Galileo asked in his Dialogue of the Two New Sciences what relationship exists between the size of the set of all natural numbers and the size of the set of all square natural numbers. Although one is a proper subset of the other, suggesting that there are strictly fewer squares than natural numbers, the existence of a simple one-to-one correspondence between the two sets suggests that they have, in fact, the same size. Cantor famously based the modern notion of cardinality (...) on the second intuition, but recent advances in mathematical logic (most notably, numerosity theory) have renewed an interest in the question whether Cantor’s way out of Galileo’s paradox was the only possible one. I present a new solution to Galileo’s paradox and argue that it is a better alternative to the Cantorian solution than numerosity theory. In fact, I argue that it is the best possible way out of Galileo's Paradox that can be based on the "Euclidean" intuition that the whole is always greater than any of its proper parts. (shrink)

There are empirical grounds to doubt the effectiveness of a common and intuitive approach to teaching debiasing strategies in critical thinking courses. We summarize some of the grounds before suggesting a broader taxonomy of debiasing strategies. This four-level taxonomy enables a useful diagnosis of biasing factors and situations, and illuminates more strategies for more effective bias mitigation located in the shaping of situational factors and reasoning infrastructure—sometimes called “nudges” in the literature. The question, we contend, then becomes how best to (...) teach the construction and use of such infrastructures. (shrink)

Unlike in physics, the category of thought experiment is not very common in biology. At least there are no classic examples that are as important and as well-known as the most famous thought experiments in physics, such as Galileo’s, Maxwell’s or Einstein’s. The reasons for this are far from obvious; maybe it has to do with the fact that modern biology for the most part sees itself as a thoroughly empirical discipline that engages either in real natural history or in (...) experimenting on real organisms rather than fictive ones. While theoretical biology does exist and is recognized as part of biology, its role within biology appears to be more marginal than the role of theoretical physics within physics. It could be that this marginality of theory also affects thought experiments as sources of theoretical knowledge. Of course, none of this provides a sufficient reason for thinking that thought experiments are really unimportant in biology. It is quite possible that the common perception of this matter is wrong and that there are important theoretical considerations in biology, past or present, that deserve the title of thought experiment just as much as the standard examples from physics. Some such considerations may even be widely known and considered to be important, but were not recognized as thought experiments. In fact, as we shall see, there are reasons for thinking that what is arguably the single most important biological work ever, Charles Darwin’s On the Origin of Species, contains a number of thought experiments. There are also more recent examples both in evolutionary and non-evolutionary biology, as we will show. Part of the problem in identifying positive examples in the history of biology is the lack of agreement as to what exactly a thought experiment is. Even worse, there may not be more than a family resemblance that unifies this epistemic category. We take it that classical thought experiments show the following characteristics: They serve directly or indirectly in the non-empirical epistemic evaluation of theoretical propositions, explanations or hypotheses. Thought experiments somehow appeal to the imagination. They involve hypothetical scenarios, which may or may not be fictive. In other words, thought experiments suppose that certain states of affairs hold and then try to intuit what would happen in a world where these suppositions are true. We want to examine in the following sections if there are episodes in the history of biology that satisfy these criteria. As we will show, there are a few episodes that might satisfy all three of these criteria, and many more if the imagination criterion is dropped or understood in a lose sense. In any case, this criterion is somewhat vague in the first place, unless a specific account of the imagination is presupposed. There will also be issues as to what exactly “non-empirical” means. In general, for the sake of discussion we propose to understand the term “thought experiment” here in a broad rather than a narrow sense here. We would rather be guilty of having too wide a conception of thought experiment than of missing a whole range of really interesting examples. (shrink)

Although Wilhelm Dilthey and Franz Brentano apparently were pursuing roughly the same objective—to offer a description of our mental functions and of their relations to objects—and both called their respective research programs ‘descriptive psychology’, they seem to have used the term to refer to two different methods of psychological research. In this article, I compare analyses of these differences. Against the reading of Orth but also against a possible application of recent relativist accounts of the epistemology of peer disagreement to (...) this case, I argue that their apparent shared objective is not enough to support an understanding of their views as two alternatives within a given historical or scientific context, or as a mutual peer disagreement. I show that the impression of a shared objective can be explained away as stemming from the influence of their teacher Adolf Trendelenburg, and I stress that the case of introspection strongly suggests that an account in terms of peer disagreement is not plausible. Finally, I conclude that the opposition between two traditions, Austrian philosophy and historicism, might be better suited to account for the dispute and its apparent common historical context. (shrink)

