Traditionally Gifford Lectures have dealt with questions connected with religion. In recent years, although reference to religion has never been wholly absent, they have sometimes been given by scientists and philosophers of science, and have dealt with the latest knowledge in cosmology, elementary particle physics, and so on. No doubt the change reflects a change in the culture, and particularly in the philosophical culture. But these facts about the Gifford Lectures—their historical concern with religion and their more recent concern with science—both speak to me. As a practicing Jew, I am someone for whom the religious dimension of life has become increasingly important, although it is not a dimension that I know how to philosophize about except by indirection; and the study of science has loomed large in my life. In fact, when I first began to teach philosophy, back in the early 1950s, I thought of myself as a philosopher of science (although I included philosophy of language and philosophy of mind in my generous interpretation of the phrase “philosophy of science”). Those who know my writings from that period may wonder how I reconciled my religious streak, which existed to some extent even back then, and my general scientific materialist worldview at that time. The answer is that I didn't reconcile them. I was a thorough-going atheist, and I was a believer. I simply kept these two parts of myself separate.
In the main, however, it was the scientific materialist that was dominant in me in the fifties and sixties. I believed that everything there is can be explained and described by a single theory. Of course we shall never know that theory in detail, and even about the general principles we shall always be some what in error. But I believed that we can see in present-day science what the general outlines of such a theory must look like. In particular, I believed that the best metaphysics is physics, or, more precisely, that the best metaphysics is what the positivists called “unified science”, science pictured as based on and unified by the application of the laws of fundamental physics. In our time, Bernard Williams has claimed that we have at least a sketch of an “absolute conception of the world” in present-day physics.1 Many analytic philosophers today subscribe to such a view, and for a philosopher who subscribes to it the task of philosophy becomes largely one of commenting on and speculating about the progress of science, especially as it bears or seems to bear on the various traditional problems of philosophy.
When I was young, a very different conception of philosophy was represented by the work of John Dewey. Dewey held that the idea of a single theory that explains everything has been a disaster in the history of philosophy. Science itself, Dewey once pointed out, has never consisted of a single unified theory, nor have the various theories which existed at any one time ever been wholly consistent. While we should not stop trying to make our theories consistent—Dewey did not regard inconsistency as a virtue—in philosophy we should abandon the dream of a single absolute conception of the world, he thought. Instead of seeking a final theory—whether it calls itself an “absolute conception of the world” or not—that would explain everything, we should see philosophy as a reflection on how human beings can resolve the various sorts of “problematical situations” that they encounter, whether in science, in ethics, in politics, in education, or wherever. My own philosophical evolution has been from a view like Bernard Williams’ to a view much more like John Dewey's. In this book I want to explain and, to the extent possible in the space available, to justify this change in my philosophical attitude.
In the first three chapters, I begin with a look at some of the ways in which philosophers have suggested that modern cognitive science explains the the link between language and the world. This chapter deals with Artificial Intelligence. Chapter 2 will discuss the idea that evolutionary theory is the key to the mysteries of intentionality (i.e., of truth and reference), while Chapter 3 will discuss the claim made by the philosopher Jerry Fodor that one can define reference in terms of causal/counterfactual notions. In particular, I want to suggest that we can and should accept the idea that cognitive psychology does not simply reduce to brain science cum computer science, in the way that so many people (including most practitioners of “cognitive science”) expect it to.
I just spoke of a particular picture of what the scientific worldview is, the view that science ultimately reduces to physics, or at least is unified by the world picture of physics. The idea of the mind as a sort of “reckoning machine” goes back to the birth of that “scientific worldview” in the seventeenth and eighteenth centuries. For example, Hobbes suggested that thinking is appropriately called “reckoning”, because it really is a manipulation of signs according to rules (analogous to calculating rules), and La Mettrie scandalized his time with the claim that man is just a machine (L'Homme Machine).2 These ideas were, not surprisingly, associated with materialism. And the question which anyone who touches on the topic of Artificial Intelligence is asked again and again is “Do you think that a computing machine could have intelligence, consciousness, and so on, in the way that human beings do?” Sometimes the question is meant as “could it in principle” and sometimes as “could it really, in practice” (to my mind, the far more interesting question).
