Sections 1 through 3 present all of the main ideas behind the probabilistic logic of evidential support. For most readers these three sections will suffice to provide an adequate understanding of the subject. Those readers who want to know more about how the logic applies when the implications of hypotheses about evidence claims (called likelihoods) are vague or imprecise may, after reading sections 1-3, skip to section 6. Sections 4 and 5 are for the more advanced reader who wants a (...) detailed understanding of some telling results about how this logic may bring about convergence to the truth. (shrink)

Peter Achinstein has argued at length and on many occasions that the view according to which evidential support is defined in terms of probability-raising faces serious counterexamples and, hence, should be abandoned. Proponents of the positive probabilistic relevance view have remained unconvinced. The debate seems to be in a deadlock. This paper is an attempt to move the debate forward and revisit some of the central claims within this debate. My conclusion here will be that while Achinstein may be right (...) that his counterexamples undermine probabilistic relevance views of what it is for e to be evidence that h, there is still room for a defence of a related probabilistic view about an increase in being supported, according to which, if p > p, then h is more supported given e than it is without e. My argument relies crucially on an insight from recent work on the linguistics of gradable adjectives. (shrink)

This paper is a sequel to my 'Theological Misinterpretations of Current Physical Cosmology' (Foundations of Physics [1996], 26 (4); revised in Philo [1998], 1 (1)). There I argued that the Big Bang models of (classical) general relativity theory, as well as the original 1948 versions of the steady state cosmology, are each logically incompatible with the time-honored theological doctrine that perpetual divine creation ('creatio continuans') is required in each of these two theorized worlds. Furthermore, I challenged the perennial theological doctrine (...) that there must be a divine creative cause (as distinct from a transformative one) for the very existence of the world, a ratio essendi. This doctrine is the theistic reply to the question: 'Why is there something, rather than just nothing?' I begin my present paper by arguing against the response by the contemporary Oxford theist Richard Swinburne and by Leibniz to what is, in effect, my counter-question: 'But why should there be just nothing, rather than something?' Their response takes the form of claiming that the a priori probability of there being just nothing, vis-à-vis the existence of alternative states, is maximal, because the non-existence of the world is conceptually the simplest. On the basis of an analysis of the role of simplicity in scientific explanations, I show that this response is multiply flawed, and thus provides no basis for their three contentions that (i) if there is a world at all, then its 'normal', natural, spontaneous state is one of utter nothingness or total non-existence, so that (ii) the very existence of matter, energy and living beings constitutes a deviation from the allegedly 'normal', spontaneous state of 'nothingness', and (iii) that deviation must thus have a suitably potent (external) divine cause. Related defects turn out to vitiate the medieval Kalam Argument for the existence of God, as espoused by William Craig. Next I argue against the contention by such theists as Richard Swinburne and Philip L. Quinn that (i) the specific content of the scientifically most fundamental laws of nature, including the constants they contain, requires supra-scientific explanation, and (ii) a satisfactory explanation is provided by the hypothesis that the God of theism willed them to be exactly what they are. Furthermore, I contend that the theistic teleological gloss on the 'Anthropic Principle' is incoherent and explanatorily unavailing. Finally, I offer an array of considerations against Swinburne's attempt to show, via Bayes's theorem, that the existence of God is more probable than not. (shrink)

The paper builds on the basically Humean idea that A is a cause of B iff A and B both occur, A precedes B, and A raises the metaphysical or epistemic status of B given the obtaining circumstances. It argues that in pursuit of a theory of deterministic causation this ‘status raising’ is best explicated not in regularity or counterfactual terms, but in terms of ranking functions. On this basis, it constructs a rigorous theory of deterministic causation that successfully deals (...) with cases of overdetermination and pre-emption. It finally indicates how the account's profound epistemic relativization induced by ranking theory can be undone. Introduction Variables, propositions, time Induction first Causation Redundant causation Objectivization. (shrink)

Logical analyses of scientific representations of the world have usually focused on axiomatized or axiomatizable theories. As practiced, science seldom employs such theories. Rather, we find aggregations of claims, the logical relations of which are not as neat as philosophers of science might like them to be. Indeed, a common feature of such aggregations is the presence of certain “theoretical anomalies,” statements that are in some way incompatible with the remainder of the corpus. Huygens’ description of light as exhibiting an (...) asymmetry with respect to its direction of propagation in polarization phenomena was such an anomaly because of its inconsistency with his account of light as longitudinal waves in a medium. (See Sabra 1981, pp. 226-227.) Although the occurrence of these anomalies is indicative of a problem that must be dealt with, inconsistent representations of the world are not without significant heuristic value. (shrink)

