Showing papers in "Synthese in 1978"

Catastrophe theory as applied to the social and biological sciences: A critique

Abstract: Examen critique approfondi de la theorie des catastrophes appliquee, principalement au domaine biologique (E. C. Zeeman). Que ce soit dans ses applications neurophysiologiques ou ethologiques, etc., cette theorie, qui n'est pas discutee ici sur le plan mathematique pur, se revele peu feconde, et surtout peu informative.

Why You Can’t Make a Computer that Feels Pain

Abstract: It has seemed important to many people to claim that computers cannot in principle duplicate various human feats, activities, happenings. Such aprioristic claims, we have learned, have an embarrassing history of subsequent falsification. Coa~Ltrary to recently held opinion, for instance, computers can play superb che~zkers and good chess, can produce novel and unexpected proofs of nontrivial theorems, can conduct sophisticated conversations in ordinary if tightly circumscribed English. The materialist or computerphile who grounds an uncomplicated optimisim in this ungraceful retreat of the skeptics, however, is in danger of installing conceptual confusion in the worst place, in the foundations of his own ascendant view of the mind. The triumphs of Artificial Intelligence have been balanced by failures and false starts. Some have asked if there is a pattern to be discerned here. Keith Gunderson has pointed out that the successes have been with task-oriented, sapient features of mentality, the failures and false starts with sentient features of mentality, and has developed a distinction between program-receptive and programresistant feature~ of mentality. 1 Gunderson's point is not what some have hoped. Some have hoped he had found a fall-back position for them: viz., maybe machines can think but they can't feel. His point is rather that the task of getting a machine to feel is a very different task from getting it to think; in particular it is not a task that invites solution simply by sophisticated imlovations in programming, but rather, if at all, by devising new sorts of hardware. This goes some way to explaining the recalcitrance of mental features like pain to computer simulation, but not far enough. Since most of the discredited aprioristic thinking about the limitations of computers can be seen in retrospect to have stumbled over details, I propose to conduct a more detailed than usual philosophic thought experiment. Let us imagine setting out to prove the skeptic wrong about pain by actually writing a pain program, or designing a pain-feeling robot. I think the complications eEountered will prove instructive. The research strategy of computer simulation has often been misconstrued by philosophers. Contrary to the misapprehensions innocently engendered by

On the logic of relevance

Abstract: When we judge the probability of a statement r we try to take into account as much information as possible. But not all information that we have, or can obtain, is relevant to r, and it is only relevant information that is of any importance. Thus ‘relevance’ ought to be a central concept in the philosophy of science. However, the logical foundations of this concept have not been discussed very much. The purpose of this paper is to show that the traditional account is unsatisfactory and to suggest an alternative analysis of the relevance relation.

Fodor on language learning

Abstract: At least since Wittgenstein aired the matter in the Philosophical Investigations, the Augustinian theory of language learning has generally been regarded as a quaint old relic, as naive and uncontroversially wrong. It has been virtually a commonplace in contemporary discussions of language that however a language is learned by the aspiring child, it is evidently not through the auspices of an unlearned language over which he innately has command and by means of which he conducts his cognitive ruminations. Surprising it is then, that this very theory has been rescued from the curio shop by Fodor in his latest book, The Language o f Thought (1975). Surprising also is the strength of the defense Fodor discovers can be marshalled on behalf o f the Augustinian view. He argues that its status as a mere curio is undeserved, and that not the least of its virtues is that it is the only decent theory of tanguage learning in contention. The book will be widely read, indeed it should be widely read, by philosophers and psychologists alike, and it contains the potential to influence greatly the direction and development of psycholinguistic research. I hope that its potential to so influence will not be realized however, for, as I shall argue anon, it is thoroughly misconceived. The undoing of the theory, at least in the form Fodor presents it, is not so much that innate wherewithal is posited; it is rather the consummate richness and fixity attributed to the innate wherewithal. According to Fodor, the innate structure needed for learning a language is an innate language, and this endowed accoutrement is no pale prototype of the language vocalis that the child will acquire, nor indeed is it a mere germ which grows and develops to reflect the sort of Weltanschauung embodied in the particular language of the child's milieu. Mentalese, Fodor argues, is as rich and powerful, as complex and complete, as any language, be it English or Urdu, the child comes to learn. Fodor is forthright in putting the point:

