Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We (...) explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. (shrink)

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We (...) explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. (shrink)

A characterization of epistemic rationality, or epistemic justification, is typically taken to require a process of conceptual clarification, and is seen as comprising the core of a theory of (epistemic) rationality. I propose to explicate the concept of rationality. -/- It is essential, I argue, that the normativity of rationality, and the purpose, or goal, for which the particular theory of rationality is being proposed, is taken into account when explicating the concept of rationality. My position thus amounts to an (...) instrumentalist position about theories of epistemic rationality. Since there are different purposes, or goals, for which theories of rationality are proposed, the method of explication leaves room for different characterizations of rationality. I focus on two such (kinds of) purposes: first, the purpose of guiding the formation (or maintenance) of doxastic states and, second, the purpose of assessing (the formation or maintenance of) doxastic states. I conclude by outlining a pluralistic picture concerning rationality. (shrink)

According to the Reasoning View about normative reasons, facts about normative reasons for action can be understood in terms of facts about the norms of practical reasoning. I argue that this view is subject to an overlooked class of counterexamples, familiar from debates about Subjectivist theories of normative reasons. Strikingly, the standard strategy Subjectivists have used to respond to this problem cannot be adapted to the Reasoning View. I think there is a solution to this problem, however. I argue that (...) the norms of practical reasoning, like the norms of theoretical reasoning, are characteristically defeasible, in a sense I make precise. Recognizing this property of those norms makes space for a solution to the problem. The resulting view is in a way analogous to the familiar defeasibility theory of knowledge, but it avoids a standard objection to that theory. (shrink)

This article shows that there are square circles in the sense that there are mathematical objects that are at the same time both perfectly circular and perfectly square. The philosophical significance of this is discussed, especially in view of philosophy's widespread use of “square circle” as a typical example of an impossibility. In particular, the focus is on what the existence of square circles means for the possibility of conceptual analysis, and more generally what we can learn about the nature (...) of non-formal concepts and their use in philosophy. (shrink)

The Univalent Foundations project constitutes what is arguably the most serious challenge to set-theoretic foundations of mathematics since intuitionism. Like intuitionism, it differs both in its philosophical motivations and its mathematical-logical apparatus. In this paper we will focus on one such difference: Univalent Foundations’ reliance on an intensional rather than extensional logic, through its use of intensional Martin-Löf type theory. To this, UF adds what may be regarded as certain extensionality principles, although it is not immediately clear how these principles (...) are to be interpreted philosophically. In fact, this framework gives an interesting example of a kind of border case between intensional and extensional mathematics. Our main purpose will be the philosophical investigation of this system, and the relation of the concepts of intensionality it satisfies to more traditional philosophical or logical concepts such as those of Carnap and Quine. (shrink)

The impossibility results of Bovens and Hartmann (2003) and Olsson (2005) call into question the strength of the connection between coherence and truth. As part of the inquiry into this alleged link, I define a notion of degree of truth-conduciveness, relevant for measuring the usefulness of coherence measures as rules-of-thumb for assigning probabilities in situations of partial knowledge. I use the concept to compare the viability of some of the measures of coherence that have been suggested so far under different (...) circumstances. It turns out that all of these, including the prior, are just about equally good in cases of very little knowledge. Nevertheless, there are differences in when they are applicable, and they also depart more from each other when more knowledge is added. CiteULike Connotea Del.icio.us What's this? (shrink)

After delineating the distinguishing features of pragmatism, and noting the resources that pragmatists have available to respond effectively as pragmatists to the two major objections to pragmatism, I examine and critically evaluate the various proposals that pragmatists have offered as a solution to the problem of induction, followed by a discussion of the pragmatic positions on the status of theoretical entities. Thereafter I discuss the pragmatic posture toward the nature of explanation in science. I conclude that pragmatism has (a) a (...) generally compelling solution to Hume's problem of induction; (b) no specific position on the status of theoretical entities, although something like the non-realism of the sort developed by van Fraassen seems a defensible candidate for most pragmatists in general, even though there are non-trivial objections to van Fraassen's position; and (c) central to the pragmatic conception of scientific explanation is the abandonment of our common conception of truth as a necessary condition for sentences to provide adequate explanations, and a drift in the direction of a contextualist account of explanation. (shrink)