The story of the computer, and of Alan Turing's role in the conception of the modern computer, has often been told. In the thirties, Turing formulated the notion of computability3 in terms which connect directly with computers (which had not yet been invented). In fact, the modern digital computer is a realization of the idea of a “universal luring machine”. A couple of decades later materialists like my former self came to claim that “the mind is a Turing machine”. It is interesting to ask why this seemed so evident to me (and still seems evident to many philosophers of mind).
If the whole human body is a physical system obeying the laws of Newtonian physics, and if any such system, up to and including the whole physical universe, is at least metaphorically a machine, then the whole human body is at least metaphorically a machine. And materialists believe that a human being is just a living human body. So, as long as they assume that quantum mechanics cannot be relevant to the philosophy of mind (as I did when I made this suggestion),4 materialists are committed to the view that a human being is—at least metaphorically—a machine. It is understandable that the notion of a Turing machine might be seen as just a way of making this materialist idea precise. Understandable, but hardly well thought out.
The problem is the following: a “machine” in the sense of a physical system obeying the laws of Newtonian physics need not be a Turing machine. (In defense of my former views, I should say that this was not known in the early 1960s when I proposed my so-called functionalist account of mind.) For a Turing machine can compute a function only if that function belongs to a certain class of functions, the so-called general recursive functions. But it has been proved that there exist possible physical systems whose time evolution is not describable by a recursive function, even when the initial condition of the system is so describable. (The wave equation of classical physics has been shown to give rise to examples.) In less technical language, what this means is that there exist physically possible analogue devices which can “compute” non-recursive functions.5 Even if such devices cannot actually be prepared by a physicist (and Georg Kreisel has pointed out that no theorem has been proved excluding the preparation of such a device),6 it does not follow that they do not occur in nature. Moreover, there is no reason at all why the real numbers describing the condition at a specified time of a naturally occurring physical system should be “recursive”. So, for more than one reason, a naturally occurring physical system might well have a trajectory which “computed” a non-recursive function.
You may wonder, then, why I assumed that a human being could be, at least as a reasonable idealization, regarded as a Turing machine. One reason was that the following bit of reasoning occurred to me. A human being cannot live forever. A human being is finite in space and time. And the words and actions—the “outputs”, in computer jargon—of a human being, insofar as they are perceivable by the unaided senses of other human beings (and we might plausibly assume that this is the level of accuracy aimed at in cognitive psychology) can be described by physical parameters which are specified to only a certain macroscopic level of accuracy. But this means that the “outputs” can be predicted during the finite time the human lives by a sufficiently good approximation to the actual continuous trajectory, and such a “sufficiently good approximation” can be a recursive function. (Any function can be approximated to any fixed level of accuracy by a recursive function over any finite time interval.) Since we may assume that the possible values of the boundary parameters are also restricted to a finite range, a finite set of such recursive functions will give the behavior of the human being under all possible conditions in the specified range to the desired accuracy. (Since the laws of motion are continuous, the boundary conditions need only to be known to within some appropriate Δ in order to predict the trajectory of the system to within the specified accuracy.) But if that is the case, the “outputs”—what the human says and does—can be predicted by a Turing machine. (In fact, the Turing machine only has to compute the values of whichever recursive function in the finite set corresponds to the values that the boundary conditions have taken on), and such a Turing machine could, in principle, simulate the behavior in question as well as predict it.