Probability and linguistic variation

Abstract: Many of the most original and well-known applications of probabilistic models and statistics have been made in fields peripheral to linguistics. We may cite Shannon's information theory [42], Zipf's law [47] and other approaches to word frequency distribution [18], the authorship attribution of the Federalist papers by Mosteller and Wallace [29], Osgood's semantic differential [31], and the psycholinguistic analysis of acoustic phonetics in conjunction with the development of multidimensional scaling [43]. In spite of all this, grammarians in the mainstream of linguistics have accorded, until recently and with few exceptions, a uniformly hostile reception to suggestions that probabilistic concepts deserve some consideration in the study of language. This rejection is usually phrased in terms of the conviction that randomness and indeterminacy play no significant role in the structure of language, particularly with respect to the linguistic competence, or internalized linguistic 'knowledge', of the individual speaker-hearer. The genesis of this attitude is threefold, and we will discuss the three aspects in order of increasing importance• The first is historical. Since the publication in 1957 of Chomsky's Syntactic Structures [6], the prevailing viewpoint in linguistics has been that of the generative grammarian• The book began by destroying two 'straw man' theories of grammar, both of which were naive probabilistic models. While this attack served as a useful motivation for the phrase structure and transformational types of generative grammars, as a byproduct it more generally discredited probability notions in the eyes of many linguists and linguistics students• This rejection of probability has since been reaffirmed by Chomsky, for example in his authoritative Aspects of the Theory of Syntax [7], published in 1965.

On the structuralist approach to the dynamics of theories

Abstract: One of the main events at the Fifth International Congress of Logic, Methodology and Philosophy of Science (London, Ontario, 1975) was a symposium on theory-change. The participants of this symposium were Professors J. Sneed, W. Stegm?ller, and T. Kuhn. In their talks Sneed and Stegm?ller presented their set-theoretical (or 'structuralistic') view on the structure and dynamics of theories (cf. Sneed, 1976; Stegm?ller, 1976b). Sneed's talk was a further elaboration of the approach developed in his book The Logical Structure of Mathematical Physics (1971). This book contains a partial explication of some of Kuhn's ideas on normal science and scientific revolutions. This explication was adopted by Stegm?ller, who in his book Theorienstrukturen und Theorien dynamik (1973) made an attempt to further elaborate these Sneedian views and to relate them to contemporary philosophical discussions of theory change. Stegm?ller (1976b) contains a partial summary and a further development of the results of this book. Kuhn (1976), in his comments on the set-theoretic or structuralistic Sneed-Stegm?ller approach, strongly endorses this explication of his thoughts. This fact considerably adds to the importance of this new explication. I will below undertake a critical evaluation of Sneed's and Stegm?ller's approach in order to see to what extent we now have a viable paradigm (or the beginnings of such) for research in the science of science. My detailed comments will mainly concern Stegm?ller's book, which recently appeared as an English translation entitled The Structure and Dynamics of Theories (1976a). The page references will be to this English edition. My discussion below will be conducted in two parts. First I will give a critical exposition of the Sneed-Stegm?ller approach. After that I will present some, both general and specific, criticisms against this approach from the point of view of scientific realism. Let me point out right at the beginning that, in spite of the criticisms to be presented, I regard Sneed's and

The distance between constituents

Abstract: One thing on which Hilpinen (1977), Niiniluoto (1977), (1978), Tichy (1974), (1976), and I seem to be in agreement is that, at least for a finite language, the problem of verisimilitude, or o? distance from the truth, is in some way reducible to the problem of specifying a satisfactory measure of the distance between constituents for the language under consideration. For every theory A can be represented as a set of constituents (that is, complete consistent theories), namely the set of all those constituents that extend (or entail) A; and the truth Tis itself a single constituent. Thus the distance of A from T is reasonably supposed to be some function of the distances between the various constituents of the language. Exactly which function is most suitable is something on which Hilpinen, Niiniluoto, Tichy, and I are in disagreement; certainly collectively, and even, I suspect, pairwise.1 But that is not my topic here. What I am exclusively concerned with in this paper is the problem of providing a non-arbitrary measure of the distance between any two constituents (and therefore, in particular, between any constituent and T) of a finite language. I maintain that the simple measures proposed by Tichy for sentential languages and by Niiniluoto for monadic predicate languages are seriously arbitrary. Tichy's sentential measure I have discussed on several previous occasions ((1974), Section 6, (1975), Section IV, (1976), Sections 1 and 5), and I return to it here (in Section I) only because it provides an easily comprehensible introduction to the not so easily comprehensible com plexities involved when we turn to the constituents of the predicate calculus. Commenting on Tichy's proposal Niiniluoto writes ((1977), note 19): "He specifies a distance measure between constituents of propositional logic only; this measure is not very plausible, however"; he refers directly to my (1975). Later ((1978), note 10) he goes on to say that "Tichy (1974) develops this suggestion [to define all distances from the truth in terms of distances between constituents] only in the case of propositional logic; his treatment of this case has been effectively criticized by Miller". In Section II of the present paper I intend to establish that a similar criticism is effective against

