Showing papers in "Synthese in 1973"
TL;DR: In this paper, the authors define the notion of belief as degree of confidence, which can be ordered as to strength and admits of quantatization, and discuss the justification of condition (ii) from the point of view of a frequency interpretation of probability or reasonable degree of belief.
Abstract: I take bayesianism to be the doctrine which maintains that (i) a set of reasonable beliefs can be represented by a probability function defined over sentences or propositions, and that (ii) reasonable changes of belief can be represented by a process called conditionalization. Bayesians have produced several ingenious arguments in support of (i); but the equally important second condition they often seem to take completely for granted. My main aim is to fill this gap in those bayesian positions which characterize reasonable belief directly as a probability function. Thus, what follows applies equally to the bayesian personalists' views which characterize reasonable belief as having subjective sources and to views such as that of Carnap which attempt to explicitly define a function which characterizes the degree of belief it would be objectively reasonable for an idealized rational agent to have in a given proposition in stated circumstances. Many frequentist views are also classifiable as bayesian, and I will briefly discuss the justification of condition (ii) from the point of view of a frequency interpretation of probability or reasonable degree of belief. Along the way I will also have occasion to touch on the connection between conditionalization and observation. Throughout the discussion I will rely on several common bayesian presuppositions. The object of study is a notion of belief, perhaps most aptly described as degree of confidence, which can be ordered as to strength and admits of quantatization. Such beliefs, or degrees of confidence, are assumed to reveal themselves in an agent's disposition to make bets voluntarily or under duress. The agent whose beliefs are under discussion is assumed to be an ideal logician, and the set of propositions about which the agent has beliefs is assumed to be closed under all logical operations. Also, the set of propositions for which the agent entertains beliefs is assumed to be fixed. Quite clearly, when this assumption is violated, the bayesian model does not apply; and the most cogent arguments against
187 citations
TL;DR: The difficulties raised in this paper have, then, wider purport, and should serve as something of a touchstone for those who would construct a theory of evidence adequate to statistics without recourse to the notion of inductive probability as mentioned in this paper.
Abstract: The pre-designationist, anti-inductivist and operationalist tenor of Neyman-Pearson theory give that theory an obvious affinity to several currently influential philosophies of science, most particularly, the Popperian. In fact, one might fairly regard Neyman-Pearson theory as the statistical embodiment of Popperian methodology. The difficulties raised in this paper have, then, wider purport, and should serve as something of a touchstone for those who would construct a theory of evidence adequate to statistics without recourse to the notion of inductive probability.
78 citations
TL;DR: In this paper, the ambiguities found in the following sentences are investigated: (1) Bill loves his wife, and so does Harry; (2) John thinks he is smart, and Bill thinks John is smart; (3) Only Sam loves his own wife.
Abstract: How is a grammar to account for the ambiguities found in the following sentences ? (1) Bill loves his wife, and so does Harry. Possible interpretations: Bill loves his wife, and Harry loves (a) Harry's wife, (b) Bill's wife. 1 (2) John thinks he is smart, and so does Bill. Possible interpretations: John thinks he is smart, and Bill thinks (a) Bill is smart, (b) John is smart. (3) Only Sam loves his wife. Possible interpretations: (a) Sam is the only person such that that person loves his own wife. (b) Sam is the only person such that he loves Sam's wife. (4) It was Spiro'who voted for himself. Possible interpretations: (a) Spiro is the person who voted for himself. (b) Spiro is the person who voted for Spiro. Let us for lack of any better names call the (a) readings the 'nonreferential' readings and the (b) readings the 'referential' readings.
44 citations
TL;DR: Carnap's theory of inductive probability and his philosophy of induction were discussed in this article, where the basic system of Inductive Logic and its philosophy of inductivity were discussed.
Abstract: During his life Carnap published two extensive, systematic works on inductive logic: Logical Foundations of Probability [4] and The Continuum of Inductive Methods [5]. These works report Carnap's research in induc tion and probability in the 1940's and early 1950's. After the publication of the Continuum in 1952 Carnap continued his research in inductive logic, and in the course of this research both his theory of inductive probability and his philosophy of induction underwent development. Most of Carnap's publications since 1952 have dealt with the philosophy and methodology of induction rather than inductive logic proper.1 A part of his recent research in inductive logic will be published in an extensive work 'The Basic System of Inductive Logic', forthcoming in Studies in Inductive Logic and Probability, I?II (edited by Rudolf Carnap and Richard Jeffrey).2 This paper discusses the development of Carnap's system of inductive logic and his philosophy of induction during the past twenty years. Our exposition and discussion of Carnap's inductive logic is based mainly on 'The Basic System of Inductive Logic' [13B-C] and partly on an earlier (unpublished) version of the same work, 'An Axiom System of Inductive Logic' [13A]. The theory presented in the 'Basic System' will be termed 'Carnap's New System' or the 'Basic System', and that presented in Log ical Foundations of Probability and the Continuum will be called 'Carnap's Old System'. Sections II?III of this paper discuss Carnap's philosophy of induction, Sections IV-VII contain an exposition of the main features of the 'Basic System', and the concluding Sections VIII-IX discuss the philosophical implications of Carnap's New System.