What does the way we clarify and revise concepts reveal about the nature of concepts? This paper investigates the ontological commitments of conceptual analysis and explication regarding their supposed subject matter – concepts. It demonstrates the benefits of a cognitivist account of concepts, according to which they are not items on which the subject operates cognitively, but rather ways in which the subject operates. The proposed view helps to handle alternating references to ‘concepts’ and ‘terms’ in instructions on analysis and (...) explication. Furthermore, its virtue lies not in the capacity to render concepts ‘shareable’ but in its ontological parsimony. (shrink)

Marc Lange offers a stale anthology that reflects the sad state of affairs in the camp of analytic philosophy. It is representative in a few respects, even in its maltreatment of Russell, Wittgenstein, and Popper. Despite its neglect of Wittgenstein, it shows again that Wittgenstein is the patron saint of the analytic school despite the fact that it does not abide by his theory of metaphysics as inherently meaningless.

This Companion to the philosophy of science reflects fairly well the gloomy state of affairs in this subfield at its best—concerns, problems, prejudices, and all. The field is still stuck with the problem of justification of science, refusing to admit that there is neither need nor possibility to justify science and forbid dissent from it.

An inexact generalization like ‘ravens are black’ will be symbolized as a prepositional function with free variables thus: ‘Rx ⇒ Bx.’ The antecedent ‘Rx’ and consequent ‘Bx’ will themselves be called absolute formulas, while the result of writing the non-boolean connective ‘⇒’ between them is conditional. Absolute formulas are arbitrary first-order formulas and include the exact generalization ‘(x)(Rx → Bx)’ and sentences with individual constants like ‘Rc & Bc.’ On the other hand the non-boolean conditional ‘⇒’ can only occur as (...) the main connective in a formula. We shall also need to consider formulas with more than one free variable such as ‘xHy ⇒ xTy,’ which might express ‘if x is the husband of y then x is taller than y.’ Though it is inessential, it will simplify things to work in ‘n-languages’ with a finite number of individual constants c1,…, cn, which are interpreted as denoting the elements of the domains of the ‘n-models’ to be described below. (shrink)

According to an infinite frequency principle, it is rational, under certain conditions, to set your credence in an outcome to the limiting frequency of that outcome if the experiment were repeated indefinitely. I argue that most infinite frequency principles are undesirable in at least one of the following ways: accepting the principle would lead you to accept bets with sure losses, the principle gives no guidance in the case of deterministic experiments like coin tosses and the principle relies on a (...) metaphysical property, ‘chanciness’, whose necessary and sufficient conditions are unknown. I show that a frequency principle that is based on the principal principle suffers from problems related to the definition of ‘chance’ or ‘chanciness’, which could lead to all three of the above problems. I introduce a version of the infinite frequency principle that does not rely on a notion of chance or chanciness and does not suffer from any of these problems. (shrink)

There are two reasons, I claim, scientists do and should ignore standard philosophical theories of objective evidence: (1) Such theories propose concepts that are far too weak to give scientists what they want from evidence, viz., a good reason to believe a hypothesis; and (2) They provide concepts that make the evidential relationship a priori, whereas typically establishing an evidential claim requires empirical investigation.

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 chapter presents the reception of Leo Strauss by analytic philosophers after Strauss’s emigration to the United States. It gives a brief survey of the polemics against Strauss and his school by analytic philosophers, which aided in the self-constitution of analytic philosophy as a rival school of thought in philosophy. But most of the chapter is devoted to recovering the significance and influence of a criticism of Strauss by Ernest Nagel. The chapter argues that this response is of intrinsic interest (...) because it involves the relationship between science and values. Nagel’s response was foundational to Felix Oppenheim’s political philosophy or what Oppenheim called his project of ‘conceptual reconstruction.’ Lurking in Oppenheim’s response to Strauss are questions about the role of the principle of sufficient reason in philosophy. Rge chapter argues that an opportunity was missed to clarify questions pertaining to the inductive risk of philosophy more than a half century before these issues became fashionable again. (shrink)