This paper introduces the category of b-frames as a new tool in the study of complete lattices. B-frames can be seen as a generalization of posets, which play an important role in the representation theory of Heyting algebras, but also in the study of complete Boolean algebras in forcing. This paper combines ideas from the two traditions in order to generalize some techniques and results to the wider context of complete lattices. In particular, we lift a representation theorem of Allwein (...) and MacCaull to a duality between complete lattices and b-frames, and we derive alternative characterizations of several classes of complete lattices from this duality. This framework is then used to obtain new results in the theory of complete Heyting algebras and the semantics of intuitionistic propositional logic. (shrink)

Many theories about the teaching of logic and critical thinking take for granted that theoretical learning, the learning of formal rules for example, and its practical application are sufficient to master the tools taught and to take the habit of using them. However, this way of teaching is not efficient, a conclusion supported by much work in cognitive science. Approaching cognition evolutionarily with dual-process theories allows for an explanation of these insufficiencies and offers clues on how we could teach critical (...) thinking and logic more efficiently. In this article, we want to present this approach and explore these leads in order to make some pedagogical recommendations and lay the foundations of a framework. We will put forward an example of the application of this research program with philosophy for children. (shrink)

The development of phenomenology in nineteenth‐century German philosophy is that of a particular stream within the larger historical‐philosophical complex of Austro‐German philosophy. As the “grandfather of phenomenology” resp. the “disgusted grandfather of phenomenology,” but also as the key figure on the “Anglo‐Austrian Analytic Axis”, Brentano is at the source of the two main philosophical traditions in twentieth‐century philosophy. This chapter focuses mainly on his place in nineteenth‐century European philosophy and on the central themes and concepts in his philosophy that were (...) determinant in the development of the philosophy of his most gifted student: Edmund Husserl. Despite the variety of stances which Brentano expressed on ontology, metaphysics, and psychology over the course of his career, the five general principles remain central to his whole philosophy throughout: they have an important place in what could be called Brentano's philosophical worldview or system. By extension, they also are essential to his conception of phenomenology. (shrink)

Many results in logic and mathematics rely on techniques that allow for concrete, often visual, representations of abstract concepts. A primary example of this phenomenon in logic is the distinction between syntax and semantics, itself an example of the more general duality in mathematics between algebra and geometry. Such representations, however, often rely on the existence of certain maximal objects having particular properties such as points, possible worlds or Tarskian first-order structures. -/- This dissertation explores an alternative to such representations (...) known as possibility semantics. Its core idea is to replace maximal objects with ordered systems of partial approximations. Although it originates in the semantics of modal logic and the representation of abstract ordered structures, I argue that it has far-reaching mathematical, foundational and philosophical significance, especially in the context of semiconstructive mathematics, a foundational framework that does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. -/- The dissertation is divided in two main parts. The first part explores various applications of the mathematical framework underlying possibility semantics to lattice theory and non-classical propositional logics. A major theme is the development of constructive dualities for various categories of lattices, which are related to standard non-constructive dualities via Vietoris constructions. -/- The second part of the dissertation explores the alternative foundational setting of semi-constructive mathematics, focusing on three applications of possibility semantics for classical first-order logic to the philosophy of the mathematical infinite. In particular, we introduce generic powers, a semi-constructive analogue of ultrapowers in classical model theory, and we explore the merits of these structures from a foundational, conceptual and historical viewpoint. (shrink)

Uncertainty is recognized as a key issue in water resources research, amongst other sciences. Discussions of uncertainty typically focus on tools and techniques applied within an analysis, e.g. uncertainty quantification and model validation. But uncertainty is also addressed outside the analysis, in writing scientific publications. The language that authors use conveys their perspective of the role of uncertainty when interpreting a claim —what we call here “framing” the uncertainty. This article promotes awareness of uncertainty framing in four ways. 1) It (...) proposes a typology of eighteen uncertainty frames, addressing five questions about uncertainty. 2) It describes the context in which uncertainty framing occurs. This is an interdisciplinary topic, involving philosophy of science, science studies, linguistics, rhetoric, and argumentation. 3) We analyze the use of uncertainty frames in a sample of 177 abstracts from the Water Resources Research journal in 2015. This helped develop and tentatively verify the typology, and provides a snapshot of current practice. 4) Provocative recommendations promote adjustments for a more influential, dynamic science. Current practice in uncertainty framing might be described as carefully-considered incremental science. In addition to uncertainty quantification and degree of belief (present in ~5% of abstracts), uncertainty is addressed by a combination of limiting scope, deferring to further work (~25%) and indicating evidence is sufficient (~40%) – or uncertainty is completely ignored (~8%). There is a need for public debate within our discipline to decide in what context different uncertainty frames are appropriate. Uncertainty framing cannot remain a hidden practice evaluated only by lone reviewers. (shrink)