20 citations
TL;DR: There are two explicanda, both called "probability": (1) logical or inductive probability, (2) statistical probability, and (3) degree of confirmation as discussed by the authors.
Abstract: There are two explicanda, both called 'probability': (1) logical or inductive probability (probability0, (2) statistical probability (probabilityz). Read: [Prob.] Ch. II, esp. §§ 9 and 10. The logical concept of probability appears in three forms ([Prob.] § 8): (a) the classificatory concept (confirming evidence), (b) the comparative concept (higher confirmation), (c) the quantitative concept (degree of confirmation).
15 citations
12 citations
TL;DR: The contribution of Jiirgen Habermas and N. Luhmann as discussed by the authors in the 'Vorbereitende Bemerkungen zu einer Theorie der kommunikativen Kompetenz' which form one chapter (pp. 101-141) of the book by J.H.
Abstract: Having spent a good amount of my free time during the academic year 1971/72 1 stayed in Germany in studying the recently published (and some of the as yet unpublished) work of German hermeneuticians in philosophy of language, I would like to submit to the reader some of my reactions. The present paper will deal with the contributions of Jiirgen Habermas, more specifically with those contained in the 'Vorbereitende Bemerkungen zu einer Theorie der kommunikativen Kompetenz' which form one chapter (pp. 101-141) of the book by J. Habermas and N. Luhmann, Theorie der Gesellschaft oder Sozialtechnologie (Suhrkamp Verlag, Frankfurt, 1971). I hope to publish my reactions to the contributions of Karl-Otto Apel elsewhere. Though Habermas has dealt with philosophy of language in prior publications 1 and deals with it in a couple of sections of another chapter of the same book (pp. 117if) and though the subtitle of the chapter to be discussed is 'Vorlage f/Jr Zwecke einer Seminardiskussion' indicating the somewhat tentative nature of its content and I understand that Habermas is working on a more polished version I do not think it unfair to concentrate on this particular chapter since it seems to be fully self-contained. The first page (p. 101) begins promising enough. I had some trouble understanding what Habermas meant by his critique of the Chomskyan distinction between linguistic competence and linguistic performance, to the effect that it does not account for \"the circumstance that the general structures of possible speech situations are themselves produced by speech acts\" but finally decided that he must have something in mind like the fact that sometimes when a speaker is about to utter a sentence in order to perform thereby a certain speech act but realizes that the hearer might perhaps misunderstand the kind of speech act intended, he is in a position to alleviate the situation by prefixing (or postfixing, or even, on occasion, infixing) the sentence to be uttered by an appropriate phrase such as one o f the performative phrases of Austinian fame. Should a speaker be in
11 citations
9 citations
TL;DR: In this paper, the problem of distinguishing the factual and conventional components was solved by R. Carnap for finite sets of postulates as follows [4], [5, pp. 958-66].
Abstract: The attempt to distinguish within an empirical theory between a factual and a conventional component is an important task. It bears especially on the following methodological issues. 'Cognitive status' of theories: The dispute between conventionalism and its critics concerns just where this distinction should be drawn. But equally, if the conventional part of a theory determines the reference of some of its expressions, the question whether theoretical assertions of empirical science include non-conventional statements of determinate truth-value cannot be settled until an exact characterization of the con ventional part is given. Inter-theory relations: It is clear that logical relations between theories inconsistency, equivalence, reducibility, etc. - depend critically on intra theoretic relations. These are determined for each theory in a way which depends on the choice of conventional component. Evidential support: It is to be expected that an adequate measure of support furnished to theory by evidence should assign the highest value to statements belonging to the conventional part. It follows that the measure appropriate to the language of a given theory depends on how its factual and conventional components are distinguished. The problem of distinguishing the factual and conventional component was solved by R. Carnap for finite sets of postulates as follows [4], [5, pp. 958-66]. Let n be the conjunction of theoretical postulates and correspondence postulates and let the descriptive constants of n be distinguished into O-terms and T-terms. Let Rn be the existential closure of the formula obtained from n by proper simultaneous substitution of predicate variables for T-terms. Then the factual part of n is identified with the consequence class of Rn and its conventional part with the con sequence class of Rn;:) n. It is understood in addition that a partial inter pretation is effected for T-terms by restricting their proper interpre tations to those that establish the truth of Rn;:) n given prior interpretations of O-terms. Carnap made the following expository observations:
7 citations
TL;DR: The main theme of this paper is : How can the authors confirm causal laws by ex perience!