It is well known that Ernest Gellner made substantial use of his knowledge of the social sciences in philosophy. Here I discuss how he used it on the basis of a few examples taken from Gellner’s philosophical output. It is argued that he made a number of highly original “translations”, or re-interpretations, of philosophical theories and problems using his knowledge of the social sciences. While this method is endorsed, it is also argued that some of Gellner’s translations crossed the line (...) between the original and the idiosyncratic. (shrink)

This chapter presents a typology of the different kinds of inductive inferences we can draw from our evidence, based on the explanatory relationship between evidence and conclusion. Drawing on the literature on graphical models of explanation, I divide inductive inferences into (a) downwards inferences, which proceed from cause to effect, (b) upwards inferences, which proceed from effect to cause, and (c) sideways inferences, which proceed first from effect to cause and then from that cause to an additional effect. I further (...) distinguish between direct and indirect forms of downwards and upwards inferences. I then show how we can subsume canonical forms of inductive inference mentioned in the literature, such as inference to the best explanation, enumerative induction, and analogical inference, under this typology. Along the way, I explore connections with probability and confirmation, epistemic defeat, the relation between abduction and enumerative induction, the compatibility of IBE and Bayesianism, and theories of epistemic justification. (shrink)

Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...) proposition, the higher her confidence in the truth of that proposition. For instance, Sophia’s degree of belief that it will be sunny in Vienna tomorrow might be .52, whereas her degree of belief that the train will leave on time might be .23. The precise meaning of these statements depends, of course, on the underlying theory of degrees of belief. These theories offer a formal tool to measure degrees of belief, to investigate the relations between various degrees of belief in different propositions, and to normatively evaluate degrees of belief. (shrink)

"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...) aspects of the tight relation and the complementarity of ranks and probabilities. It closes with comparative remarks on predecessors and other philosophical proposals as well as formal models developed in AI. (shrink)

Conditionalization is a widely endorsed rule for updating one’s beliefs. But a sea of complaints have been raised about it, including worries regarding how the rule handles error correction, changing desiderata of theory choice, evidence loss, self-locating beliefs, learning about new theories, and confirmation. In light of such worries, a number of authors have suggested replacing Conditionalization with a different rule — one that appeals to what I’ll call “ur-priors”. But different authors have understood the rule in different ways, and (...) these different understandings solve different problems. In this paper, I aim to map out the terrain regarding these issues. I survey the different problems that might motivate the adoption of such a rule, flesh out the different understandings of the rule that have been proposed, and assess their pros and cons. I conclude by suggesting that one particular batch of proposals, proposals that appeal to what I’ll call “loaded evidential standards”, are especially promising. (shrink)

This paper explores one way in which the view that emotions can be epistemically justified stands in tension with two common views in epistemology; namely, that doxastic justification entails propositional justification, and that propositional justification is entirely determined by the (inferential) support relations between one's evidence and a given proposition. A tentative solution to the tension is provided.

The use of multiple means of determination to “triangulate” on the existence and character of a common phenomenon, object, or result has had a long tradition in science but has seldom been a matter of primary focus. As with many traditions, it is traceable to Aristotle, who valued having multiple explanations of a phenomenon, and it may also be involved in his distinction between special objects of sense and common sensibles. It is implicit though not emphasized in the distinction between (...) primary and secondary qualities from Galileo onward. It is arguably one of several conceptions involved in Whewell’s method of the “consilience of inductions” (Laudan 1971) and is to be found in several places in Peirce. (From M. Brewer and B. Collins, eds., (1981); Scientific Inquiry in the Social Sciences (a festschrift for Donald T. Campbell), San Francisco: Jossey-Bass, pp. 123–162.). (shrink)

Extreme Permissivism is the view that a body of evidence could rationally permit both the attitude of belief and disbelief towards a proposition. This paper puts forward a new argument against Extreme Permissivism, which improves on a similar style of argument due to Roger White (2005, 2014). White’s argument is built around the principle that the support relation between evidence and a hypothesis is objective: so that if evidence E makes it rational for an agent to believe a hypothesis H, (...) then E makes it rational to believe H, for all agents. In this paper, I construct a new argument against Extreme Permissivism that appeals to a logically weaker, less demanding view about evidential support, Relational Objectivity: whether a body of evidence E is more likely if H is true than if H is false is an objective matter and does not depend on how any agent interprets the relationship between E and H. Relational Objectivity is solely concerned with the conditional probabilities called likelihoods and does not put substantive constraints on an agent’s prior and posterior credences. For this reason, the presented argument avoids the standard permissivist criticism levelled against White’s argument. (shrink)