In the present paper, I try to shed some light on the Munich-Göttingen conception of essences, laws of essence, and ideal objects. I first start with a preliminary account of their conception of the synthetic a priori at the basis of their conception of essence (§2); I then offer a first characterization of this conception, which I label as metaphysical realism (§3), highlighting its key concept: foundation (§4). In the last four sections (§§5-8), I discuss different outcomes of this conception (...) of essences: the nature of laws of essences (§5), different categories of essences (§6) and anumericity (§7). (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the idea of statistical frequency. (...) The puzzle is not, however, merely a legal one. Our unwillingness to base beliefs on statistical evidence is by no means limited to the courtroom, and is at odds with almost every general principle that epistemologists have proposed as to how we ought to manage our beliefs. (shrink)

Recent developments in Continental philosophy have included the emergence of a school of “speculative realism,” which rejects the human-centered orientation that has long dominated Continental thought. Proponents of speculative realism differ on several issues, but many agree on the need for an object-oriented ontology. Some speculative realists identify realism with materialism, while others accord equal reality to objects that are non-material, even fictional. Several thinkers retain a focus on difference, a well-established theme in Continental thought. This paper looks at speculative (...) realism from the perspective of systems theory. Many of the tenets of speculative realism have long been features of systems metaphysics and are expressed clearly in a systems framework. However, some views of some speculative realists differ substantially from systems theoretic ideas. (shrink)

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

Dans son article From Nihilism to Monism, Jonathan Schaffer montre que les partisans du Nihilisme de la Composition ont de bonnes raisons d’accepter le Monisme d’Existence plutôt que le Nihilisme. De manière analogue, nous souhaitons montrer ici que les partisans de l’Universalisme de la Composition ont de bonnes raisons d’accepter le Monisme de Priorité. Pour montrer cela, nous allons proposer et défendre l’argument suivant : Prémisse 1. Si l’Universalisme de la Composition est vrai alors le Cosmos existe. Prémisse 2. Si (...) le Cosmos existe alors le Cosmos est la seule entité concrète basique. Conclusion. Si l’Universalisme de la Composition est vrai alors le Cosmos est la seule entité concrète basique. (shrink)

Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...) with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

The low representation (< 30%) of women in philosophy in English-speaking countries has generated much discussion, both in academic circles and the public sphere. It is sometimes suggested (Haslanger 2009) that unconscious biases, acting at every level in the field, may be grounded in gendered schemas of philosophers and in the discipline more widely, and that actions to make philosophy a more welcoming place for women should address such schemas. However, existing data are too limited to fully warrant such an (...) explanation, which therefore will not satisfy those in favor of the status quo or those who argue against the need to address gender imbalance. In this paper, we propose measures to improve the profession that ought to be implemented without referring explicitly to this underrepresentation or to the climate for women and other underrepresented groups. Such recommendations are based on empirical research already carried out in other disciplines and do not rest on whether it is possible to identify the cause of this low representation. We argue that we need not wait for new or better data to ensure that fairer practices are enacted for women, other underrepresented groups, and everybody else, if only out of precaution. (shrink)

Recent developments in generalized probability theory have renewed a debate about whether regularity (i.e., the constraint that only logical contradictions get assigned probability 0) should be a necessary feature of both chances and credences. Crucial to this debate, however, are some mathematical facts regarding the interplay between the existence of regular generalized probability measures and various cardinality assumptions. We improve on several known results in the literature regarding the existence of regular generalized probability measures. In particular, we give necessary and (...) sufficient conditions for the existence of regular generalized probability measures defined on the whole powerset of any sample space. (shrink)

My concern in this paper is with the claim that knowledge is a mental state – a claim that Williamson places front and centre in Knowledge and Its Limits. While I am not by any means convinced that the claim is false, I do think it carries certain costs that have not been widely appreciated. One source of resistance to this claim derives from internalism about the mental – the view, roughly speaking, that one’s mental states are determined by one’s (...) internal physical state. In order to know that something is the case it is not, in general, enough for one’s internal physical state to be a certain way – the wider world must also be a certain way. If we accept that knowledge is a mental state, we must give up internalism. One might think that this is no cost, since much recent work in the philosophy of mind has, in any case, converged on the view that internalism is false. This thought, though, is too quick. As I will argue here, the claim that knowledge is a mental state would take us to a view much further from internalism than anything philosophers of mind have converged upon. (shrink)

