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Switch to: References
Citations of:
A purely syntactical definition of confirmation
Journal of Symbolic Logic 8 (4):122-143 (1943)
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Knowledge is closed under implication, according to standard theories. Orthodoxy can allow, though, that apparent counterexamples to closure exist, much as Kripkeans recognize the existence of illusions of possibility which they seek to explain away. Should not everyone, orthodox or not, want to make sense of “intimations of openness”? This paper compares two styles of explanation: evidence that boosts P’s probability need not boost that of its consequence Q; evidence bearing on P’s subject matter may not bear on the subject (...) |
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According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) |
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In a recent paper James Bogen and James Woodward denounce a set of views on confirmation that they collectively brand 'IRS'. The supporters of these views cast confirmation in terms of Inferential Relations between observational and theoretical Sentences. Against 1RS accounts of confirmation, Bogen and Woodward unveil two main objections: (a) inferential relations are not necessary to model confirmation relations since many data are neither in sentential form nor can they be put in such a form and (b) inferential relations (...) |
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This essay describes a variety of contributions which relate to the connection of probability with logic. Some are grand attempts at providing a logical foundation for probability and inductive inference. Others are concerned with probabilistic inference or, more generally, with the transmittance of probability through the structure (logical syntax) of language. In this latter context probability is considered as a semantic notion playing the same role as does truth value in conventional logic. At the conclusion of the essay two fully (...) |
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Influential classical and recent approaches to explicate confirmation, explanation, or explanatory power define these relations or degrees between hypotheses and evidence. This holds for both deductive and Bayesian approaches. However, this neglects the role of data, which for many everyday and scientific examples cannot simply be classified as evidence. I present arguments to sharply distinguish data from evidence in Bayesian approaches. Taking into account this distinction, we can rewrite Schupbach and Sprenger’s measure of explanatory power and show the strengths of (...) |
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Hypothetico-deductive (H-D) confirmation builds on the idea that confirming evidence consists of successful predictions that deductively follow from the hypothesis under test. This article reviews scope, history and recent development of the venerable H-D account: First, we motivate the approach and clarify its relationship to Bayesian confirmation theory. Second, we explain and discuss the tacking paradoxes which exploit the fact that H-D confirmation gives no account of evidential relevance. Third, we review several recent proposals that aim at a sounder and (...) |
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This paper synthesizes confirmation by instances and confirmation by successful predictions, and thereby the Hempelian and the hypothetico-deductive traditions in confirmation theory. The merger of these two approaches is subsequently extended to the piecemeal confirmation of entire theories. It is then argued that this synthetic account makes a useful contribution from both a historical and a systematic perspective. |
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This is a philosophical and historical investigation of the role of inconsistent representations of the same scientific phenomenon. The logical difficulties associated with the simultaneous application of inconsistent models are discussed. Internally inconsistent scientific proposals are characterized as structures whose application is necessarily tied to the confirming evidence that each of its components enjoys and to a vision of the general form of the theory that will resolve the inconsistency. Einstein's derivation of the black body radiation law is used as (...) |
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There are two important traditions in the philosophy of induction. According to one tradition, which has dominated for the last couple of centuries, inductive arguments are warranted by rules. Bayesianism is the most popular view within this tradition. Rules of induction provide functional accounts of inductive support, but no rule is universal; hence, no rule is by itself an accurate model of inductive support. According to another tradition, inductive arguments are not warranted by rules but by matters of fact. Norton’s (...) |
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Extant literature on Goodman’s ‘New Riddle of Induction’ deals mainly with two versions. I consider both of them, starting from the (‘epistemic’) version of Goodman’s classic of 1954. It turns out that it belongs to the realm of applications of inductive logic, and that it can be resolved by admitting only significant evidence (as I call it) for confirmations of hypotheses. Sect. 1 prepares some ground for the argument. As much of it depends on the notion of evidential significance, this (...) |
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I I set out my view that all inference is essentially deductive and pinpoint what I take to be the major shortcomings of the induction rule.II The import of data depends on the probability model of the experiment, a dependence ignored by the induction rule. Inductivists admit background knowledge must be taken into account but never spell out how this is to be done. As I see it, that is the problem of induction.III The induction rule, far from providing a (...) |