An inconsistency in functionalism

Abstract: Behaviorism and naive physiological reductionism are the forerunners of functionalism in psychology and philosophy of mind. Like its forerunners, functionalism is not a single, unified theory. Rather, it is an intellectual movement. Consequently generalizations about functionalism run a risk of over-simplification. Bearing this in mind, I will distinguish two forms of functionalism one oriented toward behavior and the other oriented toward physiology. In this discussion I will count a given doctrine as functionalistic (whether it be behavioristic or physiological in orientation) if an only if it is committed to ~L certain relevant pair of t he se s -one negative and one positive. The negative thesis of behavioral functionalism is tantamount to the rejection of behaviorism itself. The thesis is that (terms which express) mental properties, relations or states do not have ordinary explicit definitions which appeal solely to (terms which express) behavioral properties, relations or states. The positive thesis of behavioral functionalism is that (terms which express) mental properties, relations or states do, by contrast, have purely behavioral functional definitions, i.e., they can be defined solely in terms of how they function together in (theories concerning) the typical psychobehavioral causal manifold. The negative and positive theses of physiological functionalism are just what one would expect: (terms which express) mental properties, relations or states do not have ordinary explicit definitions which appeal solely to (terms which express) physiological properties, relations or states; however, (terms which express) mental properties or states do have purely physiological functional definitions; i.e., they can be defined solely in terms of how they function together in (theories concerning) the typical psycho-physiological causal manifold. If his positive thesis is correct, the functionalist is then free to uphold some form of physicalism despite the failure of behaviorism and naive

The logical structure of Spinoza'sEthics, Part I

Abstract: In this paper I will present Part I of!Spinoza's 'Ethics as a formalized axiomatic theory. The theory itself will be found in Section Ill following a discussion of the text from Definition (i) through Proposition (xi) (since considerations of space prohibit a discussion of all thirty-six propositions of Part I). The formal theory will be presented in a quantified modal logic which contains two necessity operators. The question whether this language is adequate for the representation of Spinoza's metaphysics is a large one, which I touch upon, but do not attempt to settle here. Two types of reservations might be expressed: first, that the language, with its inference rules, is too strong, in the sense that it contains theses which Spinoza would not (or worse, could not) accept. The 'paradoxes' of material and strict implication might be cited, and the thesis, in the modal system $5, that MLp -+ Lp. I do not think that these examples present any difficulty, however, since a rejection of them would, prima facie, block a number of inferences which Spinoza needs to make. A more difficult question is whether Spinoza can correctly be represented in a language that has an 'absolute' identity predicate, or whether it should merely have various predicates expressing equivalence relations such as 'is the same substance as' and 'is the same mode as'. This question is bound up with the classical problem of the attributes, which I cannot discuss fully here. Nevertheless, an alternative formalization will be given in a language without identity (see Section IIIB). The philosophical implications of this I leave for another occasion. The second type of reservation is the worry that a quantified modal logic is insufficient for the expression of certain theses and inferences made by Spinoza. There is little question, I think, that this is in fact the case i f we have in mind the whole of the Ethics. For it is clear that some means is needed of expressing propositional attitudes. This can presumably be handled

The old and the new logic of metascience

Abstract: J. D. Sneed's approach to the philosophy of science (Sneed, 1971) has had, among other things, the following very important effect. It has compelled philosophers to reconsider what are the most appropriate logical tools in the study on the structure and dynamics of empirical theories. In Stegmiiller (1976) (translated from StegmiiUer, 1973), this reevaluation results in the claim that the traditional methods, where the specific language used and its formal properties play a central role and which thus imitate metamathematical studies, have led the philosophy of science astray. On the one hand, Stegmtiller seems to claim that the traditional logical methods in the philosophy of science have almost solely been syntactical and prooftheoretical (Stegmi~ller, 1976, pp.2, 12) and research in modern logic likewise concentrates on such aspects (p. 2). On the other hand, he nevertheless also claims that results in mathematical logic can be of great metascientific relevance. For instance, without the instrumentarium provided by modern model theory the precise articulation of the nonstatement view (that is, the Sneedian view) of physical theories would not have been possible (p. 9). I do not feel competent to take a definite stand here in regard to StegmOller's claim that the traditional approach has led the philosophy of science astray. I nevertheless strongly suspect that the new ideas which Sneed's work contains are due to his ingenuity and arose independently of any recent developments in mathematical logic. It also seems to me that if methodology of the traditional kind had kept step with these developments, the Sneedian type of theorizing would have been possible on its basis. One of the 15urposes of this paper is to clarify these two points. It is easy to agree with Stegmt~ller's claim that results in mathematical logic can have a great metascientific relevance. For mathematical logic is obviously relevant to the study of the logical structure of theories. But it is not easy to admit that the methods in the traditional approach to the philosophy of science would have been as completely syntactic as Stegmfiller seems to claim, even though syntactic considerations have played an