In this paper I draw attention to a peculiar epistemic feature exhibited by certain deductively valid inferences. Certain deductively valid inferences are unable to enhance the reliability of one's belief that the conclusion is true—in a sense that will be fully explained. As I shall show, this feature is demonstrably present in certain philosophically significant inferences—such as GE Moore's notorious 'proof' of the existence of the external world. I suggest that this peculiar epistemic feature might be correlated with the much (...) discussed phenomenon that Crispin Wright and Martin Davies have called 'transmission failure'—the apparent failure, on the part of some deductively valid inferences to transmit one's justification for believing the premises. (shrink)

A de minimis risk is defined as a risk that is so small that it may be legitimately ignored when making a decision. While ignoring small risks is common in our day-to-day decision making, attempts to introduce the notion of a de minimis risk into the framework of decision theory have run up against a series of well-known difficulties. In this paper, I will develop an enriched decision theoretic framework that is capable of overcoming two major obstacles to the modelling (...) of de minimis risk. The key move is to introduce, into decision theory, a non-probabilistic conception of risk known as normic risk. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...) of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...) these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic. (shrink)

The Catastrophe Theory of Rene Thom and E. C. Zeeman suggests a mathematical interpretation of certain aspects of Hegelian and Marxist dialectics. Specifically, the three 'classical' dialectical principles, (1) the transformation of quantity into quality, (2) the unity and struggle of opposites, and (3) the negation of negation, can be modeled with the seven 'elementary catastrophes' given by Thorn, especially the catastrophes known as the 'cusp' and the 'butterfly'. Far from being empty metaphysics or scholasticism, as critics have argued, the (...) dialectical principles embody genuine insights into a class of phenomena, insights which can now be expressed within a precise mathematical formalism. This fact does not, however, support the claim that these principles, possibly modified or supplemented, constitute the laws of motion for human thought and for natural and social processes or even just the last of these. (shrink)

Graham Harman writes that the “basic dualism in the world lies…between things in their intimate reality and things as confronted by other things.” However, dualism implies irreconcilable difference; what Harman points to is better expressed as a dyad, where the two components imply one another and interact. This article shows that systems theory has long asserted the fundamental character of Harman’s dyad, expressing it as the union of internal structure and external function, which correspond exactly to what Levi Bryant, characterizing (...) Harman’s views, refers to as the intra-ontic and the inter-ontic, respectively. After interpreting Harman’s dyad in terms of the ontology of systems theory, the article illustrates his dyad with a variety of examples, including conceptions about truth, ethics, value, and intelligence. The structure–function dyad is a spatial conception of a system as an object. It is usefully augmented with a temporal dimension, expressed in a third component or with an additional orthogonal dyad. Adding a temporal dyad to the structure–function dyad joins the idea of an event and/or process to the idea of an object. (shrink)

In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this (...) new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG. (shrink)

Is it right to convict a person of a crime on the basis of purely statistical evidence? Many who have considered this question agree that it is not, posing a direct challenge to legal probabilism – the claim that the criminal standard of proof should be understood in terms of a high probability threshold. Some defenders of legal probabilism have, however, held their ground: Schoeman (1987) argues that there are no clear epistemic or moral problems with convictions based on purely (...) statistical evidence, and speculates that our aversion to such convictions may be nothing more than an irrational bias. More recently, Hedden and Colyvan (2019, section VI) describe our reluctance to convict on the basis of purely statistical evidence as an ‘intuition’, but suggest that there may be no ‘in principle’ problem with such convictions (see also Papineau, forthcoming, section 6). In this paper, I argue that there is, in some cases, an in principle problem with a conviction based upon statistical evidence alone – namely, it commits us to a precedent which, if consistently followed through, could lead to the deliberate conviction of an innocent person. I conclude with some reflections on the idea that the criminal justice system should strive to maximise the accuracy of its verdicts – and the related idea that we should each strive to maximise the accuracy of our beliefs. (shrink)

In 1990 Edward Craig published a book called Knowledge and the State of Nature in which he introduced and defended a genealogical approach to epistemology. In recent years Craig’s book has attracted a lot of attention, and his distinctive approach has been put to a wide range of uses including anti-realist metaepistemology, contextualism, relativism, anti-luck virtue epistemology, epistemic injustice, value of knowledge, pragmatism and virtue epistemology. While the number of objections to Craig’s approach has accumulated, there has been no sustained (...) attempt to develop answers to these objections. In this paper we provide answers to seven important objections in the literature. (shrink)

In this paper I respond to Marcello Di Bello’s criticisms of the ‘normic account’ of the criminal standard of proof. In so doing, I further elaborate on what the normic account predicts about certain significant legal categories of evidence, including DNA and fingerprint evidence and eyewitness identifications.