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 (...) an example application of such a strategy and is contrasted with planck's derivation. (shrink)

On analogy with testimony, I define a notion of a scientific theory’s lacking or having candor, in a testing situation, according to whether the theory under test is probabilistically relevant to the processes in the test procedures, and thereby to the reliability of test outcomes. I argue that this property identifies what is distinctive about those theories that Karl Popper denounced as exhibiting “reinforced dogmatism” through their self-protective behavior (e.g., psychoanalysis, Hegelianism, Marxism). I explore whether lack of candor interferes with (...) the testing of theories, and conclude that (1) our default attitude toward theories that lack candor in a given test should be suspicion, but (2) the circumstance that a theory lacks candor in a testing situation does not preclude obtaining independent evidence for the auxiliary assumptions to which the theory is probabilistically relevant, and thereby eliminating the problem that lack of candor creates. Thus, Popper was right to think that lack of candor is a bad thing, but wrong to conclude that candor is a criterion of the scientificity of a theory. Seeing this requires recognition of some differences between intuitive relevance and probabilistic relevance, and proper appreciation of the notion of screening off and of the fact that probabilistic relevance is not transitive. (shrink)

This paper reviews all major theories of evidence such as the Bayesian theory, hypothetico-deductivism, satisfaction theories, error-statistics, Achinstein's explanationist theory and Cartwright's argument theory. All these theories fail to take adequate account of the context in which a hypothesis is established and used. It is argued that the context of an inquiry determines important facts about what evidence is, and how much and what kind has to be collected to establish a hypothesis for a given purpose.

In this paper, I explore Larry Laudan's and Jarrett Leplin's recent claim that empirically equivalent theories may be differentially confirmed. I show that their attempt to prise apart empirical equivalence and epistemic parity commits them to two principles of confirmation that Hempel demonstrated to be incompatible.

A Bayesian account of the virtue of unification is given. On this account, the ability of a theory to unify disparate phenomena consists in the ability of the theory to render such phenomena informationally relevant to each other. It is shown that such ability contributes to the evidential support of the theory, and hence that preference for theories that unify the phenomena need not, on a Bayesian account, be built into the prior probabilities of theories.

The purpose of this article is to examine the applicability of the theory of projection for Anthropological hypotheses. The claim is made that Goodman's classic statement of the problem does not apply in its entirety to actual Anthropological hypotheses. The recent Freeman-Mead debate is employed as a framework for the discussion, illustrating that the issue of projectibility, while central for the social sciences, is best used as a backdrop to illustrate several important methodological problems. For Anthropology, and other related social (...) sciences, the central methodological problem, which is directly related to the projectibility one, is the development and justification of evidence-rules that can be used for a theory of confirmation. A preliminary attempt is then made to articulate the nature of these rules within the general Hempelian framework of qualitative confirmation. (shrink)

Peter Achinstein has argued at length and on many occasions that the view according to which evidential support is defined in terms of probability-raising faces serious counterexamples and, hence, should be abandoned. Proponents of the positive probabilistic relevance view have remained unconvinced. The debate seems to be in a deadlock. This paper is an attempt to move the debate forward and revisit some of the central claims within this debate. My conclusion here will be that while Achinstein may be right (...) that his counterexamples undermine probabilistic relevance views of what it is for e to be evidence that h, there is still room for a defence of a related probabilistic view about an increase in being supported, according to which, if p > p, then h is more supported given e than it is without e. My argument relies crucially on an insight from recent work on the linguistics of gradable adjectives. (shrink)

Two notions of evidence are focused on in this essay, Carnap's positive-relevance notion of evidence (1962, pp. 462 ff.), and Achinstein's notion of potential evidence (1978; and 1983, pp. 322–350). Achinstein creates several interesting examples in his attempt to find faults in Carnap's notion of evidence; his motive, ultimately, is to impel us towards potential evidence. The purpose of this essay is to show that positive relevance is significantly more promising than potential evidence with respect to capturing the scientific sense (...) of the term evidence. This is accomplished by finding faults in the notion of potential evidence, and by defending positive relevance against Achinstein's examples. (shrink)