This argument proves too much and too little, however. On the one hand, it proves that every physical system whose behavior we want to know only up to some specified level of accuracy and whose “lifetime” is finite can be simulated by an automaton! But it does not prove that such a simulation is in any sense a perspicuous representation of the behavior of the system. When an airplane is flying through the air at less than supersonic speeds, it is perspicuous to represent the air as a continuous liquid, and not as an automaton. On the other hand it proves too little from the point of view of those who want to say that the real value of computational models is that they show what our “competence” is in idealization from such limitations as the finiteness of our memory or our lifetimes. According to such thinkers,7 if we were able to live forever, and were allowed access to a potentially infinite memory storage, still all our linguistic behavior could be simulated by an automaton. We are best “idealized” as Turing machines, such thinkers say, when what is at stake is not our actual “performance” but our “competence”. Since the proof of the little theorem I just demonstrated depended essentially on assuming that we do not live forever and on assuming that the boundary conditions have a finite range (which excludes a potentially infinite external memory), it offers no comfort to such a point of view.
Again, it might be said that any non-recursivities either in our initial conditions or in our space-time trajectories could not be reliably detected and hence would have no “cognitive” significance. But it is one thing to claim that the particular non-recursive function a human might compute if the human (under a certain idealization) were allowed to live forever has no cognitive significance, and another to say that the whole infinite trajectory can therefore be approximated by a Turing machine. Needless to say, what follows the “therefore” in this last sentence does not follow logically from the antecedent! (Recall how in the “chaos” phenomena small perturbations become magnified in the course of time.)
In sum, it does not seem that there is any principled reason why we must be perspicuously representable as Turing machines, even assuming the truth of materialism. (Or any reason why we must be representable in this way at all—even nonperspicuously—under the idealization that we live forever and have potentially infinite external memories). That is all I shall say about the question whether we are (or can be represented as) Turing machines “in principle”.
On the other hand, the interesting question is precisely whether we are perspicuously representable as Turing machines, even if there are no a priori answers to be had to this question. And this is something that can be found out only by seeing if we can “simulate” human intelligence in practice. Accordingly, it is to this question that I now turn.
Induction and Artificial Intelligence
A central part of human intelligence is the ability to make inductive inferences, that is, to learn from experience. In the case of deductive logic, we have discovered a set of rules which satisfactorily formalize valid inference. In the case of inductive logic this has not so far proved possible, and it is worthwhile pausing to ask why.
In the first place, it is not clear just how large the scope of inductive logic is supposed to be. Some writers consider the “hypothetico-deductive method”—that is, the inference from the success of a theory's predictions to the acceptability of the theory—the most important part of inductive logic, while others regard it as already belonging to a different subject. Of course, if by induction we mean “any method of valid inference which is not deductive”, then the scope of the topic of inductive logic will be simply enormous.
If the success of a large number of predictions—say, a thousand, or ten thousand—which are not themselves consequences of the auxiliary hypotheses alone always confirmed a theory, then the hypothetico-deductive inference, at least, would be easy to formalize. But problems arise at once. Some theories are accepted when the number of confirmed predictions is still very small—this was the case with the general theory of relativity, for example. To take care of such cases, we postulate that it is not only the number of confirmed predictions that matters, but also the elegance or simplicity of the theory: but can such quasi-aesthetic notions as “elegance” and “simplicity” really be formalized? Formal measures have indeed been proposed, but it cannot be said that they shed any light on real-life scientific inference. Moreover, a confirmed theory sometimes fits badly with background knowledge; in some cases, we conclude the theory cannot be true, while in others we conclude that the background knowledge should be modified; again, apart from imprecise talk about “simplicity”, it is hard to say what determines whether it is better, in a concrete case, to preserve background knowledge or to modify it. And even a theory which leads to a vast number of successful predictions may not be accepted if someone points out that a much simpler theory would lead to those predictions as well.
In view of these difficulties, some students of inductive logic would confine the scope of the subject to simpler inferences—typically, to the inference from the statistics in a sample drawn from a population to the statistics in the population. When the population consists of objects which exist at different times, including future times, the present sample is never going to be a random selection from the whole population, however; so the key case is this: I have a sample which is a random selection from the members of a population which exist now, here (on Earth, in Scotland, in the particular place where I have been able to gather samples, or wherever); what can I conclude about the properties of future members of the population (and of members in other places)?
