People have worried for many years — centuries — about how you perform large changes in your body of beliefs. How does the new evidence lead you to replace a geocentric system of planetary motion by a heliocentric system? How do we decide to abandon the principle of the conservation of mass?The general approach that we will try to defend here is that an assumption, presupposition, framework principle, will be rejected or altered when a large enough number of improbabilities must (...) be accepted on be basis of our experience. If I think that all swans are white, and a student claims to have a counterexample, I will assume that he has made some observational error. I will reject his result, and continue to accept the generalization. When a lot of people claim to have seen counterexamples, I will come around: to continue to accept the generalization would require me to accept too many improbabilities. (shrink)

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.

Probability and logic are two branches of mathematics that have important philosophical applications. This article discusses several areas of intersection between them. Several involve the role for probability in giving semantics for logic or the role of logic in governing assignments of probability. Some involve probability over non-classical logic or self-referential sentences.

In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol- ogy, and statistics, and criticisms of these applications.

I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.

A distinction often drawn is one between conservative versus revisionary conceptions of philosophical analysis with respect to commonsensical beliefs and intuitions. This paper offers a comparative investigation of two revisionary methods: Carnapian explication and ameliorative analysis as developed by S. Haslanger. It is argued that they have a number of common features, and in particular that they share a crucial political dimension: they both have the potential to serve as instrument for social reform. Indeed, they may produce improved versions of (...) key concepts of everyday life, for example those pertaining to social categories such as gender and race, which in turn may lead to social change. The systematic comparison of these two frameworks offered here, where similarities as well as differences are discussed, is likely to provide useful guidance to practitioners of both approaches, as it will highlight important aspects of each of them that tend to remain implicit and under-theorized in existing applications of these methodologies to specific questions. (shrink)

Traditional arguments against the identification of the language of thought with natural language assume a picture of natural language which is largely inconsistent with that suggested by contemporary linguistic theory. This has led certain philosophers and linguists to suggest that this identification is not as implausible as it once seemed. In this paper, I discuss the prospects for such an identification in light of these developments in linguistic theory. I raise a new challenge against the identification thesis: the existence of (...) ungrammatical but acceptable expressions seems to require a gap between thought and language. I consider what must be the case in order for this objection to be dealt with. (shrink)

In this paper, I shall provide a novel response to the argument from context-sensitivity against truth-conditional semantics. It is often argued that the contextual influences on truth-conditions outstrip the resources of standard truth-conditional accounts, and so truth-conditional semantics rests on a mistake. The argument assumes that truth-conditional semantics is legitimate if and only if natural language sentences have truth-conditions. I shall argue that this assumption is mistaken. Truth-conditional analyses should be viewed as idealised approximations of the complexities of natural language (...) meaning. From this perspective, disparity between the scientific model and its real-world target is to be expected. I elaborate on what such an approach to semantics would look like. (shrink)

Confirmation is a graded notion: evidence can confirm a hypothesis to a greater or lesser degree. There has been debate about how to measure degree of confirmation. Starting from the observation that we would like evidence to be a discriminating indicator of truth, we conduct computer simulations to determine how well the various known measures of confirmation predict the extent to which a given piece of evidence fulfills that role, given a hypothesis of interest. The outcomes show that some measures (...) are markedly better indicators of truth than others. (shrink)

This paper aims to contribute to our understanding of the notion of coherence by explicating in probabilistic terms, step by step, what seem to be our most basic intuitions about that notion, to wit, that coherence is a matter of hanging or fitting together, and that coherence is a matter of degree. A qualitative theory of coherence will serve as a stepping stone to formulate a set of quantitative measures of coherence, each of which seems to capture well the aforementioned (...) intuitions. Subsequently it will be argued that one of those measures does better than the others in light of some more specific intuitions about coherence. This measure will be defended against two seemingly obvious objections. (shrink)

Anti-exceptionalists about logic claim that logical methodology is not different from scientific methodology when it comes to theory choice. Two anti-exceptionalist accounts of theory choice in logic are abductivism and predictivism. These accounts have in common reliance on pre-theoretical logical intuitions for the assessment of candidate logical theories. In this paper, I investigate whether intuitions can provide what abductivism and predictivism want from them and conclude that they do not. As an alternative to these approaches, I propose a Carnapian view (...) on logical theorizing according to which logical theories do not simply account for pre-theoretical intuitions, but rather improve on them. In this account, logical theories are ameliorative, rather than representational. (shrink)