Truthlikeness: Comments on recent discussion

Abstract: The modern discussion on the notion of 'truthlikeness' was started in 1960. In his Word and Object, W. V. Quine argued that Peirce's definition of truth as the limit of inquiry is faulty for the reason that the notion 'nearer than' is only \"defined for numbers and not for theories\" (Quine, 1960, p. 23). In his contribution to the 1960 International Congress for Logic, Methodology, and Philosophy of Sc, ience at Stanford, Karl Popper defended the opposite view; he proposed a positive solution to the problem of defining a comparative notion of 'truthlikeness' or 'verisimilitude' for theories (Popper, 1962; see also Popper, 19'63, p.233, and Popper, 1966). In his Conjectures and Refutations, Popper further introduced a quantitative measure of verisimilitude (Popper, 1963, p. 397). Popper's definition of verisimilitude did not awake much serious discussion in the sixties. At least two different reasons for this fact can be suggested. First, the Carnap-Popper controversy over induction was generally held to be more topical than the issue about truthlikeness. Many philosophers outside the Popperian camp felt that the problem of verisimilitude is irrelevant, since they thought that it is only an idiosyncratic problem for the critical rationalists: it becomes interesting only if one wholly accepts Popper's notoriously questionable criticism of induction. Secondly, it was thought that the notion of verisimilitude is useless: if one cannot be certain about the truth, how could one ever measure the 'distances' of theories from the truth? (Cf. for example Ayer, 1974.) The situation has changed in the seventies, however. Several philosophers some of whom cannot be considered as representatives of any of the subgroups of the Popperian s choo l have seriously considered the notion of trutk~ikeness both from the logical and from the methodological viewpoint. To give a personal report, my own interest in this problem area arose in 1973 from my earlier work on induction which was at the same time both anti-inductivist and anti-Popperian (see Niiniluoto and Tuomela, 1973);

Theory-distance and verisimilitude

Abstract: There are quite a few methodological contexts in which it seems appropriate or even necessary to speak about the distance or (dis)similarity between statements (e.g., scientific theories). For instance, we may claim that a revolutionary theory T correctively explains the theory T that it supersedes (cf. Tuomela, 1973). By this we mean, roughly, that (a) T' strictly explains a theory T* such that T is an approximation of T* and that (b) T has greater verisimilitude (truthlikeness) than T. (We adopt a realist conception of science, and it requires that sense can be made of the concept of verisimilitude.) Here both clauses (a) and (b), as we explicate them, involve implicit reference to theory-distance. Other examples requiring the comparison between the dissimilarity or distance between what two theories (and other statements) say about the world are easy to come by (cf., e.g., the distance between two sets of meaning postulates). As theories are conceptual entities we are here speaking about the distance between conceptual entities in the first place. Therefore it is important to clearly specify the conceptual framework (for us, language) in which the theories are couched. (Our technical developments below will mainly be concerned with theories formulated in the same first-order language.) However, as theories are supposed to represent and describe reality, we also come to compare the distances between suitable patterns and organized chunks of reality. I take such concepts as distance, verisimilitude, and approximation to be in a central sense 'pragmatic' concepts. They are, for instance, relativized to the conceptual framework accepted by a scientific community (broadly understood) or, perhaps better, a scientific culture or subculture. This entails that in speaking about, e.g., distance we have to ultimately rely on the scientist's (more or less institutionalized) way of using language, on his way of putting (intentionally or non-intentionally) the conceptual framework to use, and more generally, on the scientist's meaningful behavior on the whole.