If the sample is a sample of uranium atoms, and the future members are in the near as opposed to the cosmological future, then we are prepared to believe that the future members will resemble present members, on the average. If the sample is a sample of people, and the future members of the population are not in the very near future, then we are less likely to make this assumption, at least if culturally variable traits are in question. Here we are guided by background knowledge, of course. This has suggested to some inquirers that perhaps all there is to induction is the skilful use of background knowledge—we just “bootstrap” our way from what we know to additional knowledge. But then the cases in which we don't have much background knowledge at all, as well as the exceptional cases in which what we have to do is question background knowledge, assume great importance; and here, as just remarked, no one has much to say beyond vague talk about “simplicity”.
The problem of induction is not by any means the only problem confronting anyone who seriously intends to simulate human intelligence. Induction, indeed all cognition, presupposes the ability to recognize similarities among things; but similarities are by no means just constancies of the physical stimulus, or simple patterns in the input to the sense organs. For this reason, the success certain computer programs have had in detecting patterns (e.g., the shapes of letters of the alphabet) does not solve the “similarity” problem in the form in which it confronts someone learning a natural language. What makes knives similar, for example, is not that they all look alike (they don't), but that they are all manufactured to cut or stab;8 any system that can recognize knives as relevantly similar needs to be able to attribute purposes to agents. Humans have no difficulty in doing this; but it is not clear that we do this by unaided induction; we may well have a “hard-wired-in” ability to “put ourselves in the shoes” of other people which enables us to attribute to them any purposes we are capable of attributing to ourselves—an ability that Evolution the Tinker found it convenient to endow us with, and which helps us to know which of the infinitely many possible inductions we might consider is likely to be successful. Again, to recognize that a chihuahua and a Great Dane are similar in the sense of belonging to the same species requires the ability to realize that, appearances notwithstanding,9 chihuahuas can impregnate Great Danes and produce fertile offspring. Thinking in terms of potential for mating and potential for reproduction is natural for us; but it need not be natural for an artificial intelligence—unless we deliberately simulate this human propensity when we construct the artificial intelligence. Such examples can be multiplied indefinitely.
Similarities expressed by adjectives and verbs rather than nouns can be even more complex. A non-human “intelligence” might know what white is on a color chart, for example, without being able to see why pinko-grey humans are called “white”, and it might know what it is to open a door without being able to understand why we speak of opening a border (or opening trade). There are many words (as Wittgenstein pointed out) that apply to things that have only a “family resemblance” to one another; there need not be one thing all X's have in common. For example, we speak of the Canaanite tribal chiefs mentioned in the bible as kings although their kingdoms were probably little more than villages, and we speak of George VI (who did not literally rule England at all) as a king; and there are even cases in history in which “the kingship was not hereditary”, we say. Similarly (Wittgenstein's example), there is no property all games have in common which distinguishes them from all the activities which are not games.
The notional task of artificial intelligence is to simulate intelligence, not to duplicate it. So, perhaps one might finesse the problems I just mentioned by constructing a system that reasoned in an ideal language10—one in which words did not change their extensions in a context-dependent way (a sheet of typing paper might be “white1” and a human being might be “white2”, in such a language, where white1 is color-chart white, and white2 is pinko-grey). Perhaps all “family resemblance” words would have to be barred from such a language. (How much of a vocabulary would be left?) But my budget of difficulties is not yet finished.
Because the project of symbolic inductive logic appeared to run out of steam after Carnap, the thinking among philosophers of science has run in the direction of talking about so-called bootstrapping methods—that is, methods which attribute a great deal to background knowledge. It is instructive to see why this has happened, and also to realize how unsatisfactory such an approach is if our aim is to simulate intelligence.