Building on Wittgenstein’s ideas, I defend a brand of pluralism that associates words with conceptual families and appeals to this notion in the course of philosophical problem solving. I argue that certain problems that the received view of conceptual engineering (‘improvement by replacement’) faces can be more easily overcome if we adopt a pluralist perspective. I show that the proposed approach can circumvent the problem of topic discontinuity, whilst also avoiding the threat of trivialisation, since it can easily accommodate both (...) coarse-grained and fine-grained topics. Finally, I argue that my variant of pluralism is compatible with de novo conceptual engineering insofar as it allows that the paradigm associated with a word may shift overtime thus creating an opportunity for new candidate members to join a conceptual family. (shrink)

In recent analytic philosophy, there is a growing interest in the project of conceptual engineering. This paper examines two ways this project might be applied to scientific research, specifically anthropological research. It argues that both of them are harmful to this research. Specifically, it argues that a reliance on the axiological standards of analytic philosophy conflicts with the goal of empirical adequacy. Section one proffers two forms that the engineering project might take when applied to the science. Section two proffers (...) a case study drawn from anthropology. Specifically, it lays out Evans-Pritchard’s Witchcraft, Oracles, and Magic Among the Azande, paying particular attention to the inconsistency he discovered in Azande witchcraft. Sections three and four argue that attempting to remove this inconsistency via the two forms of engineering disable critical features of emic research and discard empirical findings. Finally, I close by noting how the conflict between axiological standards and empirical adequacy might generalize beyond anthropology. (shrink)

We live in a world in which scientific expertise and its epistemic authority become more important. On the other hand, the financial interests in research, which could potentially corrupt science, are increasing. Due to these two tendencies, a concern for the integrity of scientific research becomes increasingly vital. This concern is, however, hollow if we do not have a clear account of research integrity. Therefore, it is important that we explicate this concept. Following Rudolf Carnap’s characterization of the task of (...) explication, this means that we should develop a concept that is (1) similar to our common sense notion of research integrity, (2) exact, (3) fruitful, and (4) as simple as possible. Since existing concepts do not meet these four requirements, we develop a new concept in this article. We describe a concept of epistemic integrity that is based on the property of deceptiveness, and argue that this concept does meet Carnap’s four requirements of explication. To illustrate and support our claims we use several examples from scientific practice, mainly from biomedical research. (shrink)

A number of philosophers of science have argued that there are important differences between robustness in modeling and experimental contexts, and—in particular—many of them have claimed that the former is non-confirmatory. In this paper, I argue for the opposite conclusion: robust hypotheses are confirmed under conditions that do not depend on the differences between and models and experiments—that is, the degree to which the robust hypothesis is confirmed depends on precisely the same factors in both situations. The positive argument turns (...) on the fact that confirmation theory doesn’t recognize a difference between different sources of evidence. Most of the paper is devoted to rebutting various objections designed to show that it should. I end by explaining why philosophers of science have (often) gone wrong on this point. (shrink)

William Whewell’s account of induction differs dramatically from the one familiar from twentieth-century debates. I argue that Whewell’s induction can be usefully understood by comparing the difference between his views and more standard accounts to contemporary debates between semantic and syntactic views of theories: rather than understanding inductive inference as capturing a relationship between sentences or propositions, Whewell understands it as a method for constructing a model of the world. The difference between this view and the more familiar picture of (...) induction is reflected in other aspects of Whewell’s philosophy of science, particularly his treatment of consilience and the order of discovery. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

In the last decades, experimental philosophers have introduced the notion that conceptual analysis could use empirical evidence to back some of its claims. This opens up the possibility for the development of a corpus-based conceptual analysis. However, progress in this direction is contingent on the development of a proper account of concepts and corpus-based conceptual analysis itself that can be leveraged on textual data. In this essay, I address this problem through the question of similarity: how do we evaluate similarity (...) between two concepts, as similarity relates to identity? After a survey of prominent conceptual analysis methods, I propose a cursory account of corpus-based conceptual analysis. Then I formulate the question of similarity, and argue for an account that is functionalist in Millikan's (1984) sense. In this process, I propose a new account of concept that bases itself on millikanian teleosemantics in order to account for concepts' contribution in discourse. I then illustrate its fruitfulness by showing how it enables accounts of concept presence detection in textual data, both automatically and by a human judge. (shrink)

