Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what counts as a mathematical object, and how (...) we can have knowledge about an unchanging object. (shrink)

Like all of Nagel's work, this is a book with a message: an apparently clear, simple message, forcefully presented and repeated. The message is that there is a limit to the extent to which we can "get outside" fundamental forms of thought, including logical, mathematical, scientific, and ethical thought. "Getting outside" means taking up a biological or psychological or sociological or economic or political view of ourselves as thinkers. It also inclines many people to talk of the contingency or subjectivity (...) or arbitrariness or "relativity" of our thoughts. Nagel believes that the standpoint is impossible, and the relativism it is apt to engender is self-refuting: "we cannot criticize some of our own claims of reason without employing reason at some point to formulate and support those criticisms". The general message is that first-order thoughts, the elementary certainties of mathematics, logic, science, and ethics, "dominate" any attempt to displace them. The book ends with the peroration: "Even if we distance ourselves from some of our thoughts and impulses, and regard them from outside, the process of trying to place ourselves in the world leads eventually to thoughts that we cannot think of as merely `ours'. If we think at all, we must think of ourselves, individually and collectively, as submitting to the order of reasons rather than creating it.". (shrink)

In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There simply is no intelligible problem (...) that satisfies all of the constraints which have been placed on the Benacerraf Problem. The point generalizes to all arguments with the structure of the Benacerraf Problem aimed at realism about a domain meeting certain conditions. Such arguments include so-called "Evolutionary Debunking Arguments" aimed at moral realism. I conclude with some suggestions about the relationship between the Benacerraf Problem and the Gettier Problem. (shrink)

It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (shrink)

…entities? 2. How to be a nominalist 2.1. “Speak with the vulgar …” 2.2. “…think with the learned” 3. Arguments for nominalism 3.1. Intelligibility, physicalism, and economy 3.2. Causal..

Quine's areas of interest are panoramic, as this lively book amply demonstrates.

Benjamin Callard has recently suggested that causation between Platonic objects—standardly understood as atemporal and non-spatial—and spatio-temporal objects is not ‘a priori’ unintelligible. He considers the reasons some have given for its purported unintelligibility: apparent impossibility of energy transference, absence of physical contact, etc. He suggests that these considerations fail to rule out a priori Platonic-object causation. However, he has overlooked one important issue. Platonic objects must causally affect different objects differently, and different Platonic objects must causally affect the same objects (...) differently. How are Platonic objects—ones outside space and time—supposed to do that? CiteULike Connotea Del.icio.us What's this? (shrink)

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.

It is widely believed that platonists face a formidable problem: that of providing an intelligible account of mathematical knowledge. The problem is that we seem unable, if the platonist is right, to have the causal relationships with the objects of mathematics without which knowledge of these objects seems unintelligible. The standard platonist response to this challenge is either to deny that knowledge without causation is unintelligible, or to make room for causal interactions by softening the platonism at issue. In this (...) essay I argue that the idea of causal relations with fully platonist objects is unproblematic. (shrink)

Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly (...) turns out to be logical space for a response to the improved challenge where no such space appeared to exist. (shrink)

Mechanism is undoubtedly a causal concept, in the sense that ordinary definitions and philosophical analyses explicate the concept in terms of other causal concepts such as production and interaction. Given this fact, many philosophers have supposed that analyses of the concept of mechanism, while they might appeal to philosophical theories about the nature of causation, could do little to inform such theories. On the other hand, methods of causal inference and explanation appeal to mechanisms. Discovering a mechanism is the gold (...) standard for establishing and explaining causal connections. This fact suggests that it might be possible to provide an analysis of causation that appeals to mechanisms. (shrink)

Jody Azzouni has offered the following argument against the existence of mathematical entities: if, as it seems, mathematical entities play no role in mathematical practice, we therefore have no reason to believe in them. I consider this argument as it applies to mathematical platonism, and argue that it does not present a legitimate novel challenge to platonism. I also assess Azzouni's use of the ‘epistemic role puzzle’ (ERP) to undermine the platonist's alleged parallel between skepticism about mathematical entities and external-world (...) skepticism. I conclude that ERP fails to undermine this parallel. (shrink)

This chapter locates moral epistemology within general moral theory, introduces the central questions of moral epistemology, and then distinguishes several versions of moral skepticism. It ends with a discussion of whether there is a presumption against moral skepticism which places the burden of proof on moral skeptics.