One huge problem might be described as the existence of conflicting inductions. To use an example from Nelson Goodman:11 as far as I know, no one who has ever entered Emerson Hall in Harvard University has been able to speak Inuit (Eskimo). Thinking formalistically, this suggests the induction that if any person X enters Emerson Hall, then X does not speak Inuit. Let Ukuk be an Eskimo in Alaska who speaks Inuit. Shall I predict that if Ukuk enters Emerson Hall, then Ukuk will no longer be able to speak Inuit? Obviously not, but what is wrong with this induction?
Goodman answers that what is wrong with the inference is that it conflicts with the “better entrenched” inductively supported law that people do not lose their ability to speak a language upon entering a new place. But how am I supposed to know that this law does have more confirming instances than the regularity that no one who enters Emerson Hall speaks Inuit? Background knowledge again?
As a matter of fact, I don't believe that as a child I had any idea how often either of the conflicting regularities in the example (conflicting in that one of them must fail if Ukuk enters Emerson Hall) had been confirmed, but I would still have known enough not to make the “silly” induction that Ukuk would stop being able to speak Inuit if he entered a building (or a country) where no one had spoken Inuit. Again it is not clear that the knowledge that one doesn't lose a language just like that is really the product of induction—perhaps this is something we have an innate propensity to believe or, if that seems unreasonable, something that we have an innate propensity to conclude on the basis of only a little experience. The question that won't go away is how much what we call “intelligence” presupposes the rest of human nature.
Moreover, if what matters really is “entrenchment” (that is, number and variety of confirming instances), and if the information that the universal statement “one doesn't lose one's ability to speak a language upon entering a new place” is better entrenched than the universal statement “no one who enters Emerson Hall speaks Inuit” is part of my background knowledge, it isn't clear how it got there. Perhaps this information is implicit in the way people speak about linguistic abilities; but then one is faced with the question of how one “decodes” the implicit information conveyed by the utterances one hears.
The problem of conflicting inductions is a ubiquitous one even if one restricts attention to the simplest inductive inferences. If the solution is really just to give the system more background knowledge, then what are the implications for Artificial Intelligence? It is not easy to say, because Artificial Intelligence as we know it doesn't really try to simulate intelligence at all; simulating intelligence is only its notional activity, while its real activity is just writing clever programs for a variety of tasks. This is an important and useful activity, although, of course, it does not sound as exciting as “simulating human intelligence” or “producing artificial intelligence”. But if Artificial Intelligence existed as a real rather than a notional research activity, there would be two alternative strategies its practitioners could follow in the face of the problem of background knowledge.
(1) One could simply try to program into the machine all of the information a sophisticated human inductive judge has (including the tacit information). At the least it would require generations of researchers to formalize this information (probably it could not be done at all, because of the sheer quantity of information involved); and it is not clear that the result would be more than a gigantic “expert system”. No one would find this very exciting; and such an “intelligence” would be dreadfully unimaginative, unable to realize that in many cases it is precisely background knowledge that needs to be given up.
(2) One could undertake the more exciting and ambitious task of constructing a device that could learn the background knowledge by interacting with human beings, as a child learns a language and all the cultural information, explicit and tacit, that comes with growing up in a human community.
The Natural Language Problem
The second alternative is certainly the project that deserves the name of Artificial Intelligence. But consider the problems: to figure out the information implicit in the things people say, the machine must simulate “understanding” a human language. Thus the idea mentioned above, of sticking to an artificial “ideal language” and ignoring the complexities of natural language, has to be abandoned if this strategy is adopted; abandoned because the cost is too high. Too much of the information the machine would need is retrievable only via natural language processing.
