Hume on the social construction of mathematical knowledge

Mathematics for Hume is the exemplary field of demonstrative knowledge. Ideally, this knowledge is a priori as it arises only from the comparison of ideas without any further empirical input; it is certain because demonstration consist of steps that are intuitively evident and infallible; and it is also necessary because the possibility of its falsity is inconceivable as it would imply a contradiction. But this is only the ideal, because demonstrative sciences are human enterprises and as such they are just as fallible as their human practitioners. According to the reading suggested here, Hume develops a radical sceptical challenge for mathematics, and thereby he undermines the knowledge claims associated with demonstrative reasoning. But Hume does not stop there: he also offers resources for a sceptical solution to this challenge, one that appeals crucially to social practices, and sketches the social genealogy of a community-wide mathematical certainty. While explaining this process, he relies on the conceptual resources of his faculty psychology that helps him to distinguish between the metaphysics and practices of mathematical knowledge. His account explains why we have reasons to be dubious about our reasoning capacities, and also how human nature and sociability offers some remedy from these epistemic adversities.

     

Counterexamples to Recovery and the Filtering Condition

David Makinson has argued that the compelling character of counterexamples to the Recovery Condition on contraction is due to an appeal to justificational structure. In “naked theories” where such structure is ignored or is not present, Recovery does apply. This note attempts to show that Makinson is mistaken on both counts. Recovery fails when no appeal is made to justificational structure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mistakes and Mental Disturbances: Pleasants, Wittgenstein, and Basic Moral Certainty

In his article, “Wittgenstein and Basic Moral Certainty,” Nigel Pleasants argues that killing an innocent, non-threatening person is wrong. It is, he argues, “a basic moral certainty.” He believes our basic moral certainties play the “same kind of foundational role as [our] basic empirical certaint[ies] do.” I believe this is mistaken. There is not “simply one kind of foundational role” that certainty plays. While I think Pleasants is right to affiliate his proposition with a Wittgensteinian form of certainty, he exposes himself to a tension that exists in On Certainty regarding how we acquire it: is certainty natural, is it social? In this paper, I present two ways in which we come to possess certainty: a bottom-up approach, where certainty is part of our instinctual predisposition, and a top-down approach, where certainty is acquired through positive reinforcement by family and culture.     

Imperfect epistemic duties and the justificational fecundity of evidence

Mark Nelson argues that we have no positive epistemic duties. His case rests on the evidential inexhaustibility of sensory and propositional evidence—what he calls their ‘infinite justificational fecundity’. It is argued here that Nelson’s reflections on the richness of sensory and propositional evidence do make it doubtful that we ever have an epistemic duty to add any particular beliefs to our belief set, but that they fail to establish that we have no positive epistemic duties whatsoever. A theory of epistemic obligation based on Kant’s idea of an imperfect duty is outlined. It is suggested that such a theory is consistent with the inexhaustibility of sensory and propositional evidence. Finally, one feature of our epistemic practice suggestive of the existence of imperfect epistemic duties is identified and promoted.     

World‐Pictures and Wittgensteinian Certainty

Although certainty is a fundamental notion in epistemology, it is less studied in contemporary analytic epistemology than other important notions such as knowledge or justification. This paper focuses on Wittgensteinian certainty, according to which the very basic dimension of our epistemic practices, the elements of our world‐pictures, are objectively certain, in that we cannot legitimately doubt them. The aim of the paper is to offer the best philosophical way to clarify Wittgensteinian certainty, in a way that is consonant with Wittgenstein's fundamental insights. The paper critiques two alternative proposals for clarifying Wittgensteinian certainty that are philosophically unsatisfying: the rule view and the proposition view. Finally, it instead shows how viewing world‐pictures as pictures, in the sense of unclear conceptions, is a more philosophically fruitful approach to understanding world‐pictures.     

