There is a long tradition comparing moral knowledge to mathematical knowledge. In this paper, I discuss apparent similarities and differences between knowledge in the two areas, realistically conceived. I argue that many of these are only apparent, while others are less philosophically significant than might be thought. The picture that emerges is surprising. There are definitely differences between epistemological arguments in the two areas. However, these differences, if anything, increase the plausibility of moral realism as compared to mathematical realism. It (...) is hard to see how one might argue, on epistemological grounds, for moral antirealism while maintaining commitment to mathematical realism. But it may be possible to do the opposite. (shrink)

It is commonly suggested that evolutionary considerations generate an epistemological challenge for moral realism. At first approximation, the challenge for the moral realist is to explain our having many true moral beliefs, given that those beliefs are the products of evolutionary forces that would be indifferent to the moral truth. An important question surrounding this challenge is the extent to which it generalizes. In particular, it is of interest whether the Evolutionary Challenge for moral realism is equally a challenge for (...) mathematical realism. It is widely thought not to be. In this paper, I argue that the Evolutionary Challenge for moral realism is equally a challenge for mathematical realism. Along the way, I substantially clarify the Evolutionary Challenge, discuss its relation to more familiar epistemological challenges, and broach the problem of moral disagreement. The paper should be of interest to ethicists because it places pressure on anyone who rejects moral realism on the basis of the Evolutionary Challenge to reject mathematical realism as well. And the paper should be of interest to philosophers of mathematics because it presents a new epistemological challenge for mathematical realism that bears, I argue, no simple relation to Paul Benacerraf's familiar challenge. (shrink)

In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles.” What is the epistemological relevance of this contrast, if genuine? This chapter argues that ethicists and philosophers of mathematics have misunderstood it. They have confused what the chapter calls the justificatory challenge for realism about an area, D—the (...) challenge to justify our D-beliefs—with the reliability challenge for D-realism—the challenge to explain the reliability of our D-beliefs. Harman’s contrast is relevant to the first, but not, evidently, to the second. One upshot of the discussion is that genealogical debunking arguments are fallacious. Another is that indispensability considerations cannot answer the Benacerraf–Field challenge for mathematical realism. (shrink)

0.0. Theistic Ethics as a Challenge and a Diagnostic Tool. Naturalistic conceptions in metaethics come in many varieties. Many philosophers who have sought to situate moral reasoning in a naturalistic metaphysical conception have thought it necessary to adopt non-cognitivist, prescriptivist, projectivist, relativist, or otherwise deflationary conceptions. Recently there has been a revival of interest in non-deflationary moral realist approaches to ethical naturalism. Many non-deflationary approaches have exploited the resources of non-empiricist “causal” or “naturalistic” conceptions of reference and of kind definitions (...) in service of the “naturalistic” metaphilosophical conception that substantive moral questions, and questions about the metaphysics of morals, are broadly a posteriori questions, somewhat analogous to scientific questions, and are not amenable to a priori resolution by “conceptual analysis.”. (shrink)

3.0. Well-being as a Challenge to Naturalism. In Chapter Three Adams discusses and criticizes those accounts of a person’s well being which characterize it in terms of counterfactuals regarding her actual desires and preferences. These criticisms are important for the question of ethical naturalism because any plausible naturalist position will have to portray a person’s well-being as somehow or other supervening on features of her psychology and her environment. The sorts of analyses Adams criticizes are the most prominent analyses consistent (...) with this constraint, so it is important to see whether or not Adams’ criticisms of them undermine the prospects for ethical naturalism generally. (shrink)

0.0. Theistic Ethics as a Challenge and a Diagnostic Tool. Naturalistic conceptions in metaethics come in many varieties. Many philosophers who have sought to situate moral reasoning in a naturalistic metaphysical conception have thought it necessary to adopt non-cognitivist, prescriptivist, projectivist, relativist, or otherwise deflationary conceptions. Recently there has been a revival of interest in non-deflationary moral realist approaches to ethical naturalism. Many non-deflationary approaches have exploited the resources of non-empiricist “causal” or “naturalistic” conceptions of reference and of kind definitions (...) in service of the “naturalistic” metaphilosophical conception that substantive moral questions, and questions about the metaphysics of morals, are broadly a posteriori questions, somewhat analogous to scientific questions, and are not amenable to a priori resolution by “conceptual analysis.”. (shrink)

3.0. Well-being as a Challenge to Naturalism. In Chapter Three Adams discusses and criticizes those accounts of a person’s well being which characterize it in terms of counterfactuals regarding her actual desires and preferences. These criticisms are important for the question of ethical naturalism because any plausible naturalist position will have to portray a person’s well-being as somehow or other supervening on features of her psychology and her environment. The sorts of analyses Adams criticizes are the most prominent analyses consistent (...) with this constraint, so it is important to see whether or not Adams’ criticisms of them undermine the prospects for ethical naturalism generally. (shrink)

The topic of a priori knowledge is approached through the theory of evidence. A shortcoming in traditional formulations of moderate rationalism and moderate empiricism is that they fail to explain why rational intuition and phenomenal experience count as basic sources of evidence. This explanatory gap is filled by modal reliabilism -- the theory that there is a qualified modal tie between basic sources of evidence and the truth. This tie to the truth is then explained by the theory of concept (...) possession: this tie is a consequence of what, by definition, it is to possess (i.e., to understand) one’s concepts. A corollary of the overall account is that the a priori disciplines (logic, mathematics, philosophy) can be largely autonomous from the empirical sciences. (shrink)

Mark Balaguer has written a provocative and original book. The book is as ambitious as a work of philosophy of mathematics could be. It defends both of the dominant views concerning the ontology of mathematics, Platonism and Anti-Platonism, and then closes with an argument that there is no fact of the matter which is right.