But the natural language problem presents many of the same difficulties all over again. Some thinkers—Chomsky and his school—believe that a “template” for natural language, including the semantic or conceptual aspects, is innate—hard-wired-in by Evolution the Tinker. Although this view is taken to extremes by Fodor, who holds that there is an innate language of thought, with primitives adequate for the expression of all concepts that humans are able to learn to express in a natural language, Chomsky himself has hesitated to go this far: it seems that what he is committed to is the existence of a large number of innate conceptual abilities which give us a propensity to form certain concepts and not others. (In conversation, he has suggested that the difference between postulating innate concepts and innate abilities is not important if the postulated abilities are sufficiently structured.) At the opposite extreme, there is the view of classical behaviorism, which sought to explain language learning as a special case of the application of general rules for acquiring “habits”—i.e., as just one more bundle of inductions. (An in-between position is, of course, possible: why should language learning not depend partly on special-purpose heuristics and partly on general learning strategies—both developed by evolution?)
The view that language learning is not really learning, but rather the maturation of an innate ability in a particular environment (somewhat like the acquisition of a bird call by a species of bird that has to hear the call from an adult bird of the species to acquire it, but which also has an innate propensity to acquire that sort of call) leads, in its extreme form, to pessimism about the likelihood that human use of natural language can be successfully simulated on a computer—which is why Chomsky is pessimistic about projects for natural language computer processing, although he shares the computer model of the brain, or at least of the “language organ”, with AI researchers. Notice that this pessimistic view of language learning parallels the pessimistic view that induction is not a single ability, but rather a manifestation of a complex human nature whose computer simulation would require a vast system of subroutines—so vast that generations of researchers would be required to formalize even a small part of the system. Similarly, the optimistic view that there is an algorithm (of manageable size) for inductive logic is paralleled by the optimistic view of language learning: that there is a more or less topic-neutral heuristic for learning, and that this heuristic suffices (without the aid of an unmanageably large stock of hard-wired-in background knowledge, or topic-specific conceptual abilities) for the learning of one's natural language, as well as for the making of inductive inferences in general. Perhaps the optimistic view is right; but I do not see anyone on the scene, in either Artificial Intelligence or inductive logic, who has any interesting ideas as to how the topic-neutral learning strategy works.
The Mind as Chaos
Up to now I have been discussing the prospects of simulating human intelligence, not the prospects of finding informative models of the way the brain works. Dennett is connecting the two tasks: in effect, he is claiming that pessimism about the success of AI in simulating human intelligence amounts to pessimism about the possibility of describing the functioning of the brain. Hidden in this charge is a variant of Pascal's wager: you have nothing to lose if you assume AI will succeed and you are wrong, but if you assume AI will not succeed, you will lose the only chance there is to describe the brain. But what connection is there between simulating intelligence and describing the brain?
Even if the computer model of the brain is correct, it does not at all follow that AI will succeed. As mentioned above, Noam Chomsky believes the computer model is correct, but he does not expect AI to succeed. Language-using, he once put it to me in conversation, is not a separable ability of human beings: you can simulate baseball-throwing without simulating total human intellectual capacity, but you cannot simulate language-using—even language-using in a fixed context, such as going to the store and buying some milk, without simulating total human intellectual capacity. Yet Chomsky does not despair of understanding the brain; we can understand the weather without being able to predict it any better than we could before, and we may understand the brain, as a hierarchically structured system of computational systems (“modules”), without being able to describe all of them and all of their interactions well enough to predict or even simulate the brain's activities.
Another example which makes the same point is the current interest in computer models of the brain which do not assume that the brain computes using “representations” and rules for manipulating those representations in the style of a logical calculus.14 Perhaps the most interesting of these is the “neural Darwinist” model suggested by Gerald Edelman.15 Knowing that such a model of the brain was correct would not, in and of itself, enable us to predict which inductions the person whose brain that was would make; that depends on the system(s) of hard-wired-in basic similarities, and (in the “neural Darwinist” model, on the operation of an analogue to natural selection in the unique individual brain) there may be a vast number of such systems (and selection events) at different levels of the brain's processing activity. Yet, if we verified that such a model was correct, we would hardly express the discovery by saying “the mind has turned out to be chaos”. And the same thing goes if we discover that some model that does not come from computer science at all is the best model for the brain's activity. Many systems are too complex for us to survey and predict or simulate their activity in detail; this is not to say that we cannot seek useful theoretical models of such systems. To take an example from a totally different field, pessimism about the possibility of ever realistically simulating the behavior of an economy over a reasonably long period of time is not the same thing as pessimism about the possibility of a science of economics.