Demonstratives and indexicals in montague grammar

Abstract: Preface 1. Previous Work by Montague and Kaplan 2. Times and Places 3. Lexical Ambiguity 4. The Demonstrative Modifiers here and there 5. The Demonstrative Quantifiers this and that 6. The Indexical the 7. The Demonstrative Terms this and that 8. The Demonstrative Pronouns he and she 9. Some Historical Remarks 10. The First and Second Person in the Singular and Nondenoting Terms 11. Demonstratives and Indexicals in the Plural 12. aetually, presently, and their Adjectival Cognates 13. Synonymy and Logical Equivalence 14. The Distinction between Demonstratives and other Indexicals 15. Transitive and Intransitive Verbs of Motion 16. Fillmore on come and go 17. The Syntax of the Fragment 18. Natural Logic 19. Translating the Fragment into Natural Logic History and Acknowledgements Notes Bibliography 1 2 7 9 10 15 22 22 27 29 31 35 38 40 41 42 46 48 59 65 74 75 79

Popper's evolutionary epistemology: A critique

Abstract: In recent years Popper has developed what he calls an 'evolutionary epistemology'. According to this theory, knowledge is 'a natural product of the human animal' but which, once created, becomes both objective and autonomous, in the sense of having a reality not contingent upon human subjective awareness.a Knowledge, according to Popper, exists, in as strong a sense as physical and (perhaps) mental things exist. ~ Man's intellectual creations transcend his own subjective awareness: we created the natural numbers but no one will ever think of all the natural numbers, just as nobody will ever know all the consequences of a theory. But these consequences are there, waiting to be discovered. Some of these consequences, when discovered, may be subjectively surprising, and may enrich our culture or our technology. In this way the world of theories, problem situations, etc. influences man's mental and physical life. When for instance, a new mathematical result is proved, we discover something about this world, and that discovery may equip us to cope better with our environment by enriching our technology. It is this 'influential' character which substantiates the reality of these objects. Popper calls the world of objective ideas, problems etc. 'world three '3 , to distinguish it from 'world one' (the physical world), and 'world two' (the psychological world). As Popper himself points out, this theory is similar in some respects to platonism. But in certain vital respects it differs from that more traditional doctine. Popper's third world objects are not perfect, unchanging and timeless; they are human creations. There was a time before which the third world did not exist, and there may come a time when it no longer exists. Human activity not only creates the third world, it continually augments it by inventing ever new theories. Also mistakes are as much a part of the third world as are successes; a bad solution to a problem is as much a third world object as is a good one; a false conjecture as much as a true one.

An overview of Spinoza'sEhics

Abstract: It is generally acknowledged that the Ethics is Spinoza's greatest work He is supposed to have completed it in 1675, less than two years before his death in 1677, although early drafts of various parts had been circulating among friends and intellectual peers as early as 16651 Spinoza even showed Leibniz the manuscript of his Ethics in 1676 when Leibniz visited him at the Hague2 Indeed, Leibniz owed a great debt to Spinoza, since in the Ethics we find so many characteristic Leibnizian doctrines, either explicitly or implicitly For example, one finds an explicit version of the Principle of Sufficient Reason, a special version of the Identity of Indiscernibles (P4, El), a version of the Principle of Plenitude (correspond ing to Leibniz' Principle of Perfection), a distinction between logical and causal necessity, an implicit distinction between finitary versus infinitary analysis, hints of reflection principles, an implicit doctrine of unconscious perception, and hints of a relational view of space and time All these doctrines were developed to a very great degree by Leibniz, but they can already be found in Spinoza's Ethics, in some form or other One of the distinctive features of the Ethics is that it is written in the deductive style of Euclidean Geometry Indeed, Spinoza was quite right to hold that the formal deductive apparatus of Euclidean Geometry could just as well be applied to substances, modes, and attributes as to planes, points, and lines Thus, Spinoza starts out with axioms, definitions, and postulates, which contain his philosophical terms, and proceeds to deduce propositions, as well as give explanations, all in the manner of Euclid However, the subject matter of the Ethics has very little to do with Geometry While Spinoza's deductions are not that rigorous, I have shown in other papers ('A Formalization of Spinoza's Ethics, Part I' and 'Spinoza's Denial of Free Will in Man and God') that they can be formalized according to the standards of mathematical logic, provided that one is willing to supply quite a number of suppressed premises3 These premises, however, are in no way

On Constraining the Class of Transformational Languages

Abstract: The need to add constraints to the theory of transformational grammar has been one (perhaps the) central goal of research by generative grammarians over the last decade. A number of important proposals have resulted from this research, most notably those due to Bresnan (1976), Chomsky (1973), Culicover and Wexler (1977), Emonds (1976), and Ross (1967). The first section of this paper is devoted to distinguishing between and considering the relative merits of two different views of the purpose of such constraints. The second and third sections attempt to add substance to my position by showing how progress towards the goals defended in the first section can be achieved.