Abstract: The main theme of this paper is : How can we confirm causal laws by ex perience! What we call 'empirical knowledge' must be justified or con firmed by referring, in some way, to experience. But our knowledge has a certain structure or hierarchy; it is not just a bunch of unclassified records of particular facts. Then we should expect that there is also a certain structure or order in the process of confirmation of our empirical knowledge; it is not just a matching between particular items in our knowledge, on one hand, and particular facts in the world, on the other. There must be some sort of organizing principles in the process of con firmation. Here is where Hume's observation comes in:
Journal Article•
TL;DR: In this paper, W. Quine discusses the relationship between coordination and convention, and the meaning of signals and their application in the context of semantics in a possible language and in a population.
Abstract: Acknowledgements. Foreword by W.V. Quine. Introduction. I. Coordination and Convention. Sample Coordination Problems. Analysis of Coordination Problems. Solving Coordination Problems. Convention. Sample Conventions. II. Convention Refined. Common Knowledge. Knowledge of Conventions. Alternatives to Convention. Degrees of Convention. Consequences of Conventions. III. Convention Contrasted. Agreement. Social Contracts. Norms. Rules. Conformative Behavior. Imitation. Meaning of Signals. IV. Convention and Communication. Sample Signals. Analysis of Signaling. Verbal Signaling. Conventional Meaning of Signals. V. Conventions of Language. Possible Languages. Grammars. Semantics in a Possible Language. Conventions of Truthfulness. Semantics in a Population. Conclusion. Index.
TL;DR: Carnap's Aufbau as discussed by the authors is an attempt to explain certain features of the World or Reality (the World, or Reality, of Science), or of our knowledge thereof, by studying a model.
Abstract: In his work Der logische Aufbau der Welt, first published in 1928, Carnap appeared as a philosopher with ambitions no smaller than those of the great system builders. 1 In less than 300 pages he hoped to solve practically all the classical problems of philosophy, and he thought he could do so with something of the logical rigor of Principia Mathematica. On more than one score, Carnap's work invites comparison with Wittgenstein's Tractatus logico-philosophicus, published seven years earlier. Carnap's ideas in the Aufbau are in part influenced by Wittgenstein's in the Traetatus. The world models of both are sketched by reference to the coordinate system of the logic of Frege and Russell. Whereas Wittgenstein did not wish to say anything about the world beyond what could be said a priori, Carnap aimed at a kind of inventory of the total contents of the world. Whereas Wittgenstein speaks in aphorisms, Carnap is the pedagogical teacher. The view that the Tractatus is the expression of mystical vision and the Aufoau that of rationalistic systematics no doubt contains a measure of truth. In contrast with the Tractatus, the Auj'bau may indeed appear as a model of clarity. The more one studies the Aufoau, however, the more this contrast tends to vanish, the more obscure and ambiguous the argument of this work seems. Since I am not aware of the existence of any clarifying analysis of this argument, I shall here make a second attempt to analyze it. 2 My exegesis has taken a critical turn, but its aim is exegesis, not criticism. What is only vaguely hinted at in the Aufbau I have tried to state explicitly. Roughly speaking, the Aufbau is an attempt to explain certain features of the World or Reality (the World, or Reality, of Science), or of our knowledge thereof, by studying a model. The world model of the Aufbau is 'phenomenalistic' and even 'solipsistic'. Its basic concepts belong to introspective psychology and, in particular, to the phenomenology of perception. In Section I I shall try to explain the psychological contents of
TL;DR: Indefinite probability statements can be analysed in terms of statements which attribute probability to propositions and there is no need to find a special place in probability theory for them.
Abstract: Indefinite probability statements can be analysed in terms of statements which attribute probability to propositions. Therefore, there is no need to find a special place in probability theory for them; once we have an adequate account of statements that straightforwardly attribute probability to propositions, we will automatically have an adequate account of indefinite probability statements.
TL;DR: A two-dimensional system will be constructed that describes a learning process both for relative frequencies of properties and for the size of the family; it may be called a generalization of Carnap's continuum.
