A Logical Transmission Principle for Conclusive Reasons

Dretske's conclusive reasons account of knowledge is designed to explain how epistemic closure can fail when the evidence for a belief does not transmit to some of that belief's logical consequences. Critics of Dretske dispute the argument against closure while joining Dretske in writing off transmission. This paper shows that, in the most widely accepted system for counterfactual logic (David Lewis's system VC), conclusive reasons are governed by an informative, non-trivial, logical transmission principle. If r is a conclusive reason for believing p in Dretske's sense, and if p logically implies q, and if p and q satisfy one additional condition, it follows that r is a conclusive reason for believing q. After introducing this additional condition, I explain its intuitive import and use the condition to shed new light on Dretske's response to scepticism, as well as on his distinction between the so-called ‘lightweight’ and ‘heavyweight’ implications of a piece of perceptual knowledge.     

Conclusive Reasons and Epistemic Luck

What is it to have conclusive reasons to believe a proposition P? According to a view famously defended by Dretske, a reason R is conclusive for P just in case [R would not be the case unless P were the case]. I argue that, while knowing that P is plausibly related to having conclusive reasons to believe that P, having such reasons cannot be understood in terms of the truth of this counterfactual condition. Simple examples show that it is possible to believe P on the basis of reasons that satisfy the counterfactual, and still get things right about P only as a matter of luck. Seeing where this account of conclusive reasons goes wrong points to an important distinction between having conclusive reasons and relying on reasons that are in point of fact conclusive. It also has wider consequences for whether modal principles like sensitivity and safety can rule out the pernicious kind of epistemic luck, or the kind of luck that interferes with knowledge.     

Defending the Indispensability Argument: Atoms, Infinity and the Continuum

This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue that these new versions accommodate Maddy’s history of the atomic theory. Counter-examples are provided regarding the role of the mathematical continuum and mathematical infinity in science.     

What's Wrong With Indispensability?

For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objectshas provided the best (and perhaps only) evidence for mathematicalrealism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997),on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is indispensable in the wrong way), and, taking my cue from Mark Colyvan's (1998) attempt to provide a Quinean account of unapplied mathematics as `recreational', suggest that, if one approaches the problem from a Quinean naturalist starting point, one must conclude that all mathematics is recreational in this way.     

Stalnaker on Mathematical Information

Robert Stalnaker has argued that mathematical information is information about the sentences and expressions of mathematics. I argue that this metalinguistic account is open to a variant of Alonzo Church's translation objection and that Stalnaker's attempt to get around this objection is not successful. If correct, this tells not only against Stalnaker's account of mathematical truths, but against any metalinguistic account of truths that are both necessary and informative.     

Grim’s arguments against omniscience and indefinite extensibility

Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the set theoretical argument and make explicit some ways in which it depends on mathematical Platonism. Then we sketch a non Platonistic account of inconsistent multiplicities, based on the notion of indefinite extensibility, and show how Grim??s set theoretical argument could fail to be conclusive in such a context. Finally, we confront Grim??s model theoretical argument suggesting a way to define a being as omniscient without quantifying over any inconsistent multiplicity.     

Why Believe Infinite Sets Exist?

The axiom of infinity states that infinite sets exist. I will argue that this axiom lacks justification. I start by showing that the axiom is not self-evident, so it needs separate justification. Following Maddy’s (J Symb Log 53(2):481–511, 1988) distinction, I argue that the axiom of infinity lacks both intrinsic and extrinsic justification. Crucial to my project is Skolem’s (in: van Heijnoort (ed) From Frege to Gödel: a source book in mathematical logic, 1879–1931, Cambridge, Harvard University Press, pp. 290–301, 1922) distinction between a theory of real sets, and a theory of objects that theory calls “sets”. While Dedekind’s (in: Essays on the theory of numbers, pp. 14–58, 1888. http://www.gutenberg.org/ebooks/21016) argument fails, his approach was correct: the axiom of infinity needs a justification it currently lacks. This epistemic situation is at variance with everyday mathematical practice. A dilemma ensues: should we relax epistemic standards or insist, in a skeptical vein, that a foundational problem has been ignored?     