Scientists often diverge widely when choosing between research programs. This can seem to be rooted in disagreements about which of several theories, competing to address shared questions or phenomena, is currently the most epistemically or explanatorily valuable—i.e. most successful. But many such cases are actually more directly rooted in differing judgments of pursuit-worthiness, concerning which theory will be best down the line, or which addresses the most significant data or questions. Using case studies from 16th-century astronomy and 20th-century geology and (...) biology, I argue that divergent theory choice is thus often driven by considerations of scientific process, even where direct epistemic or explanatory evaluation of its final products appears more relevant. Broadly following Kuhn’s analysis of theoretical virtues, I suggest that widely shared criteria for pursuit-worthiness function as imprecise, mutually-conflicting values. However, even Kuhn and others sensitive to pragmatic dimensions of theory ‘acceptance’, including the virtue of fruitfulness, still commonly understate the role of pursuit-worthiness—especially by exaggerating the impact of more present-oriented virtues, or failing to stress how ‘competing’ theories excel at addressing different questions or data. This framework clarifies the nature of the choice and competition involved in theory choice, and the role of alternative theoretical virtues. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

The account of meta-induction (G. Schurz, Hume’s problem solved: the optimality of meta-induction, MIT Press, Cambridge, 2019) proposes a two-step solution to the problem of induction. Step 1 consists in a mathematical a priori justification of the predictive optimality of meta-induction, upon which step 2 builds a meta-inductive a posteriori justification of object-induction based on its superior track record (Sect. 1). Sterkenburg (Br J Philos Sci, forthcoming. 10.1086/717068/) challenged this account by arguing that meta-induction can only provide a (non-circular) justification (...) of inductive predictions for now and for the next future, but not a justification of inductive generalizations (Sect. 2). This paper develops a meta-inductive method that does provide an a posteriori justification of inductive generalizations, in the form of exchangeability conditions (Sect. 3). In Sect. 4, a limitation of the proposed method is worked out: while the method can justify weakly lawlike generalizations, the justification of strongly lawlike generalizations (claimed to hold for all eternity) requires epistemic principles going beyond meta-induction based on predictive success. (shrink)

Philosophy strives to give us a firmer hold on our concepts. But what about their hold on us? Why place ourselves under the sway of a concept and grant it the authority to shape our thought and conduct? Another conceptualization would carry different implications. What makes one way of thinking better than another? This book develops a framework for concept appraisal. Its guiding idea is that to question the authority of concepts is to ask for reasons of a special kind: (...) reasons for concept use, which tell us which concepts to adopt, adhere to, or abandon, thereby shoring up—or undercutting—the reasons for action and belief that guide our deliberations. Traditionally, reasons for concept use have been sought either in timeless rational foundations or in concepts’ inherent virtues, such as precision and consistency. Against this, the book advances two main claims: that we find reasons for concept use in the conceptual needs we discover when we critically distance ourselves from a concept by viewing it from the autoethnographic stance; and that sometimes, concepts that conflict, or exhibit other vices such as vagueness or superficiality, are just what we need. By considering not what concepts are absolutely best, but what concepts we now need, we can reconcile ourselves to the contingency of our concepts, determine the proper place of efforts to tidy up thought, and adjudicate between competing conceptions of things,—even things as contested as liberty or free will. A needs-based approach separates helpful clarification from hobbling tidy-mindedness, and authoritative definition from conceptual gerrymandering. (shrink)

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)