There is another side to Dennett's charge that I think the mind is chaos, however. Dennett is saying—and Fodor often says16—that pessimism about the power of computational models is scepticism about the possibility of “cognitive science”. But the hidden premise in both thinkers’ minds is a reductionist one. There is, in fact, an enormous amount of cognitive psychology that is not at all reductionist. There is no reason why the study of human cognition requires that we try to reduce cognition either to computations or to brain processes. We may very well succeed in discovering theoretical models of the brain which vastly increase our understanding of how the brain works without being of very much help to most areas of psychology, and in discovering better theoretical models in psychology (cognitive and otherwise) which are not of any particular help to brain science. The idea that the only understanding worthy of the name is reductionist understanding is a tired one, but evidently it has not lost its grip on our scientific culture.
Bernard Williams, Descartes: The Project of Pure Enquiry (Harmondsworth, Middlesex: Penguin Books, 1978), pp. 245–247. See also Williams’ Ethics and the Limits of Philosophy (Cambridge. Mass.: Harvard University Press, 1985), where Williams makes sustained use of the notion of an “absolute conception of the world”.
All this is well described in Justin Webb, Mechanism, Mentalism and Metamathematics (Dordrecht: Reidel, 1980).
See The Undecidable: Basic Papers on Undecidable Propositions, Undecidable Problems, and Computable Functions, ed. Martin Davis (Hewlett, N.Y.: Raven Press, 1965). Turing's was not, however, the first mathematical formulation of the notion of computability; that notion had already been analyzed by Gödel and Herbrand, and Turing showed that his notion was equivalent to theirs.
The view I introduced in “The Nature of Mental States” (reprinted in my Philosophical Papers, vol. 2, Mind, Language, and Reality (Cambridge: Cambridge University Press, 1975) to the effect that the mental states of human beings are to be viewed as simply the computational states of Turing machines, became widely held under the name “functionalism”. I explain my reasons for giving it up in detail in Representation and Reality (Cambridge, Mass.: MIT Press, 1988).
Marian Boykan Pour-El and Ian Richards, “The Wave Equation with Computable Initial Data Such That Its Unique Solution Is Not Computable,” Advances in Mathematics 39 (1981):215–239.
Georg Kreisel, review of paper cited in note 5, The Journal of Symbolic Logic 47:4 (1982):900–902.
This view is popular with Chomskians, although I am not sure that Noam Chomsky himself would endorse it.
I neglect such cases as ceremonial knives, of course.
Note that, if one had only appearance to go by, it would be quite natural to regard Great Danes and chihuahuas as animals of different species.
This idea was one of the foundation stones of logical positivism. Although the positivists’ goal was to reconstruct scientific reasoning rather than to mechanize it, they ran into every one of the problems mentioned here; in many ways the history of Artificial Intelligence is a repeat of the history of logical positivism (the second time as farce?).
Nelson Goodman, Fact, Fiction, and Forecast, 4th ed. (Cambridge, Mass.: Harvard University Press, 1983).
“Much Ado about Not Very Much,” Daedalus (Winter 1988):269–282.
Daniel Dennett, “When Philosophers Encounter Artificial Intelligence,” Daedalus (Winter 1988):283–295.
The best known of these is the “Parallel Distributed Processing” model. See David E. Rummelhart and James L. McLelland and the PDP Research Group, eds., Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vols. 1 and 2 (Cambridge, Mass.: MIT Press, 1986).
See The Remembered Present (Basic Books, 1990).
Jerry Fodor, RePresentations: Philosophical Essays on the Foundations of Cognitive Science (Cambridge, Mass.: MIT Press, 1981).