EPISTEMIC VALUE AND ACHIEVEMENT

Knowledge seems to be a good thing, or at least better than epistemic states that fall short of it, such as true belief. Understanding too seems to be a good thing, perhaps better even than knowledge. In a number of recent publications, Duncan Pritchard tries to account for the value of understanding by claiming that understanding is a cognitive achievement and that achievements in general are valuable. In this paper, I argue that coming to understand something need not be an achievement, and so Pritchard's explanation of understanding's value fails. Next, I point out that Pritchard's is just one of many attempts to account for the value of an epistemic state – whether it be understanding, knowledge, or whatever – by appeal to the notion of achievement or, more generally, the notion of success because of ability. Tentatively, I offer reasons to be sceptical about the prospects of any such account.     

Two notions of intentional action? Solving a puzzle in Anscombe’s Intention

The account of intentional action Anscombe provides in her (1957) Intention has had a huge influence on the development of contemporary action theory. But what is intentional action, according to Anscombe? She seems to give two different answers, saying first that they are actions to which a special sense of the question ‘Why?’ is applicable, and second that they form a sub-class of the things a person knows without observation. Anscombe gives no explicit account of how these two characterizations converge on a single phenomenon, leaving us with a puzzle. I solve the puzzle by elucidating Anscombe's two characterizations in concert with several other key concepts in ‘Intention’, including, ‘practical reasons’, the sui generis kind of explanation these provide, the distinction between ‘practical’ and ‘speculative’ knowledge, the formal features which mark this distinction, and Anscombe's characterization of practical knowledge as knowledge ‘in intention’.     

自然主义集合实在论与数学哲学研究范式

In recent 50 years,the debate between mathematical realism and anti-realism has been dominating the mainstream development in the contemporary philosophy of mathematics. Penelope Maddy proposed a naturalistic set theoretic realism in 1990. This project brings the philosophy of mathematics a new research idea,that is,philosophy should attach importance to mathematical practice. This article will critically analyze Maddy's naturalistic set theoretic realism on the basis of research paradigm background belief....     

Transparent emotions? A critical analysis of Moran's transparency claim

I critically analyze Richard Moran's account of knowing one's own emotions, which depends on the Transparency Claim (TC) for self-knowledge. Applied to knowing one's own beliefs, TC states that when one is asked “Do you believe P?”, one can answer by referencing reasons for believing P. TC works for belief because one is justified in believing that one believes P if one can give reasons for why P is true. Emotions, however, are also conceptually related to concerns; they involve a response to something one cares about. As a consequence, acquiring self-knowledge of one's emotions requires knowledge of other mental attitudes, which falls outside the scope of TC. Hence, TC cannot be applied to emotions.     

Sound Advice and Internal Reasons

Reasons internalism holds that reasons for action contain an essential connection with motivation. I defend an account of reasons internalism based on the advisor model. The advisor model provides an account of reasons for action in terms of the advice of a more rational version of the agent. Contrary to Pettit and Smith's proposal and responding to Sobel's and Johnson's objections, I argue that the advisor model can provide an account of internal reasons and that it is too caught up in the psychology of the actual agent to be able to account for anything other than internal reasons.     

Logical structuralism and Benacerraf’s problem

There are two general questions which many views in the philosophy of mathematics can be seen as addressing: what are mathematical objects, and how do we have knowledge of them? Naturally, the answers given to these questions are linked, since whatever account we give of how we have knowledge of mathematical objects surely has to take into account what sorts of things we claim they are; conversely, whatever account we give of the nature of mathematical objects must be accompanied by a corresponding account of how it is that we acquire knowledge of those objects. The connection between these problems results in what is often called “Benacerraf’s Problem”, which is a dilemma that many philosophical views about mathematical objects face. It will be my goal here to present a view, attributed to Richard Dedekind, which approaches the initial questions in a different way than many other philosophical views do, and in doing so, avoids the dilemma given by Benacerraf’s problem.     