Optimality justifications: new foundations for foundation-oriented epistemology

In this paper a new conception of foundation-oriented epistemology is developed. The major challenge for foundation-oriented justifications consists in the problem of stopping the justificational regress without taking recourse to dogmatic assumptions or circular reasoning. Two alternative accounts that attempt to circumvent this problem, coherentism and externalism, are critically discussed and rejected as unsatisfactory. It is argued that optimality arguments are a new type of foundation-oriented justification that can stop the justificational regress. This is demonstrated on the basis of a novel result in the area of induction: the optimality of meta-induction. In the final section the method of optimality justification is generalized to deductive and abductive inferences.     

LIBERTY,NECESSITY AND CHANCE: HOBBES'S GENERAL THEORY OF EVENTS

Locke characterizes sensitive knowledge as knowledge of the existence of external objects present to the senses, and in terms of an ‘assurance’ that falls short of the certainty of intuition and demonstration. But it is unclear how this fits with his general definition of knowledge, as the perception of the agreement or disagreement of ideas, and it is unclear how that assurance can amount to knowledge, rather than amounting to mere probability (which he contrasts with knowledge). Some contend that Locke does not regard sensitive knowledge as genuine knowledge, but only honourifically calls it knowledge. In contrast, I argue that Locke holds that sensitive knowledge is knowledge, though he takes the conditions for it to be very different from the conditions for intuitive and demonstrative knowledge. It is not the assurance alone which Locke thinks qualifies sensitive knowledge as such: it is also the fact that the assurance arises from the actual employment of the senses upon external objects, and the fact that the senses do not generally deceive us, which he thinks qualifies sensitive knowledge as genuine knowledge. That there is a (tacit) form of externalism in Locke's account of sensitive knowledge is the main thesis of this paper.     

Logical Theories of Intention and the Database Perspective

While logical theories of information attitudes, such as knowledge, certainty and belief, have flourished in the past two decades, formalization of other facets of rational behavior have lagged behind significantly. One intriguing line of research concerns the concept of intention. I will discuss one approach to tackling the notion within a logical framework, based on a database perspective.     

Spinoza on the Problem of Akrasia

Abstract: Two common ways of explaining akrasia will be presented, one which focuses on strength of desire and the other which focuses on action issuing from practical judgment. Though each is intuitive in a certain way, they both fail as explanations of the most interesting cases of akrasia. Spinoza's own thoughts on bondage and the affects follow, from which a Spinozist explanation of akrasia is constructed. This account is based in Spinoza's mechanistic psychology of cognitive affects. Because Spinoza's account explains action asissuing from modes of mind that are both cognitive and affective, it captures the intuitions that motivate the two traditional views while avoiding the pitfalls that result from their one-sided approaches. This project will allow us a fuller understanding of Spinozist moral psychology. In addition to this historical value, the Spinozist theory may offer a satisfactory explanation of certain hard cases of akrasia while avoiding the problems be set by other theories. For this reason, the Spinozist account could also be seen as a useful contribution to our philosophical understanding of the phenomenon of akrasia.     

Fixing Descartes: Ethical Intellectualism in Spinoza's Early Writings

This paper aims at reconstructing the ethical issues raised by Spinoza's early Treatise on the Emendation of the Intellect. Specifically, I argue that Spinoza takes issue with Descartes’ epistemology in order to support a form of “ethical intellectualism” in which knowledge is envisaged as both necessary and sufficient to reach the supreme good. First, I reconstruct how Descartes exploits the distinction between truth and certainty in his Discourse on the Method. On the one hand, this distinction acts as the basis for Descartes’ epistemological rules while, on the other hand, it implies a “morale par provision” in which adequate knowledge is not strictly necessary to practice virtue. Second, I show that Spinoza rejects the distinction between truth and certainty and thus the methodological doubt. This move leads Spinoza to substitute the Cartesian Cogito with the idea of God as the only adequate standard of knowledge, through which the mind can attain the rules to reach the supreme good. Third, I demonstrate that in the Short Treatise Spinoza develops this view by equating intellect and will and thus maintaining that only adequate knowledge can help to contrast affects. However, I also insist that Spinoza's early epistemology is unable to explain why human beings drop conceive of the idea of God inadequately. Thus, I suggest that in his later writings Spinoza accounts for the insufficiency of adequate knowledge in opposing the power of the imagination and passions by reconnecting the nature of ideas with the mind's conatus.     