This essay addresses the question of when evidence for a stronger claim H1 also constitutes evidence for a weaker claim H2. Although the answer “Always” is tempting, it is false on a natural Bayesian conception of evidence. This essay first describes some prima facie counterexamples to this answer and surveys some weaker answers and rejects them. Next, it proposes an answer, which appeals to the “Dragging Condition.” After explaining and arguing for its use of the Dragging Condition, the essay argues (...) that the Dragging Condition provides a general account of, and solution to, the counterexamples with which the essay began. The essay briefly discusses the relevance of the Dragging Condition to the recently much-discussed topic of “transmission failure” in epistemology, applies the Dragging Condition to the problem of “bootstrapping” in epistemology, and discusses three important objections to the view defended in the essay. (shrink)

, Peter Achinstein argues against the long-standing claim that ‘evidence’ is ambiguous in possessing a sense of confirming evidence and a sense of supporting evidence. He argues that explications of supporting evidence will necessarily violate his contentions that evidence is a discontinuous ‘threshold concept’ and that any philosophical account of supporting evidence will be too weak to be useful to working scientists. But an account of supporting evidence may be formulated which includes Achinstein's notion of epistemic thresholds that finds examples (...) in Achinstein's own historical case studies. Thresholds and the denial of ambiguity Achinstein's new account of confirming evidence Achinstein's argument against the ‘ambiguity response’ A threshold-based approach for restoring the ambiguity Maxwell and ‘a subject of rational curiosity’ Bohr and ‘future development of our understanding’ Perrin and the edge of reasonable belief Restoring ambiguity. (shrink)

In this note, I consider various precisifications of the slogan ‘evidence of evidence is evidence’. I provide counter-examples to each of these precisifications (assuming an epistemic probabilistic relevance notion of ‘evidential support’).

Among the most serious challenges to scientific realism are arguments for the underdetermination of theory by evidence. This paper defends a version of scientific realism against what is perhaps the most influential recent argument of this sort, viz. Kyle Stanford’s New Induction over the History of Science. An essential part of the defense consists in a probabilistic analysis of the slogan “absence of evidence is not evidence of absence”. On this basis it is argued that the likelihood of a theory (...) being underdetermined depends crucially on social and historical factors, such as the structure of scientific communities and the time that has passed since the theory first became accepted. This is then shown to serve as the epistemological foundation for a version of scientific realism which avoids Stanford’s New Induction in a principled and non-question-begging way. (shrink)

The traditional Bayesian qualitative account of evidential support (TB) takes assertions of the form 'E evidentially supports H' to affirm the existence of a two-place relation of evidential support between E and H. The analysans given for this relation is $C(H,E) =_{def} Pr(H\arrowvertE) \models Pr(H)$ . Now it is well known that when a hypothesis H entails evidence E, not only is it the case that C(H,E), but it is also the case that C(H&X,E) for any arbitrary X. There is (...) a widespread feeling that this is a problematic result for TB. Indeed, there are a number of cases in which many feel it is false to assert 'E evidentially supports H&X', despite H entailing E. This is known, by those who share that feeling, as the 'tacking problem' for Bayesian confirmation theory. After outlining a generalization of the problem, I argue that the Bayesian response has so far been unsatisfactory. I then argue the following: (i) There exists, either instead of, or in addition to, a two-place relation of confirmation, a three-place, 'contrastive' relation of confirmation, holding between an item of evidence E and two competing hypotheses H₁ and H₂. (ii) The correct analysans of the relation is a particular probabilistic inequality, abbreviated C(H₁, H₂, E). (iii) Those who take the putative counterexamples to TB discussed to indeed be counterexamples are interpreting the relevant utterances as implicitly contrastive, contrasting the relevant hypothesis H₁ with a particular competitor H₂. (iv) The probabilistic structure of these cases is such that ∼C(H₁, H₂, E). This solves my generalization of the tacking problem. I then conclude with some thoughts about the relationship between the traditional Bayesian account of evidential support and my proposed account of the three-place relation of confirmation. (shrink)