A new theory of subjunctive conditionals

Abstract: If recent literature is anything to go by, there exists a widespread consensus to the effect that the notion of sub junc t ive -o r counterfactualconditionals is logically prior to that of causation. It seems to be widely accepted that tile cause-effect relation can be legitimately explained or defined in terms (perhaps inter alia) of subjunctive conditionals. Several elaborate attempts have indeed been made to reduce the former concept to the latter.1 Yet a simple consideration seems to show quite conclusively that the order of logical priority is exactly reverse. Surely the truth of

The genetic code and human language

Abstract: The breaking of the genetic code has propagated analogies between genetic and linguistic phenomena. Biologists and linguists alike have claimed that there are similarities between the genetic code and human language. 1 In the present paper I argue that the similarity between the two systems is only misleading and that the two are fundamentally different. Before I compare particular structures and processes, let me dwell on the distinction between competence and performance. The distinction was introduced by Chomsky (1965) and is fundamental to contemporary linguistic thought. Chomsky distinguishes between the (tacitly known) rules of the language on the one hand, and the mechanisms that are involved in the production and comprehension of linguistic utterances, on the other hand. The study of competence, i.e. the study of grammar, bears on generalizations. It ignores the fact that a great portion of the linguistic utterances which are actually produced are ungrammatical sentences, semi-sentences, disconnected sequences ofwords, etc. It is up to a theory of performance to account for the psychological mechanisms that are involved in the production and comprehension of actual sentences, be they grammatical or not. At the outset of our comparison it is important to note that the distinction between competence and performance does not carry over to genetics. The bulk of our knowledge of genetics is nothing more nor less than what are believed to be actual structures and processes. No distinction between idealized and actual processors and processes is applicable. One facet of the distinction, however, may be fruitful in the analysis of any coding system, i.e. the differentiation between structure and process. Just as one can study either grammar or psycholinguistic processes (e.g. speech perception, parsing, reading and comprehension), one can study either the structure of the genetic code or the processes associated with it (e.g. transcription, translation, error detection and correction, control and regulation) The following discussion assumes familiarity with the basic notions of structural linguistics and transformational grammar on the one hand and of genetics and molecular biology on the other hand. Thus, no general introduc-

Artificial intelligence and Piagetian theory

Abstract: One of the strengths of artificial intelligence ( 'AI') as a way of thinking about thinking is that it forces one to model the movement of the mind, the way in which a particular mental phenomenon comes about. It is not enough to say that a phenomenon can happen: the programmer must specify a way in which it can happen. (Whether this is the way in which it does happen is, of course, another question.) And one of the weaknesses of Piagetian theory for all its salutary stress on action as the context and carrier of mental life is its lack of specification of detailed procedural mechanisms competent to generate the behaviour it describes. Piaget's terms assimilation and accommodation are notorious examples: a leading Piagetian has even 'explained' the parrot's lack of linguistic creativity by saying that its sensorimotor scheme for speaking is very accurate in accommodation but quite meagre in assimilative power. 1 Even Piaget's careful descriptions of the development of behaviours such as weight and lengt~ seriation are related to uncomfortably vague remarks about the progression of stages, without it being made clear just how one stage (or set of conceptuaI structures) comes to follow another. This complementarity of strength and weakness suggests that a bringing together of AI ',and Piagetian theory might be fruitful. In particular, if AI workers can take account of the detailed empirical data provided by Piaget's observations, instead of working in a psychological vacuum, some crucial questions should be clarified • and some specific answers may be suggested. This theoretical clarification, in turn, should encourage further observations, so that AI can play a role in the development of 'scientific research programmes' in psychology. 2 In the next section, I mention some work in AI that bears on Piagetian theory, even though it was not done with Piaget's research specifically in mind. In Section 3, I outline some computational models of seriation behaviour that pay careful attention to empirical data such as Piaget described. And in Section 4, I ask whether this work has the implications for Piaget's theory of developmental stages that are claimed by its author.

Counterfactuals and Newcomb's paradox

Abstract: In [1], Gibbard and Harper advocate a particular method for calculating the expected utility of an action, a method based upon the probabilities of certain counterfactuals. 1 This method is then used by Gibbard and Harper to argue for a particular solution to Newcomb's paradox. This paper argues against some of Gibbard and Harper's claims concerning the truth-values and probabilities of counterfactuals involved in Newcomb's paradox; and it is further argued that if these claims were true, then Gibbard and Harper's method of calculating expected utility would not be correct.

