding). If it is not great enough, it will not. Meanwhile, other areas of the membrane (and there may be thousands) on the cell body of the same neuron are being depolarized similarly (and their terminals may themselves be moving around on the cell body, disappearing or appearing). If the first area of depolarization, while it is expanding or contracting, is intersected by other areas, caused by transmitters from other terminals, and the sum (or product, or some other function – no one actually knows) of those depolarizations exceeds some (variable) threshold, then that neuron will fire. It is this latter process, consisting of the dynamic interaction of many areas of de- and hyper- polarization on the surface of the cell body (which may extend into a huge dendritic tree), which constitutes, for the most part, neural processing (as it is understood today – although I have not even mentioned such aspects as different neurotransmitters, effects of memory, and many others). There is no digital coding – i.e., a placeholder code employing a finite set of arbitrary basic elements - whatsoever in this huge set of processes (and the above concerns only one neuron – I have not dealt with “cell-assemblies”); it is all accomplished through what may indeed be compared to Peircean “diagrams”: analog “representations” (and I employ this term very hesitantly), in which some aspect of the real-world structure of the representation corresponds to that which it represents.

A Peircean "theorematic" machine, then, might be constructed from a model similar to the above. We might expect that it would employ “diagrammatic” symbols instead of digital symbols. These would possess structure, as physical entities, which corresponded to what they symbolized: they would be analog symbols. In addition, just as the structure corresponds, the manipulations of those symbols would have to correspond, to some extent, with the manipulations of what was symbolized. Taking the example of the slide rule, not only does the structure of the “slide” correspond to that of the number line, but the operation of sliding one piece past another literally increases or decreases the length of the rule, as the quantities it represents increase or decrease. Even such a simple analog device does not employ a finite set of well-defined symbols, and as far as its operations are concerned, in the case of a slide rule, they are finite and well-defined. However, we might consider the more general case in which the symbols (or pre-symbolic entities, e.g., the spatial patterns of depolarization on the neural cell body surface) employed possess complex analog structures, and the operations in which they engage are based on those structural characteristics. In general, even if there were clear rules having to do, say, with how differently-shaped constituents of these symbols interacted, the specifics of those shapes could vary enough to alter that interaction enough so that the rule would have to be considered to be changed. That is, there might be rules that held on a microstructural level determining interactions of the “atoms” of some analog entity or structure; yet because of variability and complexity in the way in which microstructures were combined, the regularities from which rules of the “macrostructure” of the analog entity were inferred might only be approximate. To put it more generally, if “rules” were regularities corresponding to attractor basins in a “rule state-space” generated through the dynamics of complex analog interactions, then to speak of “well-defined” rules would be to approximate the actual state of affairs. Yet this picture is not unreasonable in the CNS, given the variability and complexity of the central nervous system.

It seems possible, then, to construct devices for which assumption B of the argument above, where it involves the linearity and independence of the combining processes, does not hold (one might also speculate, here, about extensions to Turing machine theory). These devices, in addition, seem consistent with Peirce’s requirements for a lack of “external compulsion” on a “theorematic machine”, since their operations would in part determined by momentary configurations of their components, set by external input, internal noise, and/or through states too complex to be computable. Further, since these devices would at least in part consist of analog components, the “fine-grainedness” of their material parts would be relevant to their construction, and Searle’s requirement (for a system similar – in this respect – to a biological entity) would also be satisfied.

Throughout the literature, we have see paeans of praise for the digital computer as the eventual embodiment of mind (e.g., Dennett, 1991). We have also seen severe critiques of this position (e.g., Dreyfus, 1993). In the former case, these arguments against the critics have been almost irrelevant, in the sense that efforts in the field of AI have continued unabated. In the latter case, very few constructive suggestions as to how to proceed, given that the arguments against conventional AI were correct, have been offered. I have described one very abstractly above; I will put forward a concrete example below.

Have there been devices similar to the above analog systems constructed? A few examples come to mind; the first steps, so to speak, in this direction: the very early description of an analog “homeostat” by Ashby (Ashby, 1960); the modern example of the “silicon retina” (Mead, 1988; Harrison, 2000), which has been developed to the point where it is being employed medically. But these are not computers in the general sense that they manipulate abstract symbolic operations. The problem, I believe, is the following: the current notion of a “computer” relies on the implicit assumption that it is the operations themselves that are important; that logic, however it is formulated, even as fuzzy logic, must be manipulated in order to reach goals. Even “evolutionary” computer systems, creating and discarding heuristics, are centered on just that class of operation. And given the construction of the digital computer, in which the must fundamental physical components instantiate truth-tables (Boolean or not), what other choice is there?