Das Dissertationsprojekt soll eine Verbindung zwischen zwei augenscheinlich separaten Debattensträngen in der kontemporären Wissenschaftstheorie erforschen. Das ist zum einen die Debatte um die humesche Doktrin, der zufolge es keine de-re notwendigen Verbindungen respektive modale Fakten in der natürlichen Welt gibt. Diese Debatte betrifft die Grundlagen der Naturwissenschaften sowie der Natur selbst. Und das ist zum anderen die Debatte um die materiale Theorie der Induktion, welche auf John D. Norton zurückgeht und die Grundlagen der Rationalität und Logik betrifft. Nach dieser Theorie (...) werden induktive Schlüsse qua relevanter, lokaler Hintergrundfakten zuverlässig. Norton bringt viele - in meinen Augen überzeugende - Beispiele für diese Theorie, lässt uns aber im Unklaren darüber, wie diese Hintergrundfakten induktive Schlüsse lizensieren können. Ich werde argumentieren, dass es sich bei diesen relevanten Fakten zumindest in einigen paradigmatischen Fällen um irreduzibel-modale oder modal grundierte Fakten handeln muss, ansonsten können diese die ihnen zugedachte Funktion nicht erfüllen. Infolgedessen steht der Humeanismus vor einer materialen Form des Induktionsproblems. -/- Meine Forschungshypothese lautet, dass es sich bei dem materialen Induktionsproblem um das eigentliche und zentrale Problem des Humeanismus handelt. Zum einen werden viele altbekannte Probleme des Humeanismus durch das materiale Induktionsproblem motiviert und bestärkt. Zum anderen begründet das materiale Induktionsproblem ein neues und tiefgreifendes Problem des Humeanismus. Es stellt sich darin, dass der Humeanismus den empirischen Erfolg unserer verfügbaren wissenschaftlichen und alltäglichen Gesetzesannahmen nicht zirkelfrei erklären kann. Darauf aufbauend formuliere ich ein Super-Wunderargument, das im Kern in einer Inferenz von den bisherigen empirischen Erfolgen unserer verfügbaren Gesetzesannahmen auf die Wahrheit des Anti-Humeanismus besteht. Dieses Argument steht im Zentrum meiner Arbeit. Alles Weitere wird im Kontext dieses Argumentes diskutiert und illustriert. Zu diesen Untersuchungen gehören die schrittweise Motivation des Argumentes durch das materiale Induktionsproblem, die Unterscheidung und Diskussion verschiedener logischer Formen des Argumentes, das Herausarbeiten der Vorteile sowie die Antizipation von möglichen Einwänden gegen das Argument. (shrink)

Embodied cognitive science has argued that cognition is embodied principally in virtue of grossmorphological and sensorimotor features. This thesis argues that cognition is also internally embodied in affective and fine-grained physiological features whose transformative roles remain mostly unnoticed in contemporary cognitive science. I call this ‘proper embodiment’. I approach this larger subject by examining various emotion theories in philosophy and psychology. These tend to emphasise one of the many gross components of emotional processes, such as ‘feeling’ or ‘judgement’ to the (...) detriment of the others, often leading to an artificial emotion-cognition distinction even within emotion science itself. Attempts to reconcile this by putting the gross components back together, such as JessePrinz’s “embodied appraisal theory”, are, I argue, destined to failure because the vernacular concept of emotion which is used as the explanandum is not a natural kind and is not amenable to scientific explication.I examine Antonio Damasio’s proposal that emotion is involved in paradigmatic ‘cognitive’ processing such as rational decision making and argue (1) that the research he discusses does not warrant the particular hypothesis he favours, and (2) that Damasio’s account, though in many ways a step in the right direction, nonetheless continues to endorse a framework which sees affect and cognition as separate (though now highly interacting) faculties. I further argue that the conflation of ‘affect’ and 'emotion' may be the source of some confusion in emotion theory and that affect needs to be properly distinguished from ‘emotion’. I examine some dissociations in the pain literature which give us further empirical evidence that, as with the emotions, affect is a distinct component along with more cognitive elements of pain. I then argue that affect is distinctive in being grounded in homeostatic regulative activity in the body proper. With the distinction between affect, emotion, and cognition in hand, and the associated grounding of affect in bodily activity, I then survey evidence that bodily affect is also involved in perception and in paradigmatic cognitive processes such as attention and executive function. I argue that this relation is not ‘merely’ casual. Instead, affect (grounded in fine-grained details of internal bodily activity) is partially constitutive of cognition, participating in cognitive processing and contributing to perceptual and cognitive phenomenology. Finally I review some work in evolutionary robotics which reaches a similar conclusion, suggesting that the particular fine details of embodiment, such as molecular signalling between both neural and somatic cells matters to cognition. I conclude that cognition is properly embodied’ in that it is partially constituted by the many fine-grained bodily processes involved in affect (as demonstrated in the thesis) and plausibly by a wide variety of other fine-grained bodily processes that likewise tend to escape the net of contemporary cognitive science. (shrink)