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Projectible conditions are (roughly) those whose universal generalizations are con firmed by their positive instances. This paper proposes certain modifications to the above definition in order to capture the pre-analytic notion it is supposed to explicate. Then we investigate what logical operations, when performed on projectible conditionals, yield new projectible conditionals. A number of surprising theorems are proven, and these theorems indicate that few conditionals having complex antecedents and consequents are projectible. It is also shown that projectibility is not closed (...) |
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This research article revisits Hempel’s logic of confirmation in light of recent developments in categorical proof theory. While Hempel advocated several logical conditions in favor of a purely syntactical definition of a general non-quantitative concept of confirmation, we show how these criteria can be associated to specific logical properties of monoidal modal deductive systems. In addition, we show that many problems in confirmation logic, such as the tacked disjunction, the problem of weakening with background knowledge and the problem of irrelevant (...) |
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Realism is generally assumed as the correct position with regards to psychological research and the measurement of psychological attributes in psychometrics. Borsboom et al., 203–219 2003), for instance, argued that the choice of a reflective measurement model necessarily implies a commitment to the existence of psychological constructs as well as a commitment to the belief that empirical testing of measurement models can justify their correspondence with real causal structures. Hood :739–761 2013) deemphasized Borsboom et al.’s position and argued that the (...) |
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Philosophers such as Goodman, Scheffler and Glymour aim to answer the Paradox of the Ravens by distinguishing between confirmation simpliciter and selective confirmation. In the latter concept, the evidence both supports a hypothesis and undermines one of its "rivals". In this article, I argue that while selective confirmation does seem to be an important scientific notion, no attempt to formalise it thus far has managed to solve the Paradox of the Ravens. |
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A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go (...) |
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A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go (...) |
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It is argued that Hempel's original rejection of the prediction criterion of confirmation in [8] (on the grounds that it leads to a circular definition of confirmation) was ill-conceived, and that his own approach exhibits undesirable consequences to the degree that it deviates from this criterion. A version of the prediction criterion is formulated which, in addition to being-non circular, escapes the criticisms advanced against Hempel's satisfaction criterion, offers certain clear advantages over alternative approaches, and may serve as the basis (...) |
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ABSTRACTTime-consciousness has long been a focus of research in phenomenology and phenomenological psychology. We advance and extend this tradition of research by focusing on the character of temporal experience under conditions of mania. Symptom scales and diagnostic criteria for mania are peppered with temporally inflected language: increased rate of speech, racing thoughts, flight-of-ideas, hyperactivity. But what is the underlying structure of temporal experience in manic episodes? We tackle this question using a strategically hybrid approach. We recover and reconstruct three hypotheses (...) |
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In an unpublished speech from 1991, David Lewis told his audience that he counted ‘the metaphysician Carnap ’ amongst his historical ancestors. Here I provide a novel interpretation of the Aufbau that allows us to make sense of Lewis’s claim. Drawing upon Lewis’s correspondence, I argue it was the Carnap of the Aufbau whom Lewis read as a metaphysician, because Carnap’s appeal to the notion of founded relations in the Aufbau echoes Lewis’s own appeal to the metaphysics of natural properties. (...) |
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This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another (...) |
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The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: (...) |
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It is now commonly accepted that N. Goodman's predicate "grue" presents the theory of confirmation of C. G. Hempel (and other such theories) with grave difficulties. The precise nature and status of these "difficulties" has, however, never been made clear. In this paper it is argued that it is very unlikely that "grue" raises any formal difficulties for Hempel and appearances to the contrary are examined, rejected and an explanation of their intuitive appeal offered. However "grue" is shown to raise (...) |
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RÉSUMÉ : Depuis l’ouvrage classique de Goodman, on sait que toute théorie de l’induction doit comporter une composante non formelle. Or, la liberté théorique offerte par le recours à un tel élément implique des responsabilités. Cet article propose comme desideratum d’une théorie de l’induction qu’elle rende compte de la dynamique de sa composante non formelle. Ce desideratum, qui est nouveau, n’est pas satisfait par les principales théories existantes de l’induction. L’identification de l’importance de la dynamique a pourtant l’avantage de suggérer (...) |
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In his article [5], Brian Skyrms adduces some generalizations which, he claims, receive no confirmatory support from their positive instances even though all the predicates they contain are well entrenched in Goodman's sense. Invoking the principle that “a generalization is lawlike if it is capable of receiving confirmatory support from its positive instances”, he claims that his examples “provide striking demonstration of the fact that the lawlikeness of a hypothesis is not a simple function of the projectibility of its constituent (...) |
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The (recent, Bayesian) cognitive science literature on The Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on The Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, reexamining the (WT) with these historico-philosophical insights in mind. |