What is the relation or connection between formalizations of induction and the actual inductive inferences of scientists? Building from recent works in the philosophy of logic, this paper argues that these formalizations of induction are best viewed as models and not literal descriptions of inductive inferences in science. Three arguments are put forward to support this claim. First, I argue that inductive support is the kind of phenomenon that can be justifiably modeled. Second, I argue that these formalizations have the (...) features that define models—that they have representors, artefacts, and idealizations. Third, I argue that these formalizations being models explains their plurality and revisability. (shrink)

Peter Brössel and Franz Huber in 2015 argued that the Bayesian concept of confirmation had no use. I will argue that it has both the uses they discussed—it can be used for making claims about how worthy of belief various hypotheses are, and it can be used to measure the epistemic value of experiments. Furthermore, it can be useful in explanations. More generally, I will argue that more coarse-grained concepts can be useful, even when we have more fine-grained concepts available.

Should philosophers prefer simpler theories? Huemer (Philos Q 59:216–236, 2009) argues that the reasons to prefer simpler theories in science do not apply in philosophy. I will argue that Huemer is mistaken—the arguments he marshals for preferring simpler theories in science can also be applied in philosophy. Like Huemer, I will focus on the philosophy of mind and the nominalism/Platonism debate. But I want to engage with the broader issue of whether simplicity is relevant to philosophy.

This article defends the Doomsday Argument, the Halfer Position in Sleeping Beauty, the Fine-Tuning Argument, and the applicability of Bayesian confirmation theory to the Everett interpretation of quantum mechanics. It will argue that all four problems have the same structure, and it gives a unified treatment that uses simple models of the cases and no controversial assumptions about confirmation or self-locating evidence. The article will argue that the troublesome feature of all these cases is not self-location but selection effects.

Sometimes we learn what the world is like, and sometimes we learn where in the world we are. Are there any interesting differences between the two kinds of cases? The main aim of this article is to argue that learning where we are in the world brings into view the same kind of observation selection effects that operate when sampling from a population. I will first explain what observation selection effects are ( Section 1 ) and how they are relevant (...) to learning where we are in the world ( Section 2 ). I will show how measurements in the Many Worlds Interpretation of quantum mechanics can be understood as learning where you are in the world via some observation selection effect ( Section 3 ). I will apply a similar argument to the Sleeping Beauty Problem ( Section 4 ) and explain what I take the significance of the analogy to be ( Section 5 ). Finally, I will defend the Restricted Principle of Indifference on which some of my arguments depend ( Section 6 ). (shrink)

Many who take a dismissive attitude towards metaphysics trace their view back to Carnap’s ‘Empiricism, Semantics and Ontology’. But the reason Carnap takes a dismissive attitude to metaphysics is a matter of controversy. I will argue that no reason is given in ‘Empiricism, Semantics and Ontology’, and this is because his reason for rejecting metaphysical debates was given in ‘Pseudo-Problems in Philosophy’. The argument there assumes verificationism, but I will argue that his argument survives the rejection of verificationism. The root (...) of his argument is the claim that metaphysical statements cannot be justified; the point is epistemic, not semantic. I will argue that this remains a powerful challenge to metaphysics that has yet to be adequately answered. (shrink)

In this paper I examine five distinctions between deductive and inductive arguments, concluding that the best of the five defines a deductive argument as one in which conclusive favorable relevance to its conclusion is attributed to its premises, and an inductive argument as any argument that is not deductive. This distinction, unlike its rivals, is both exclusive and exhaustive; permits both good and bad arguments of each kind; and is both useful and needed in evaluating at least some arguments.

The thesis of this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its premises at all favorably relevant to its conclusion. In support of this thesis I assume two premises and argue for a third. My two assumptions are these: (1) that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion certain relative to its premises (this is widely, if not universally, acknowledged by writers (...) on logic), and (2) premises are favorably relevant to a conclusion only if it is certain or probable relative to them (I argued for this in an earlier paper). The premise I argue for in this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion probable relative to its premises. To establish this third premise, I first refute a defense of the contrary position (namely, that an argument's possessing the form of affirming the consequent suffices to make its conclusion probable relative to its premises), then offer counterexamples to that position, and finally demonstrate the failure of several attempts to save it. (shrink)