Rudolf Carnap introduced and endorsed a philosophical methodology which he called the method of ‘explication’. P.F. Strawson took issue with this methodology, but it is currently undergoing a revival. In a series of articles, Patrick Maher has recently argued that explication is an appropriate method for ‘formal epistemology’, has defended it against Strawson’s objection, and has himself put it to work in the philosophy of science in further clarification of the very concepts on which Carnap originally used it (degree of (...) confirmation, and probability), as well as some concepts to which Carnap did not apply it (such as justified degree of belief. We outline Carnap’s original idea, plus Maher’s recent application of such a methodology, and then seek to show that the problem Strawson raised for it has not been dealt with. The method is indeed, we argue, problematic and therefore not obviously superior to the ‘descriptive’ method associated with Strawson. (shrink)

By means of multi-agent simulations, it investigates the truth and consensus-conduciveness of controversial debates. The book brings together research in formal epistemology and argumentation theory.

Arthur Pap’s work played an important role in the development of the analytic tradition. This role goes beyond the merely historical fact that Pap’s views of dispositional and modal concepts were influential. As a sympathetic critic of logical empiricism, Pap, like Quine, saw a deep tension in logical empiricism at its very best in the work of Carnap. But Pap’s critique of Carnap is quite different from Quine’s, and represents the discovery of limits beyond which empiricism cannot go, where there (...) lies nothing other than intuitive knowledge of logic itself. Pap’s arguments for this intuitive knowledge anticipate Etchemendy’s recent critique of the model-theoretic account of logical consequence. Pap’s work also anticipates prominent developments in the contemporary neo-Fregean philosophy of mathematics championed by Wright and Hale. Finally, Pap’s major philosophical preoccupation, the concepts of necessity and possibility, provides distinctive solutions and perspectives on issues of contemporary concern in the metaphysics of modality. In particular, Pap’s account of modality allows us to see the significance of Kripke’s well-known arguments on necessity and apriority in a new light. (shrink)

Showcasing original arguments for well-defined positions, as well as clear and concise statements of sophisticated philosophical views, this volume is an ...

On a naive view of conceptual engineering, conceptual engineers simply aim at engineering concepts. This picture has recently come under attack. Sarah Sawyer (2018, 2020) and Derek Ball (2020) present two rather different, yet equally unorthodox, accounts of conceptual engineering, which they take to be superior to the naive picture. This paper casts doubts on the superiority of their respective accounts. By elaborating on the explanatory potential of “going meta”, the paper defends the naive view against Sawyer’s and Ball’s rival (...) proposals. (shrink)

Different people reason differently, which means that sometimes they reach different conclusions from the same evidence. We maintain that this is not only natural, but rational. In this essay we explore the epistemology of that state of affairs. First we will canvass arguments for and against the claim that rational methods of reasoning must always reach the same conclusions from the same evidence. Then we will consider whether the acknowledgment that people have divergent rational reasoning methods should undermine one’s confidence (...) in one’s own reasoning. Finally we will explore how agents who employ distinct yet equally rational methods of reasoning should respond to interactions with the products of each others’ reasoning. We find that the epistemology of multiple reasoning methods has been misunderstood by a number of authors writing on epistemic permissiveness and peer disagreement. (shrink)

My goal, in this paper, is to critically assess the categorization of “interpretations of probability” as it appears in the literature. In some sources only Carnap’s treatment of probability is understood to be the best example of “logical” probability. This is surprisingly narrow and I will here suggest otherwise. In fact, I believe that certain forms of Baysianism should also be included in the logical camp.