Verisimilitude by means of short theorems

Abstract: This paper began with the simple object of finding an account that allowed us to compare incompatible false theories. This we achieved with ρ. But that relation is language — or interest — dependent. ρ' is free from this limitation; though thus liberated it is perhaps rather unconcerned about what is true, and further fails to deliver certain intuitive comparisons. Whether ρ is to be preferred to ρ' or vice versa, seems to me a largely fruitless question: In fact it might be that as we seek to free the idea of verisimilitude from any dependence on language, interests or problems, so we gradually collapse it to nothing more than logical power.

On the generalization of the continuum of inductive methods to universal hypotheses

Abstract: Carnap's continuum of inductive methods (Carnap, 1952) has been considered, by himself and others, as a proof for the claim that the intuitive concept of rational degree of belief can be explicated, at least with respect to simple situations, in a satisfactory way. At the same time it has been considered as new evidence for the intuitive feeling that such an explication would only be possible for singular (or, individual) hypotheses but not for universal hypotheses. In particular, it was felt that it would not be possible to generalize Carn~Lp's continuum in an acceptable way so that Carnap's continuum appears as an extreme special case. In this paper it will be shown that this particular conjecture is false and that, consequently, the general conjecture is also false. The requirements for an acceptable generalization will be stated precisely and, in view of the literature on tiffs subject, we have the strong conviction that these requirements will generally be admitted to be necessary and sufficient from the finitary (inductive) point of view. The generalized continuum is not new, however. It is essentially contained in Hintikka's (1966) a-X-system and it is essentially equivalent to the class of systems which have recently been introduced by I-Iintikka and Niiniluoto (1976). The main technical result of this article is the proof that the latter class of system,; is equivalent to a particular subsystem of Hintikka's combined system. Hintikka and Niiniluoto could already conclude that it was possible to treat universal hypotheses in a fundamentally acceptable way. The equivalence theorem enables us to specify precisely why and in what sense we are justified to talk about the generalization of Carnap's continuum. Moreover it shows that this generalization is axiomatically as well as technically as simple as ever could be expected.

The competence-performance distinction in mental philosophy

Abstract: The competence-performance distinction, which has been made much of by linguistic philosophers, is examined in this paper with an attempt to clarify and settle some of the associated philosophical issues. The paper begins by making a further distinction between competence as a concept of linguistics and competence as a concept of theoretical psychology and mental philosophy. To establish a setting for the main part of the paper, I sketch several theories of mental competence, and then isolate two fundamental rationalist assumptions tor discussion and criticism. These assumptions or underlying principles are the axiom of communal competence: speakers cannot communicate unless they have the same competence, that is, have learned the same rules governing the language they all speak; and an isolation principle: a theory of language acquisition can safely abstract from the fact that language is used in a communi ty . I then go on to argue that the competence-performance (from now on C-P) distinction is already implicit in a mechanist theory of mind, which says that cognitive processes are recursive processes of some kind. I then argue, contra the rationalist axiom, that communication does not depend upon communal competence, and indeed that competence is strictly individual. Nevertheless, language acquisition does seem hard to account for without a good deal of inborn structure. This is some kind of logical structure, which does not have to be identical in all people, which is not qualitatively unlike such systems in other organisms, and yet is very likely species-specific. So far as I can see, this structure has nothing to do with the historical concept of innate ideas. I finally argue that competence is not usefully or illuminatingly regarded as propositional knowledge of anything, but is exercized (performance) as a kind of knowing how, which is quite different from knowing how to walk or wiggle the ears.

The theory of catastrophes: Some epistemological aspects

Abstract: The theory of catastrophes will follow the general pattern. It will receive the most flattering praise, as do all theories at their birth. This will be followed by the most acrimonious criticism. And after the enthusiasm of the salons has waned, and the thundering of the specialists has quietened, the judgement of meticulous minds.will fall, without recourse, like a guillotine blade. It is surprising to observe that the various criticisms which have been raised in more or less virulent opposition to the theory of catastrophes do not strike at the foundations upon which this theory has been built. Would it not be natural, however, in order to convince oneself of the solidity of an edifice or to disclose the weak zones where faults might develop, to begin by examining the architecture of the whole, and by testing the solidity of its foundations? An examination of this type would be of greater interest than one such as that of Levy-Leblond [10] which remains at the level of general philosophy, or that of Hector Sussman [ 14] which, being blinded by the imperfections of certain apphcations, fails to grasp the intrinsic value of the theory. Certainly all these criticisms have their value to the extent that they shed some light on weaknesses in the constructions and suggest, either explicitly or implicitly, means for sealing up the breaches, or perhaps even show in a definitive way, the need promptly to abandon a fortress which is headed for certain disaster. But, in order to be complete and fruitful, a critique should also take account of the positive aspects which a work manifests. In this way the critic may avoid partiality and incline more to equanimity and justice in his judgement. We now describe the basic plan of this study: a presentation of the theory of catastrophes 2 , research into its weak points, and into the contributions of the theory. For the sake of convenience of exposition, and in order to avoid a certain dryness of discourse, it will often happen that these two main parts will be imbricated each with the other.