However, we might consider a system like the CNS, not as an “approximation” to a digital computer, but as an example of a system which turns this viewpoint around. That is, instead of keeping constant the fundamental logical processes and combining them in different ways to achieve goals, would it not be possible to employ the goals themselves to alter the logical parameters, to change, not merely the truth-tables, but the operations comprising those tables; the physical parameters of the system? This is not possible in a digital computer (except perhaps in high-order “virtual” machines – and the debate as to whether such approximations serve as well as actual devices is ongoing), where the circuitry is composed of transistors that embody binary operations; and AND, OR, and NOT, or similar, gates are structures imposed on the silicon matrix.

Suppose, however, that a machine were built in which those fundamental physical structures were themselves variable, as are the neural structures in the CNS. That is, suppose that the physical components which instantiate the truth-tables, now realized as transistors whose outputs have binary read-out imposed on the actual analog signal, memory components read similarly, and the AND, OR, etc., operations, realized as circuitry operating according to similar rigid filtering, were instead comprised of neural nets or the equivalent. Then the operations which were previously fundamental would be realized at a finer level of structure, in effect, and become variables, reorienting themselves as necessary to realize the system’s goals. More specifically, suppose that one such neural net were initially trained to duplicate the responses of a logic circuit realizing a truth-table of some sort. Although the initial responses of that net would duplicate those of that table, it might a) routinely vary somewhat, and could b) radically alter its operation if the necessities of the overall system required. Given that the components of that net were analog, as in the VSLI structures of the silicon retina or the components of the CNS, we would have a device which might be described as “picturing” the logic circuit, analogous to the way that a diagram pictures its referent. And that picture could change, suddenly or gradually, depending on the requirements of the task, given that the totality of neural nets realizing the logical operations were interconnected such that a synergistic or non-additive system, as generally described above, was created. This type of general-purpose analog computer realizing, in effect, a virtual digital computer, is probably just at the edge of present technology, but certainly not theoretically impossible.

In this essay I have attempted both criticism and an explicit indication of a direction for AI research. The positions critical of digitally-implemented AI do have, I believe, very strong arguments in their favor; yet in order to make an impact on the general endeavor of creating “minded” devices, an endeavor which should be ultimately successful if a materialist position on mind is at all reasonable, positive and constructive efforts to direct that effort need to be made. In this essay the suggestion for such a direction is made in the realization that in the ongoing creation of analog/digital robot/computer hybrids, in analog sensory networks, and in the advancement of analog processing, the criticisms offered to AI are, I believe, beginning to be answered.

References

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[1] "It is widely acknowledged the intense interest Peirce manifested on logical machines since his father tried to install a Babbage's one at the Albany Observatory. During the period he stayed at the Johns Hopkins University he had Allan Marquand as one of his best students, and when this latter proposed to construct a logical machine, Peirce contributed with all his knowledge in Logic and Physics to the best execution of the project. But while he was an enthusiast of the computational findings with machines, he was very critical about the possibilities of a machine showing genuine logical reasoning." (da Silveira, 1999).

[2] Hanson terms this type of thinking “retroduction” (Hanson, 1965).

[3] This position might be derived from his reading of Leibnitz: "noticeable perceptions also come by degrees from those which are too minute to be noticed" (Wiener, 1951, p. 378).

[4] That is, the crucial difference between analog and digital symbolisms is that analog symbols, as physical entities, share structure with what they stand for. For example, in drawing a triangle, the colors of the lines are usually irrelevant, but their number is always relevant; a triangle has three sides, and so must the drawing of a triangle. Similarly, the numbers on a slide rule stand for the physical distance on that rule, and that distance is utilized to realize slide rule computation.

[5] “…we have as little hopes of doing that as we have of endowing a machine made of inorganic materials with life” (Peirce, 1998a, p. 387).

[6] This is not a sorites argument. Such an argument brings traits of the conclusion into the premises or original statements. That is, the classic induction: one crow is black, two are black, therefore all are black says nothing in any of the individual statements about any general characteristics or conclusions. The sorites argument, in contrast, in which one says: the removal of one hair does not bring about baldness, of two hairs does not, therefore the removal of all hairs does not, brings into the individual statements the general characteristic that must be demonstrated, and thus involves a kind of circularity. However the argument about the linear sequence of states is inductive; the individual statements about the absence of mind in any linear sequence of states make no claims that involve the conclusion, i.e., that involve the collective set of states, as does a sorites argument.

In addition, to claim that this is a sorites argument because of vagueness begs the question. That is, that objection assumes that mind will result if enough processes are added together. But that conclusion is just what this argument is aimed against, and of course assuming it at the outset will make this inductive argument untenable.