We compare supports $A\uparrow B$ (i.e. $pr(B| A)> pr(B)$) with conditionals $A\rightarrow B$ and prove that the basic properties of supports are exactly the opposite to those of conditionals.

After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of p-values rather than as formal procedures for ‘acceptance‘ and ‘rejection‘. A number of types of null hypothesis are described and a principle for evidential interpretation set out governing the implications of p- values in the specific circumstances of each application, as contrasted with a long-run interpretation. A number of more complicated situ- ations are discussed (...) in which modification of the simple p-value may be essential. (shrink)

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

Evidentialists say that a necessary condition of sound epistemic reasoning is that our beliefs reflect only our evidence. This thesis arguably conflicts with standard Bayesianism, due to the importance of prior probabilities in the latter. Some evidentialists have responded by modelling belief-states using imprecise probabilities (Joyce 2005). However, Roger White (2010) and Aron Vallinder (2018) argue that this Imprecise Bayesianism is incompatible with evidentialism due to “inertia”, where Imprecise Bayesian agents become stuck in a state of ambivalence towards hypotheses. Additionally, (...) escapes from inertia apparently only create further conflicts with evidentialism. This dilemma gives a reason for evidentialist imprecise probabilists to look for alternatives without inertia. I shall argue that Henry E. Kyburg’s approach offers an evidentialist-friendly imprecise probability theory without inertia, and that its relevant anti-inertia features are independently justified. I also connect the traditional epistemological debates concerning the “ethics of belief” more systematically with formal epistemology than has been hitherto done. (shrink)

In this dissertation, I seek to explain G.W.F. Hegel’s view that human accessible conceptual content can provide knowledge about the nature or essence of things. I call this view “Conceptual Transparency.” It finds its historical antecedent in the views of eighteenth century German rationalists, which were strongly criticized by Immanuel Kant. I argue that Hegel explains Conceptual Transparency in such a way that preserves many implications of German rationalism, but in a form that is largely compatible with Kant’s criticisms of (...) the original rationalist version. After providing background on Hegel’s relationship to the traditional rationalist theory of concepts and Kant’s challenge to it, I claim that Hegel’s central task is to provide a theory of conceptual content that allows a relationship to the objective world without being dependent on the specifically sensory aspect of the world, which Kant’s theory of concepts required. Since many interpreters deny that Hegel’s use of the term “concept” is comparable to other historical philosophers (or our own), I first show that Hegel’s critique of standard conceptions of concepts presupposes an agreement of subject matter. I then show how Hegel’s account of the “formal concept” provides the skeleton for a view of conceptual content that relies on negative relations between terms, rather than a relation to sensibility, to provide content. Hegel’s account of conceptual content is completed when he shows how a universal term is further specified so that it can determine singular objects. This occurs in its adequate form in a teleological process. I argue that Hegel’s account of teleology in the Science of Logic is an attempt to explain how and where Conceptual Transparency obtains. A teleological process is one in which a concept constitutes an object, and this means that a concept is perfectly adequate to express that thing’s nature and not merely to represent it. However, in the final chapter, I show that Hegel’s concept of teleology is meant paradigmatically to illuminate how human purposive processes have constituted a social world that is conceptually accessible to us. In this way, the primary “province” of Hegel’s rationalism is the human constructed world. (shrink)

Manuel Padilla Cruz has written an excellent response piece (Padilla Cruz 2019) to my initial article (Cull 2019) on dismissive incomprehension, where he raises a number of interesting issues and has put forward a number of excellent ideas for avenues for further research. Here I seek to deepen our understanding of the phenomenon by developing some responses that have come forward in thinking about and discussing dismissive incomprehension, especially in reference to what Padilla Cruz has said. Hopefully this adds to (...) his analysis and helps to provoke the further research we are both interested in seeing. (shrink)