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...) for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct. (shrink)

This book does three main things. First, it defends mathematical platonism against the main objections to that view (most notably, the epistemological objection and the multiple-reductions objection). Second, it defends anti-platonism (in particular, fictionalism) against the main objections to that view (most notably, the Quine-Putnam indispensability objection and the objection from objectivity). Third, it argues that there is no fact of the matter whether abstract mathematical objects exist and, hence, no fact of the matter whether platonism or anti-platonism is true.

A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical (...) objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist. (shrink)

Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...) potential future directions of research for each side in the debate over the existence of abstract mathematical objects. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...) both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (shrink)

This book defends a form of ethical intuitionism, according to which (i) there are objective moral truths; (ii) we know some of these truths through a kind of immediate, intellectual awareness, or "intuition"; and (iii) our knowledge of moral truths gives us reasons for action independent of our desires. The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.

This new edition of the classic Contemporary Theories of Knowledge has been significantly updated to include analyses of the recent literature in epistemology.

We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection. The central idea is that being able to correctly deductively reason conferred a (...) heritable survival advantage upon our ancestors. However, there are several arguments that purport to show that evolutionary accounts cannot even in principle explain how it is that we are reliable about logic. In this paper, I address these arguments. I show that there is no general reason to think that evolutionary accounts are incapable of explaining our reliability about logic. (shrink)

Contemporary realist theories of value claim to be compatible with natural science. In this paper, I call this claim into question by arguing that Darwinian considerations pose a dilemma for these theories. The main thrust of my argument is this. Evolutionary forces have played a tremendous role in shaping the content of human evaluative attitudes. The challenge for realist theories of value is to explain the relation between these evolutionary influences on our evaluative attitudes, on the one hand, and the (...) independent evaluative truths that realism posits, on the other. Realism, I argue, can give no satisfactory account of this relation. On the one hand, the realist may claim that there is no relation between evolutionary influences on our evaluative attitudes and independent evaluative truths. But this claim leads to the implausible skeptical result that most of our evaluative judgements are off track due to the distorting pressure of Darwinian forces. The realist’s other option is to claim that there is a relation between evolutionary influences and independent evaluative truths, namely that natural selection favored ancestors who were able to grasp those truths. But this account, I argue, is unacceptable on scientific grounds. Either way, then, realist theories of value prove unable to accommodate the fact that Darwinian forces have deeply influenced the content of human values. After responding to three objections, the third of which leads me to argue against a realist understanding of the disvalue of pain, I conclude by sketching how antirealism is able to sidestep the dilemma I have presented. Antirealist theories of value are able to offer an alternative account of the relation between evolutionary forces and evaluative facts —
an account that allows us to reconcile our understanding of evaluative truth with our understanding of the many non-rational causes that have played a role in shaping our evaluative judgements. (shrink)

This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), (...) the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy. (shrink)

Hilary Putnam deals in this book with some of the most fundamental persistent problems in philosophy: the nature of truth, knowledge and rationality. His aim is to break down the fixed categories of thought which have always appeared to define and constrain the permissible solutions to these problems.

Moderate rationalists maintain that our rational intuitions provide us with prima facie justification for believing various necessary propositions. Such a claim is often criticized on the grounds that our having reliable rational intuitions about domains in which the truths are necessary is inexplicable in some epistemically objectionable sense. In this paper, I defend moderate rationalism against such criticism. I argue that if the reliability of our rational intuitions is taken to be contingent, then there is no reason to think that (...) our reliability is inexplicable. I also suggest that our reliability is, in fact, necessary, and that such necessary reliability neither admits of, nor requires, any explanation of the envisaged sort. (shrink)

One of the key supposed 'platitudes' of contemporary epistemology is the claim that knowledge excludes luck. One can see the attraction of such a claim, in that knowledge is something that one can take credit for - it is an achievement of sorts - and yet luck undermines genuine achievement. The problem, however, is that luck seems to be an all-pervasive feature of our epistemic enterprises, which tempts us to think that either scepticism is true and that we don't know (...) very much, or else that luck is compatible with knowledge after all. In this book, Duncan Pritchard argues that we do not need to choose between these two austere alternatives, since a closer examination of what is involved in the notion of epistemic luck reveals varieties of luck that are compatible with knowledge possession and varieties that aren't. Moreover, Pritchard shows that a more nuanced understanding of the relationship between luck and knowledge can cast light on many of the most central topics in contemporary epistemology. These topics include: the externalism/internalism distinction; virtue epistemology; the problem of scepticism; metaepistemological scepticism; modal epistemology; and the problem of moral luck. All epistemologists will need to come to terms with Pritchard's original and incisive contribution. (shrink)

Being Known is a response to a philosophical challenge which arises for every area of thought: to reconcile a plausible account of what is involved in the truth of statements in a given area with a credible account of how we can know those statements. Christopher Peacocke presents a framework for addressing the challenge, a framework which links both the theory of knowledge and the theory of truth with the theory of concept-possession.

Develops an empirical argument against naive realism-disjunctivism: if naive realists accept "internal dependence", then they cannot explain the evolution of perceptual success. Also presents a puzzle about our knowledge of universals.