Modal epistemologists parse modal conditions on knowledge in terms of metaphysical possibilities or ways the world might have been. This is problematic. Understanding modal conditions on knowledge this way has made modal epistemology, as currently worked out, unable to account for epistemic luck in the case of necessary truths, and unable to characterise widely discussed issues such as the problem of religious diversity and the perceived epistemological problem with knowledge of abstract objects. Moreover, there is reason to think that this (...) is a congenital defect of orthodox modal epistemology. This way of characterising modal epistemology is however optional. It is shown that one can non-circularly characterise modal conditions on knowledge in terms of epistemic possibilities, or ways the world might be for the target agent. Characterising the anti-luck condition in terms of epistemic possibilities removes the impediment to understanding epistemic luck in the case of necessary truths and opens the door to using these conditions to shed new light on some longstanding epistemological problems. (shrink)

Modal ontological arguments argue from the possible existence of a perfect being to the actual (necessary) existence of a perfect being. But modal ontological arguments have a problem of symmetry; they can be run in both directions. Reverse ontological arguments argue from the possible nonexistence of a perfect being to the actual (necessary) nonexistence of a perfect being. Some familiar points about the necessary a posteriori, however, show that the symmetry can be broken in favour of the ontological argument.

We offer an alternative to two influential accounts of virtue epistemology: Robust Virtue Epistemology and Anti-Luck Virtue Epistemology. We argue that while traditional RVE does offer an explanation of the distinctive value of knowledge, it is unable to effectively deal with cases of epistemic luck; and while ALVE does effectively deal with cases of epistemic luck, it lacks RVE’s resources to account for the distinctive value of knowledge. The account we provide, however, is both robustly virtue-theoretic and anti-luck, having the (...) respective benefits of both rival accounts without their respective shortcomings. We describe this view here. (shrink)

Within contemporary philosophy of mind, it is taken for granted that externalist accounts of meaning and mental content are, in principle, orthogonal to the matter of whether cognition itself is bound within the biological brain or whether it can constitutively include parts of the world. Accordingly, Clark and Chalmers (Analysis 58(1):7–19, 1998) distinguish these varieties of externalism as ‘passive’ and ‘active’ respectively. The aim here is to suggest that we should resist the received way of thinking about these dividing lines. (...) With reference to Brandom’s (1994, 2000, Inquiry 47:236–253, 2008) broad semantic inferentialism, we show that a theory of meaning can be at the same time a variety of active externalism. While we grant that supporters of other varieties of content externalism (e.g., Putnam 1975 and Burge (Philosophical Review 95:3–45, 1986) can deny active externalism, this is not an option for semantic inferentialists: On this latter view, the role of the environment (both in its social and natural form) is not ‘passive’ in the sense assumed by the alternative approaches to content externalism. (shrink)

Alvin Plantinga's evolutionary argument against naturalism makes the case that the conjunction of evolutionary theory and naturalism cannot be rationally believed, as, if both evolutionary theory and naturalism were true, it would be highly unlikely that our cognitive faculties are reliable. I present Plantinga's evolutionary argument against naturalism and survey a theory of meaning espoused by Robert Brandom, known as semantic inferentialism. I argue that if one accepts semantic inferentialism, as it is developed by Brandom, then Plantinga's motivation for the (...) evolutionary argument against naturalism is undermined. (shrink)

In Romans 5, St. Paul claims that death came into the world through Adam's sin. Many have taken this to foist on us a fundamentalist reading of Genesis. If death is the result of human sin, then, apparently, there cannot have been death in the world prior to human sin. This, however, is inconsistent with contemporary evolutionary biology, which requires that death predates the existence of modern humans. Although the relationship between Romans 5, Genesis, and contemporary science has been much (...) discussed—often with goal of dissipating the idea that the two are in conflict—the specific issue of death entering the world through sin has remained difficult to resolve. I argue that the Eastern Orthodox tradition has the resources to respect both Romans 5 and contemporary science. Appealing to a broadly Irenaean notion of soul‐making, and to the idea of theosis, opens up space for an understanding of these passages that is both scientifically informed and Orthodox. (shrink)

Within contemporary philosophy of mind, it is taken for granted that externalist accounts of meaning and mental content are, in principle, orthogonal to the matter of whether cognition itself is bound within the biological brain or whether it can constitutively include parts of the world. Accordingly, Clark and Chalmers (1998) distinguish these varieties of externalism as ‘passive’ and ‘active’ respectively. The aim here is to suggest that we should resist the received way of thinking about these dividing lines. With reference (...) to Brandom’s (1994; 2000; 2008) broad semantic inferentialism, we show that a theory of meaning can be at the same time a variety of active externalism. While we grant that supporters of other varieties of content externalism (e.g., Putnam 1975 and Burge 1986) can deny active externalism, this is not an option for semantic inferentialists: On this latter view, the role of the environment (both in its social and natural form) is not ‘passive’ in the sense assumed by the alternative approaches to content externalism. (shrink)