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The (recent, Bayesian) cognitive science literature on the Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on the Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, re-examining the (WT) with these historico-philosophical insights in mind. |
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Hempel first introduced the paradox of confirmation in (Hempel 1937). Since then, a very extensive literature on the paradox has evolved (Vranas 2004). Much of this literature can be seen as responding to Hempel’s subsequent discussions and analyses of the paradox in (Hempel 1945). Recently, it was noted that Hempel’s intuitive (and plausible) resolution of the paradox was inconsistent with his official theory of confirmation (Fitelson & Hawthorne 2006). In this article, we will try to explain how this inconsistency affects (...) |
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First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed. Specifically, the analogy reveals an intimate connection between Goodman's problem, and (...) |
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According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than (...) |
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According to a much discussed argument, reliabilism is defective for making knowledge too easy to come by. In a recent paper, Weisberg aims to show that this argument relies on a type of reasoning that is rejectable on independent grounds. We argue that the blanket rejection that Weisberg recommends of this type of reasoning is both unwarranted and unwelcome. Drawing on an older discussion in the philosophy of science, we show that placing some relatively modest restrictions on the said type (...) |
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Il problema dell'induzione è tra i più dibattuti in filosofia della scienza. Il mio tentativo in questo scritto sarà di mostrare come un'indagine sull'induzione possa contribuire a chiarire i termini del dibattito intorno a relativismo, pluralismo culturale e democrazia. |
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There appears to be a widespread belief that the social sciences during the 1950s and 1960s can be characterized by an almost unquestioned faith in a positivist philosophy of science. In contrast, the article shows that even within the narrower segment of Cold War social science, positivism was not an unquestioned doctrine blindly followed by everybody, but that quite divergent views coexisted. The article analyses two ‘techniques of prospection’, the Delphi technique and political gaming, from the perspective of a comprehensive (...) |
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The current state of inductive logic is puzzling. Survey presentations are recurrently offered and a very rich and extensive handbook was entirely dedicated to the topic just a few years ago [23]. Among the contributions to this very volume, however, one finds forceful arguments to the effect that inductive logic is not needed and that the belief in its existence is itself a misguided illusion , while other distinguished observers have eventually come to see at least the label as “slightly (...) |
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1. Deductive and Inductive Inference. Within the traditional treatments of scientific method, e.g., in and, it was customary to divide scientific inference into two parts: deductive and inductive. Deductive inference was taken to mean the activity of deducing theorems from postulates and definitions, whereas inductive inference represented the activity of constructing a general statement from a set of particular “facts.” Deductive inference was relegated to the mathematical sciences, and inductive inference to the empirical sciences. As a consequence, the whole of (...) |
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The discussion about the Raven Paradox is ever-renewing: after nearly 70 years, many authors propose from time to time new solutions, and many authors state that these solutions are unsatisfactory. It is worthy to be carefully noted that though most arguments in favor or against the paradox are based on the notion of “probability” and on the application of Bayes’ law, not one of them makes use of the Kolmogorov axiomatic theory of probability and on the subsequent notion of “random (...) |
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1. Object of this note . In his lively essay, “Between Analytic and Empirical,” , Mr. J. W. N. Watkins challenges the empiricist identification of synthetic statements with empirical ones by arguing that there exists an important class of statements which are synthetic, i.e. not analytically true or false, and yet not empirical. I find Mr. Watkins's arguments very stimulating, but I do not think they provide a sound basis for his contention. In the present note, I wish to indicate (...) |
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This paper considers the relationship between G. H. von Wright's solution to the paradoxes of confirmation and his "Principal Theorem of Confirmation". The former utilizes the order of our knowledge of the qualities of confirming instances of an hypothesis; the latter states the way in which an instance contributes to the probability of an hypothesis. It is shown that these two, as stated by von Wright, are logically incompatible. Then the most thorough possible emendation of the paradoxes solution is considered, (...) |
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Inductive generalization asserts that what obtains in known instances can be generalized to all. Its original form is enumerative induction, the earliest form of inductive inference, and it has been elaborated in various ways, largely with the goal of extending its reach. Its principal problem is that it supplies no intrinsic notion of strength of support so that one cannot tell if the generalization has weak or strong support. |
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The problem adressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen 1983, 27). |
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