Mind and body in Spinoza's Ethics

Abstract: In The Concept of Mind Gilbert Ryle launched an attack on the Cartesian view of the mind as an immaterial entity which acts upon a non-mental body, the 'ghost in the machine' view. Recently a similar attack has been raised against the 'Cartesian' body: the conception of \"some purely bodily component of a human being . . . is simply a figment of a philosophical imagination\"} Both attacks are well-founded and end unsurprisingly with the same conclusion: we aren't 'bodies plus minds' but unified beings with both mental and bodily aspects, that is persons, agents, human beings. 2 This is also Spinoza's conception of man in the Ethics. Which may not, however, be immediately apparent since several features of the Ethics remind us of the Cartesian 'fallacies'. The book begins with a treatment of God and what follows from his nature, and not of man and human actions. Then Spinoza makes much use of the distinction between the attributes of thought and extension, and correspondingly between the human mind and body. Furthermore he regards the mind and body as (limited) expressions of these attributes or of God or Substance. And his thesis of innate ideas, an important ingredient in rationalism, runs counter to a more empirically oriented theory of human action. Finally, it is hardly intelligible, within the framework of an empirical theory of action, to speak as Spinoza does of an 'eternal' part of man and of knowledge of God as effecting the realization of that part. Such views, whatever their true interpretation, surely mark significant differences with modern theories of man and human actions. They need not, however, be in any way incompatible with an 'ordinary' theory of action as basic to an explanation of man. There is in fact ample evidence that the whole philosophy of the Ethics is centered around man's active (mental and physical) nature. For Spinoza the treatment of God (or Substance or Nature as a whole) is obviously only a necessary prerequisite of a proper understanding of that active nature and may be taken to represent a significant enrichment compared with modern theories of action.

Spinoza on attributes

Abstract: In his discussion of Spinoza's views on attributes, Wolfson divides the commentators on Spinoza into two groups, those who believe that attributes for Spinoza are extra inteIlectum, exist outside the mind, and those who believe that attributes fol Spinoza are in intellectu, have no existence outside the mind) I want to begin by considering an argument to the effect that attributes for Spinoza are in intelIectu. 1 think the argument is mistaken. As a preliminary to showing how it is mistaken, I will develop my own interpretation of Spinoza's doctrine on attributes, an extra intellectum interpretation. The argument for Spinoza's considering attributes to be in intellectu is the following: Spinoza says that the only things extra intelleetum are substances and modes. (See the demonstration of Prop. 4 and the demonstration of Prop. 15, Book I, Ethics.) For Spinoza, no attribute is a mode. Attributes are conceived through themselves (Prop. I0, Book I, Ethics), and modes are not conceived through themselves (Def. 5, Book I, Ethics). Spinoza believed that there is one and only one substance (God), but more than one attribute (there are infinitely many). These two positions taken together are clearly incompatible with 'every attribute is a substance'. So, Spinoza couldn't have held that every attribute is a substance. Neither would he have held the absurb position that some one attribute is a substance, and the rest are not. So, he must have held that no attribute is a substance. If Spinoza held that no attribute is a mode, and no attribute is a substance, and that the only things extra intellectum are substances and modes, he must have held that attributes are not extra intellectum. So, he must have held that attributes are in intellectu. This argument seems powerful, but the conclusion that Spinoza held that attributes are in intelleetu is hard to square with a number o f things Spinoza

Logical and empirical assumptions of validity of inductions

Abstract: The problem of the justifiability of induction has a rather long tradition in philosophy of science. On one side of the dispute we meet many advocates and codifiers of inductive thinking, and — not least — the practice of several centuries of scientific investigations based in their essential aspects upon the application of induction. On the other side, beginning with Hume, are many of its critics. Some of them — like Reichenbach — have demonstrated the lack of sufficient justifiability of inductive method, but have nevertheless sanctioned its use for pragmatic reasons as the best thing we have for trying to discover the general regularities of the world around us. Others have rejected induction in general, arguing — like Popper — for an approach whereby we should rather try to falsify the hypotheses than to confirm them inductively.