Contextualism and fallibility: pragmatic encroachment, possibility, and strength of epistemic position

A critique of conversational epistemic contextualism focusing initially on why pragmatic encroachment for knowledge is to be avoided. The data for pragmatic encroachment by way of greater costs of error and the complementary means to raise standards of introducing counter-possibilities are argued to be accountable for by prudence, fallibility and pragmatics. This theme is sharpened by a contrast in recommendations: holding a number of factors constant, when allegedly higher standards for knowing hold, invariantists still recommend assertion (action), while contextualists do not. Given the knowledge norm of assertion, if one recommendation is preferable to the other, the result favors the preferred recommendation??s account of knowledge. In the final section, I offer a unification of these criticisms centering on the contextualist use of ??epistemic position??. Their use imposes on threshold notions of justification, warrant, or knowledge tests that are suitable only to unlimited comparative or scalar notions like confidence or certainty and places them at one with an important strand of sceptical reasoning.     

Critical notice of Aaron James,Fairness in Practice: A Social Contract for a Global Economy

Nobody has offered such a comprehensive philosophical approach to trade. Nonetheless, James's approach does not succeed. First, we explore James's constructivist method, which does less work than he suggests. The second topic is James's take on the different ‘grounds’ of justice. We explore the shortcomings of approaches that focus exclusively on trade. Our third topic is why James thinks trade is such a ground. The fourth topic is how James argues for his proposed ‘structural equity.’ This proposal remains under-argued. Our fifth topic is to explore why structural equity would generate several specific principles. Finally, we discuss James's notion of autarky. Autarky sets the benchmark for James's ideas about how to divide gains of trade. We doubt that it can do so.     

Spinoza's Proof of Necessitarianism

This paper consists of four sections. The first section considers what the proof of necessitarianism in Spinoza's system requires. Also in the first section, Jonathan Bennett's (1984) reading of lpl6 as involving a commitment to necessitarianism is presented and accepted. The second section evaluates Bennett's suggestion how Spinoza might have been led to conclude necessitarianism from his basic assumptions. The third section of the paper is devoted to Don Garrett's (1991) interpretation of Spinoza's proof. I argue that Bennett's and Garrett's interpretations of Spinoza's necessitarianism have shortcomings which justify an attempt to offer an alternative proof. In the proof given in the fourth section, it is argued that Spinoza derived necessitarianism from the conjunction of the following principles: (i) necessary existence of the substances; (ii) substance-property ontology; (iii) superessentialism; and (iv) the 'no shared attribute'thesis.     

THE MIRACLE OF MOSES

In this paper, I draw out a tension between miracles, prophecy, and Spinoza's assertions about Moses in the Theological-Political Treatise (TTP). The three seem to constitute an inconsistent triad. Spinoza's account of miracles requires a naturalistic interpretation of all events. This categorical claim must therefore apply to prophecy; specifically, Moses' hearing God's voice in a manner which does not seem to invoke the imagination or natural phenomena. Thus, Spinoza seemingly cannot maintain both Moses' exalted status and his account of miracles. I consider some possible solutions, but find that they are either untrue to Spinoza's position, or would undercut his categorical argument against miracles. I therefore conclude that Spinoza leaves an unresolved tension in the TTP.     

A Recourse Stochastic Goal Programming Approach for the Multi‐objective Stochastic Vehicle Routing Problem

This paper addresses a multi‐objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi‐objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance‐constrained approach and a goal‐programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright © 2016 John Wiley & Sons, Ltd.     