Advocates of conceptual engineering as a method of philosophy face a dilemma: either they are ignorant of how conceptual engineering can be implemented, or else it is trivial to implement but of very little value, representing no new or especially fruitful method of philosophizing. Two key distinctions frame this dilemma and explain its two horns. First, the distinction between speaker’s meaning and reference and semantic meaning and reference reveals a severe implementation problem for one construal of conceptual engineering. Second, the (...) distinction between stipulating meanings and conceptually analyzing allows us to see why, on another construal of what conceptual engineering involves, the practice is neither a new nor neglected philosophical methodology. The article also argues that semantic externalism is not the root of the implementation problem for conceptual engineering, and that the usual rationale for adopting the practice, one that ties its value to the amelioration of “conceptual defects”, is unsound. (shrink)

This paper discusses the logical space of alternative conceptual engineering projects, with a specific focus on (1) the processes, (2) the targets and goals, and (3) the methods of such projects. We present an overview of how these three aspects interact in the contemporary literature and discuss those alternative projects that have yet to be explored based on our suggested typology. We show how choices about each element in a conceptual engineering project constrain the possibilities for the others, thereby giving (...) rise to distinct groupings of possible projects under the banner of conceptual engineering. We conclude with a critical reflection on the potential ethical issues that arise as a result of effectively putting conceptual engineering into practice. (shrink)

The main goal of this paper is to work out Quine's account of explication. Quine does not provide a general account, but considers a paradigmatic example which does not fit other examples he claims to be explications. Besides working out Quine's account of explication and explaining this tension, I show how it connects to other notions such as paraphrase and ontological commitment. Furthermore, I relate Quinean explication to Carnap's conception and argue that Quinean explication is much narrower because its main (...) purpose is to be a criterion of theory choice. (shrink)

In this article, I side with those who argue that the debate about the definition of “disease” should be reoriented from the question “what is disease” to the question of what it should be. However, I ground my argument on the rejection of the naturalist approach to define disease and the adoption of a normativist approach, according to which the concept of disease is normative and value-laden. Based on this normativist approach, I defend two main theses: (1) that conceptual analysis (...) is not the right method to define disease and that conceptual engineering should be the preferred method and (2) that the method of conceptual engineering should be implemented following the principles of Alexandrova’s account of social objectivity in the context of the definition of disease. (shrink)

I propose a revision of Cantor’s account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor's account if the Axiom of Choice is true, but its consequences differ from those of Cantor’s if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor’s account, blocks paradoxes—most notably, that a set can be partitioned into a set that is (...) bigger than it—that can arise from Cantor’s account if the Axiom of Choice is false, illuminates the debate over whether the Axiom of Choice is true, is a mathematically fruitful alternative to Cantor’s account, and sheds philosophical light on one of the oldest unsolved problems in set theory. (shrink)

Evidentialism and Reliabilism are two of the main contemporary theories of epistemic justification. Some authors have thought that the theories are not incompatible with each other, and that a hybrid theory which incorporates elements of both should be taken into account. More recently, other authors have argued that the resulting theory is well- placed to deal with fine-grained doxastic attitudes (credences). In this paper I review the reasons for adopting this kind of hybrid theory, paying attention to the case of (...) credences and the notion of probability involved in their treatment. I argue that the notion of probability in question can only be an epistemic (or evidential) kind of probability. I conclude that the resulting theory will be incompatible with Reliabilism in one important respect: it cannot deliver on the reductivist promise of Reliabilism. I also argue that attention to the justification of basic beliefs reveals limitations in the Evidentialist framework as well. The theory that results from the right combination of Evidentialism and Reliabilism, therefore, is neither Evidentialist nor Reliabilist. (shrink)

How to regard the weight we give to a proposition on the grounds of its being endorsed by an authority? I examine this question as it is raised within the epistemology of science, and I argue that “authority-based weight” should receive special handling, for the following reason. Our assessments of other scientists’ competence or authority are nearly always provisional, in the sense that to save time and money, they are not made nearly as carefully as they could be---indeed, they are (...) typically made on the basis of only a small portion of the available evidence. Consequently, we need to represent the authority-based elements of our epistemic attitudes in such a way as to allow the later revision of those elements, in case we decide in the light of new priorities that a more conscientious assessment is warranted. I look to the literature in confirmation theory, statistics, and economics for a semiformal model of this revision process, and make a particular proposal of my own. The discussion also casts some light on the question of why certain aspects of science’s epistemic state are not made public. (shrink)