Abstract: 1 Carnap's continuum of inductive methods for a family of monadic predicates, the so-called ?-continuum or ?-system, is restricted by the as sumption that the size of the family is known at the start of the learning process In the proper inductive situation we do not have this information In this article a two-dimensional system will be constructed that is appropriate to deal with the proper inductive situation This system describes a learning process both for relative frequencies of properties and for the size of the family; it may therefore be called a generalization of Carnap's continuum
TL;DR: The Innateness Hypothesis as mentioned in this paper posits that many of the complex features of natural languages are not learned by the child, but rather reflect the structure of the innate language learning apparatus.
Abstract: Noam Chomsky's work in linguistic theory has had a revolutionary impact on the study of language. Probably the most controversial of Chomsky's claims (and certainly the one which has received the most attention from scholars in disciplines other than linguistics) is that human beings are genetically endowed with a highly structured language learning mechanism, knowledge of which will also provide knowledge about the scope and limits of the human mind. This claim is referred to as the 'Innateness Hypothesis', and Chomsky bases it on the apparent incompatibility of two well-established facts: (i) that natural languages are immensely complex structurally so much so that nobody has ever succeeded in writing a complete grammar of any one of them (i.e., a set of rules which will specify precisely which strings of words are wellformed sentences); and (ii) that all normal children master their native tongues in a remarkably short period (generally aggreed to be no more than four years) with little or no formal instruction. Chomsky has suggested in various places that reconciling these facts is "the fundamental empirical problem of linguistics" (Chomsky, 1971). The Innateness Hypothesis makes it possible to solve this problem by positing that many of the complex features of natural languages are not learned by the child, but rather reflect the structure of the innate language learning apparatus. That is to say, any structural properties of languages which are manifestations of the structure of the innate language learning mechanisms are not themselves learned. Hence, what the child actually learns in acquiring a language may in fact be far less than it at first seems. It follows from this account of (i) and (ii) that there must be numerous structural properties common to all natural languages. Since any normal child will acquire the language to which he or she is exposed, we can assume that all humans have identical innate language learning mech-
TL;DR: A way of looking at syntax is arrived at which sheds new light on two important questions, one of which concerns the idea of 'transformations' as employed by the transformational grammarians and the other is the question of the connection between syntax and semantics.
Abstract: In the language of symbolic logic a sentence or, as the logicians call it, a well-formed formula is constructed according to recursive rules. The idea that the rules of syntax of a language must be formulated recursively has been taken over by Chomsky and other transformational grammarians of natural languages. There is, accordingly, a kind of similarity between the procedure of sentence construction adopted by transformational grammarians and the corresponding procedure in symbolic logic - both are conceived of as recursive procedures. But there the similarity ends. To be sure, Chomsky maintains that the grammars of symbolic logic are incorporated in his approach - they are, he says, special instances of what he calls 'phrase structure grammars'. But is this contention true? Are the rules of syntax employed in symbolic logic really 'phrase structure grammars' in Chomsky's sense? In any case the application of the underlying principles to ordinary languages produces forms of grammar which deviate from Chomskyan 'phrase structure grammar' in a significant way. One thing I want to point out in this paper is this difference. However, once we have seen this difference we arrive at a way of looking at syntax which sheds new light on two important questions. One of these questions concerns the idea of 'transformations' as employed by the transformational grammarians. The other is the question of the connection between syntax and semantics.
TL;DR: The authors characterise as statistical indeterminism the view that for a given type of population it is possible to determine its behaviour statistically and say, for instance, that so and so many percent of it will be found in a given state, so and such in another etc., but holding also that it is not possible to establish for any given member of this population in which of the possible states it would be found on the occasion in question.
Abstract: I shall characterise as statistical indeterminism the view that for a given type of population it is possible to determine its behaviour statistically and say, for instance, that so and so many percent of it will be found in a given state, so and so in another etc., but holding also that it is not possible to establish for any given member of this population in which of the possible states it will be found on the occasion in question.
TL;DR: In this article, a rule (AG?) formulated by Risto Hilpinen in his 'Rules of Acceptance and Inductive Logic' (1968) is discussed, which is based on one of the probability functions P defined for Lk in Hintikka's system (1966), with parameters: a finite and?(w) = w.
Abstract: My remarks will concern the rule (AG?) formulated by Risto Hilpinen in his 'Rules of Acceptance and Inductive Logic' (1968); I shall refer here to this work as 'Rules'.1 I shall use the terminology of Jaakko Hintikka adopted in 'Rules' without any explanations. (AG?) is a rule for inductive generalizations in a simple language Lk (first-order logic with ?-monadic predicates); it is based on one of the probability-functions P defined for Lk in Hintikka's system (1966), with parameters: a finite and ?(w) = w. The rule is formulated as follows ('Rules', p. 64) :