Despite its intrinsic plausibility, the sensitivity principle has remained deeply unpopular on the grounds that it violates an even more plausible closure principle. Here we show that sensitivity does not, in general, violate closure. Sensitivity only violates closure when combined with further auxiliary premises—regarding which of an agent’s commitments constitute that agent’s beliefs—which are optional for the sensitivity theorist.

Despite its intrinsic plausibility, the sensitivity principle has remained deeply unpopular on the grounds that it violates an even more plausible closure principle. Here we show that sensitivity does not, in general, violate closure. Sensitivity only violates closure when combined with further auxiliary premises—regarding which of an agent’s commitments constitute that agent’s beliefs—which are optional for the sensitivity theorist.

Logic is the study of the validity of arguments, which is to say the study of when a conclusion follows or does not follow from a set of premises. Logic is an ancient discipline pioneered by Aristotle and developed by some of the greatest thinkers in the Middle Ages. However, in the nineteenth century logic underwent a remarkable transformation into a precise branch of mathematics that changed the nature of logic, and the study of religion, forever. Both religious adherents and (...) critics of religion have sometimes claimed that logic and religion do not mix, but this is a puzzling claim since logic itself is not a set of substantive premises about the world which may come into conflict with religious claims, but a means of testing mathematically which premises come into conflict with which other premises. In fact, sense can be made of whether logic and religion mix, but the question, and the answer, turn out to be more complex than many have thought. (shrink)

The semantic inferentialist account of the social institution of semantic meaning can be naturally extended to account for social ontology. I argue here that semantic inferentialism provides a framework within which mathematical ontology can be understood as social ontology, and mathematical facts as socially instituted facts. I argue further that the semantic inferentialist framework provides resources to underpin at least some aspects of the objectivity of mathematics, even when the truth of mathematical claims is understood as socially instituted.

Mathematical Nominalism Mathematical nominalism can be described as the view that mathematical entities—entities such as numbers, sets, functions, and groups—do not exist. However, stating the view requires some care. Though the opposing view (that mathematical objects do exist) may seem like a somewhat exotic metaphysical claim, it is usually motivated by the thought that mathematical … Continue reading Mathematical Nominalism →.

Introduction: I lay out the broad contours of my thesis: a defence of mathematical nominalism, and nominalism more generally. I discuss the possibility of metaphysics, and the relationship of nominalism to naturalism and pragmatism. Chapter 2: I delineate an account of abstractness. I then provide counter-arguments to claims that mathematical objects make a di erence to the concrete world, and claim that mathematical objects are abstract in the sense delineated. Chapter 3: I argue that the epistemological problem with abstract objects (...) is not best understood as an incompatibility with a causal theory of knowledge, or as an inability to explain the reliability of our mathematical beliefs, but resides in the epistemic luck that would infect any belief about abstract objects. To this end, I develop an account of epistemic luck that can account for cases of belief in necessary truths and apply it to the mathematical case. Chapter 4: I consider objections, based on metaphysical considerations and linguistic data, to the view that the existential quantifier expresses existence. I argue that these considerations can be accommodated by an existentially committing quantifier when the pragmatics of quantified sentences are properly understood. I develop a semi-formal framework within which we can define a notion of nominalistic adequacy. I show how our notion of nominalistic adequacy can show why it is legitimate for the nominalist to make use of platonistic “assumptions” in inference-making. Chapter 5: I turn to the application of mathematics in science, including explanatory applications, and its relation to a number of indispensability arguments. I consider also issues of realism and anti-realism, and their relation to these arguments. I argue that abstraction away from pragmatic considerations has acted to skew the debate, and has obscured possibilities for a nominalistic understanding of mathematical practices. I end by explaining the notion of a pragmatic meta-vocabulary, and argue that this notion can be used to carve out a new way of locating our ontological commitments. Chapter 6: I show how the apparatus developed in earlier chapters can be utilised to roll out the nominalist project to other domains of discourse. In particular, I consider propositions and types. I claim that a unified account of nominalism across these domains is available. Conclusion: I recapitulate the claims of my thesis. I suggest that the goal of mathematical enquiry is not descriptive knowledge, but understanding. (shrink)