According to a standard account of evidence, one piece of information is stronger evidence for an hypothesis than is another iff the probability of the hypothesis on the one is greater than it is on the other. This condition, I argue, is neither necessary nor sufficient because various factors can strengthen the evidence for an hypothesis without increasing (and even decreasing) its probability. Contrary to what probabilists claim, I show that this obtains even if a probability function can take these (...) evidential factors into account in ways they suggest and yield a unique probability value. Nor will the problem be solved by appealing to second-order probabilities. (shrink)

This paper surveys and critically assesses existing theories of evidence with respect to four desiderata. A good theory of evidence should be both a theory of evidential support (i.e., be informative about what kinds of facts speak in favour of a hypothesis), and of warrant (i.e., be informative about how strongly a given set of facts speaks in favour of the hypothesis), it should apply to the non-ideal cases in which scientists typically find themselves, and it should be ‘descriptively adequate’, (...) i.e., able to adequately represent typical episodes of evidentiary reasoning. The theories surveyed here—Bayesianism, hypotheticodeductivism,satisfaction theories, error statistics as well as Achinstein’s and Cartwright’s theories—are all found wanting in important respects. I finally argue that a deficiency all these theories have in common is a neglect or underplaying of the epistemic context in which the episode of evidentiary reasoning takes place.Este artículo describe y valora críticamente diversas teorías de la evidencia en relación a cuatro desiderata. Una buena teoría de la evidencia debería ser tanto una teoría sobre el apoyo evidencial [evidential support] (ser informativa sobre qué tipos de hechos hablan a favor de la hipótesis) como sobre la justificación [warrant]; debería aplicarse en las situaciones no ideales en las que normalmente se encuentran los científicos; y debería ser ‘descriptivamente adecuada’, esto es, capaz de representar correctamente episodios típicos de razonamiento evidencial. Las teorías aquí revisadas—bayesianismo, hipotético-deductivismo, teorías de la satisfacibilidad, la estadística del error, así como las propuestas de Achinstein y Cartwright—se consideran deficientes en aspectos básicos. Argumentaré que un defecto común en todas ellas es que olvidan, o minusvaloran, el contexto epistémico en el que el episodio de razonamiento evidencial tiene lugar. (shrink)

Predictions about the future and unrestricted universal generalizations are never logically implied by our observational evidence, which is limited to particular facts in the present and past. Nevertheless, propositions of these and other kinds are often said to be confirmed by observational evidence. A natural place to begin the study of confirmation theory is to consider what it means to say that some evidence E confirms a hypothesis H.

In the first edition of LFP, Carnap [2] undertakes a precise probabilistic explication of the concept of confirmation. This is where modern confirmation theory was born (in sin). Carnap was interested mainly in quantitative confirmation (which he took to be fundamental). But, he also gave (derivative) qualitative and comparative explications: • Qualitative. E inductively supports H. • Comparative. E supports H more strongly than E supports H . • Quantitative. E inductively supports H to degree r . Carnap begins by (...) clarifying the explicandum (the informal “inductive support” concept) in various ways, including. (shrink)

The fine-tuning argument can be used to support the Many Universe hypothesis. The Inverse Gambler’s Fallacy objection seeks to undercut the support for the Many Universe hypothesis. The objection is that although the evidence that there is life somewhere confirms Many Universes, the specific evidence that there is life in this universe does not. I will argue that the Inverse Gambler’s Fallacy is not committed by the fine-tuning argument. The key issue is the procedure by which the universe with life (...) is selected for observation. Once we take account of the procedure, we find that the support for the Many Universe hypothesis remains. (shrink)

Varios teóricos del derecho han propuesto el uso de umbrales o estándares de prueba más flexibles y más finamente discriminados. En la medicina es común utilizar estándares que poseen estas características en los procedimientos diagnósticos y en los exámenes médicos. Esta ponencia ofrece un marco probabilístico para establecer estándares de prueba múltiples en cualquier disciplina. La tesis principal es que la evidencia es un concepto umbral con respecto a la probabilidad. Múltiples umbrales pueden ser establecidos en un marco de intervalos (...) de probabilidad para la hipótesis que está siendo puesta a prueba, los cuales reflejan los diferentes grados de apoyo que la evidencia le provee a la hipótesis. Examinando los mecanismos utilizados para establecer los umbrales en medicina, sugiero una manera para establecer umbrales múltiples de prueba en derecho de una manera no arbitraria. (shrink)