Animal cognition + optimal choice = behavior: A review of adaptive behavior and learning, 2nd Ed., by J. E. R. Staddon

Staddon discusses a vast array of topics in comparative psychology in this book. His view is that adaptive behavior in most cases is the result of optimal choice acting on an animal's knowledge about the world. Staddon refers to this as a functional teleonomic approach inasmuch as it attempts to understand an animal's behavior in terms of goals. He builds mathematical models based on this idea that are designed to reproduce specific sets of empirical observations, usually qualitatively. A natural consequence of Staddon's approach is that many models are developed, each of which applies to a specific set of observations. An alternative to functional teleonomy is a functional approach that builds on prior principles. In most cases, this approach favors a single‐theory account of behavior. Prior principles can be understood as functional stand‐ins for antecedent material causes, which means that these accounts are closer to mechanistic theories than are goal‐based teleonomic accounts. An ontological perspective, referred to as supervenient realism, is a means of understanding the relationship between functional theories and the material world. According to this perspective, the algorithmic operation of a successful functional theory may be understood to supervene on the material operation of the nervous system.     

Skepticism,naturalism, pyrrhonism

Skepticism and naturalism bear important connections with one another. Do they conflict or are they different sides of the same coin? In this paper, by considering the ways in which Sextus and Hume have examined these issues, I offer a Pyrrhonian response to Penelope Maddy's attempt to reject skepticism within the form of naturalism that she calls “second philosophy” (Maddy, 2007, 2017) and to Timothy Williamson's attempt to avoid skepticism from emerging within his knowledge-first approach (Williamson, 2000). Some lessons about Pyrrhonism result.     

Idealized laws,antirealism, and applied science: A case in hydrogeology

When is a law too idealized to be usefully applied to a specific situation? To answer this question, this essay considers a law in hydrogeology called Darcy's Law, both as it is used in what is called the symmetric-cone model, and as it is used in equations to determine a well's groundwater velocity and hydraulic conductivity. After discussing Darcy's law and its applications, the essay concludes that this idealized law, as well as associated models and equations in hydrogeology, are not realistic in the sense required by the D-N account. They exhibit what McMullin calls mathematical idealization, construct idealization, empirical-causal idealization, and subjunctive-causal idealization. Yet this lack of realism in hydrogeology is problematic for reasons unrelated to the status of the D-N account. These idealizations are also problematic in applied situations. Their problems require developing two supplemental criteria, necessary for their productive application.     

Arithmetic,set theory,reduction and explanation

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important and well-known case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense of this claim, I offer some evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate and successful foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences.     

Knowing‐how: Problems and Considerations

In recent years, a debate concerning the nature of knowing‐how has emerged between intellectualists who claim that knowledge‐how is reducible to knowledge‐that and anti‐intellectualists who claim that knowledge‐how comprises a unique and irreducible knowledge category. The arguments between these two camps have clustered largely around two issues: (1) intellectualists object to Gilbert Ryle's assertion that knowing‐how is a kind of ability, and (2) anti‐intellectualists take issue with Jason Stanley and Timothy Williamson's positive, intellectualist account of knowing‐how. Like most anti‐intellectualists, in this paper I will raise objections to Stanley and Williamson's account of knowing‐how and also defend the claim that ability is necessary for knowing‐how attributions. Unlike most discussions of knowing‐how, however, I will return to more Rylean considerations in order to illustrate that any intellectualist account of knowing‐how, not simply Stanley and Williamson's preferred variety, will fail because it will be unable to account for fundamental differences in the knowledge required to instantiate an ability and the knowledge involved in propositional thought.     

Conjoining Mathematical Empiricism with Mathematical Realism: Maddy’s Account of Set Perception Revisited

Penelope Maddy’s original solution to the dilemma posed by Benacerraf in his (1973) ‘Mathematical Truth’ was to reconcile mathematical empiricism with mathematical realism by arguing that we can perceive realistically construed sets. Though her hypothesis has attracted considerable critical attention, much of it, in my view, misses the point. In this paper I vigorously defend Maddy’s (1990) account against published criticisms, not because I think it is true, but because these criticisms have functioned to obscure a more fundamental issue that is well worth addressing: in general – and not only in the mathematical domain – empiricism and realism simply cannot be reconciled by means of an account of perception anything like Maddy’s. But because Maddy’s account of perception is so plausible, this conclusion raises the specter of the broader incompatibility of realism and empiricism, which contemporary philosophers are frequently at pains to forget.