Self-awareness and self-deception: a Sartrean perspective

In spite of the fact that many find Jean-Paul Sartre’s account of la mauvaise foi puzzling, unclear and troublesome, he remains a recurring figure in the debate about self-deception. Indeed, Sartre’s exposition of self-deception is as puzzling as it is original. The primary task of my paper will be to expose why this is the case and to thereby correct a recurrent misunderstanding of Sartre’s theory of consciousness. In the end, will we see that Sartre offers the following theory: self-deception is to be accounted for by assuming that there are intrinsically self-deceptive epistemic states. The latter are self-deceptive in so far as they claim certainty while nevertheless being accompanied by an inbuilt and incorruptible awareness of being unwarranted. For Sartre, developing this rather peculiar account of self-deception, is, as we will see, not primarily intended as an end in itself. Rather, Sartre thereby hopes to illuminate the nature of self-awareness as (i.) epistemically super-secure, (ii.) pre-reflexive, (iii.) non-positional and “embryonic” knowledge that (iv.) does not necessitate but can still ground epistemically super-secure reflexive knowledge, and (v.) that can replace Freud’s notion of unconscious knowledge. As an account of self-deception, Sartre’s suggestion, however, comes at a high price. Apart from the presuppositions Sartre makes in the theory of consciousness and intentionality, his account is deflationist with regard to local cases of self-deception.     

Knowledge central: A central role for knowledge attributions in social evaluations

Five experiments (N?=?1710) demonstrate the central role of knowledge attributions in social evaluations. In Experiments 1–3, we manipulated whether an agent believes, is certain of, or knows a true proposition and asked people to rate whether the agent should perform a variety of actions. We found that knowledge, more so than belief or certainty, leads people to judge that the agent should act. In Experiments 4–5, we investigated whether attributions of knowledge or certainty can explain an important finding on how people act based on statistical evidence, known as “the Wells effect”. We found that knowledge attributions, but not certainty attributions, mediate this effect on decision making.     

Kant’s conception of proper science

Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous claim that any proper natural science must be mathematical should be understood on the basis of these conditions. In order to substantiate this reading, I will show that only in this way it can be explained why Kant thought (1) that mathematics has a particular foundational function with respect to the natural sciences and (2) as such secures their scientific status.     

Desire and the Good in Plotinus

Plotinus calls the first principle the One and the Good. According to Plotinus, ‘Good’ is an appropriate name for the One because the One is that which all things desire. Since he says that the One is beyond knowledge, beyond language, beyond intellect, and beyond being, however, what philosophical evidence can he provide for his claim that the One is that which all desire? In this article I offer some philosophical evidence, aside from mystical union with the One, for why ‘the Good’ is an appropriate name for the One, and for why calling the One ‘Good’ is not at odds with the fact that it is beyond knowledge, but rather entails it. To this end, after an initial consideration of the relationship between the good and desire in Plato and Aristotle, I focus on the role that desire plays in relation to the Good in Plotinus' thought.     

Justification,knowledge, and normality

There is much to like about the idea that justification should be understood in terms of normality or normic support (Smith in Between probability and certainty, Oxford University Press, Oxford, 2016; Goodman and Salow in Philosophical Studies 175: 183–196, 2018). The view does a nice job explaining why we should think that lottery beliefs differ in justificatory status from mundane perceptual or testimonial beliefs. And it seems to do that in a way that is friendly to a broadly internalist approach to justification. In spite of its attractions, we think that the normic support view faces two serious challenges. The first is that it delivers the wrong result in preface cases. Such cases suggest that the view is either too sceptical or to externalist. The second is that the view struggles with certain kinds of Moorean absurdities. It turns out that these problems can easily be avoided. If we think of normality as a condition on knowledge, we can characterise justification in terms of its connection to knowledge and thereby avoid the difficulties discussed here. The resulting view does an equally good job explaining why we should think that our perceptual and testimonial beliefs are justified when lottery beliefs cannot be. Thus, it seems that little could be lost and much could be gained by revising the proposal and adopting a view on which it is knowledge, not justification that depends directly upon normality.