In this paper I suggest a reconstruction of the traditional concepts of con-tinent and incontinent action. This reconstruction proceeds along the lines of a standpoint of bounded rationality. My suggestion agrees with some relevant aspects of Davidson’s treatment of this topic. One of these aspects is that incontinent action is typically signalled by the following two subjective experiences: a feeling of surprise towards one’s own action and a difficulty in understanding oneself; another is that incontinence cannot simply be disposed of (...) in terms of some inability of the agent to avoid “succumbing to temptation”; still another is the view that inconti-nent action is common in real human affairs. But my suggestion dis-agrees with other relevant aspects of Davidson’s treatment of inconti-nence too. In particular, it avoids what I take to be its two major draw-backs. These are a view of continent action that falls prey to a com-pletely unrealistic concept of psychological rationality and the idea that incontinence necessarily involves a dimension of essential irrationality. (shrink)

Andrew Wiles' analytic proof of Fermat's Last Theorem FLT, which appeals to geometrical properties of real and complex numbers, leaves two questions unanswered: (i) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? (ii) Why is x^n+y^n=z^n solvable only for n<3? In this inter-disciplinary perspective, we offer insight into, and answers to, both queries; yielding a pre-formal proof of why FLT can be treated as a true (...) arithmetical proposition (one which, moreover, might not be provable formally in the first-order Peano Arithmetic PA), where we admit only elementary (i.e., number-theoretic) reasoning, without appeal to analytic properties of real and complex numbers. We cogently argue, further, that any formal proof of FLT needs---as is implicitly suggested by Wiles' proof---to appeal essentially to formal geometrical properties of formal arithmetical propositions. (shrink)

An inductive logic is a system of inference that describes the relation between propositions on data, and propositions that extend beyond the data, such as predictions over future data, and general conclusions on all possible data. Statistics, on the other hand, is a mathematical discipline that describes procedures for deriving results about a population from sample data. These results include predictions on future samples, decisions on rejecting or accepting a hypothesis about the population, the determination of probability assignments over such (...) hypotheses, the selection of a statistical model for studying the population, and so on. Both inductive logic and statistics are calculi for getting from the given data to propositions or results that transcend the data. (shrink)

A aceitação ou a escolha de uma teoria científica por parte de uma comunidade científica é um evento ou processo central na dinâmica científica. É, também, um evento ou processo complexo –já que dele participam as teorias, a experiência e alguma forma de relação inferencial entre a teoria e a experiência.

This paper defends Pragmatic Conceptual Analysis , a proposed empirical methodology for explicating philosophical concepts. This methodology attributes to our shared concepts whatever application conditions they would need to have in order best to continue delivering benefits in the ways they have regularly delivered benefits in the past. In the first stage of my argument I argue that Pragmatic Conceptual Analysis has what I call normative authority : we have practical and epistemic reason to adopt the explications that it delivers (...) even if we think doing so requires stipulative revisions in the meanings of our concepts. I then use this normative authority to argue that Pragmatic Conceptual Analysis also has what I call descriptive authority : when we understand concept-meaning in the way we ought to understand it (in the way licensed by the normative authority of Pragmatic Conceptual Analysis) we see that, rather than being revisionary, Pragmatic Conceptual Analysis is a semantically conservative tool that uncovers (what we should think of as being) the meanings our concepts already have. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

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 October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...) to read it. That is what you have in front of you. The account of Laplace’s theory of probability in Chapter 4 is very different to what I said in my seminar lectures, and also very different to any other account I have seen; it is based on a reading of important texts by Laplace that appear not to have been read by other commentators. The discussion of von Mises’ theory in Chapter 7 is also new, though perhaps less revolutionary. And the final chapter is a new attempt to come to grips with the popular, but amorphous, subjective theory of probability. The material in the other chapters has mostly appeared in previous articles of mine but things are sometimes expressed differently here. I would like to say again that this is an incomplete draft of a book, not the book I would have written if I had decided to finish it. It no doubt contains poor expressions, it may contain some errors or inconsistencies, and it doesn’t cover all the theories that I originally intended to discuss. Apart from this preface, I have done no work on the book since October 2009. (shrink)