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species (...) of variably strict conditional I hope to shed new light upon their content and their logic. (shrink)

Recent years have seen an explosion of interest in metaphysical explanation, and philosophers have fixed on the notion of ground as the conceptual tool with which such explanation should be investigated. I will argue that this focus on ground is myopic and that some metaphysical explanations that involve the essences of things cannot be understood in terms of ground. Such ‘essentialist’ explanation is of interest, not only for its ubiquity in philosophy, but for its being in a sense an ultimate (...) form of explanation. I give an account of the sense in which such explanation is ultimate and support it by defending what I call the inessentiality of essence. I close by suggesting that this principle is the key to understanding why essentialist explanations can seem so satisfying. (shrink)

The _Principle of Indifference_ was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called _problem of multiple of partitions_. In ‘Evidential symmetry and mushy credence’ Roger White suggests that we have been too quick to jettison this principle and argues that the problem of multiple partitions rests on a mistake. In this paper I will criticise White’s attempt to revive POI. In so doing, I will argue that what underlies (...) the problem of multiple partitions is a fundamental tension between POI and the very idea of _evidential incomparability_. (shrink)

One of the most intriguing claims in Sven Rosenkranz’s Justification as Ignorance is that Timothy Williamson’s celebrated anti-luminosity argument can be resisted when it comes to the condition ~K~KP—the condition that one is in no position to know that one is in no position to know P. In this paper, I critically assess this claim.

Say that two goals are normatively coincident just in case one cannot aim for one goal without automatically aiming for the other. While knowledge and justification are distinct epistemic goals, with distinct achievement conditions, this paper begins from the suggestion that they are nevertheless normatively coincident—aiming for knowledge and aiming for justification are one and the same activity. A number of surprising consequences follow from this—both specific consequences about how we can ascribe knowledge and justification in lottery cases and more (...) general consequences about the nature of justification and the relationship between justification and evidential probability. Many of these consequences turn out to be at variance with conventional, prevailing views. (shrink)

Metaphysical rationalism, the doctrine which affirms the Principle of Sufficient Reason (the PSR), is out of favor today. The best argument against it is that it appears to lead to necessitarianism, the claim that all truths are necessarily true. Whatever the intuitive appeal of the PSR, the intuitive appeal of the claim that things could have been otherwise is greater. This problem did not go unnoticed by the great metaphysical rationalists Spinoza and Leibniz. Spinoza’s response was to embrace necessitarianism. Leibniz’s (...) response was to argue that, despite appearances, rationalism does not lead to necessitarianism. This paper examines the debate between these two rationalists and concludes that Leibniz has persuasive grounds for his opinion. This has significant implications both for the plausibility of the PSR and for our understanding of modality. (shrink)

In ‘The normative role of knowledge’ (2012), Declan Smithies defends a ‘JK-rule’ for belief: One has justification to believe that P iff one has justification to believe that one is in a position to know that P. Similar claims have been defended by others (Huemer, 2007, Reynolds, forthcoming). In this paper, I shall argue that the JK-rule is false. The standard and familiar way of arguing against putative rules for belief or assertion is, of course, to describe putative counterexamples. My (...) argument, though, won’t be like this – indeed I doubt that there are any intuitively compelling counterexamples to the JK-rule. Nevertheless, the claim that there are counterexamples to the JK-rule can, I think, be given something approaching a formal proof. My primary aim here is to sketch this proof. I will briefly consider some broader implications for how we ought to think about the epistemic standards governing belief and assertion. (shrink)

This paper seeks to widen the dialogue between the “epistemology of peer disagreement” and the epistemology informed by Wittgenstein’s last notebooks, later edited as On Certainty. The paper defends the following theses: not all certainties are groundless; many of them are beliefs; and they do not have a common essence. An epistemic peer need not share all of my certainties. Which response to a disagreement over a certainty is called for, depends on the type of certainty in question. Sometimes a (...) form of relativism is the right response. Reasonable, mutually recognized peer disagreement over a certainty is possible.—The paper thus addresses both interpretative and systematic issues. It uses Wittgenstein as a resource for thinking about peer disagreement over certainties. (shrink)

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In (...) this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)