Hartry Field; XV*—The A Prioricity of Logic, Proceedings of the Aristotelian Society, Volume 96, Issue 1, 1 June 1996, Pages 359–380, https://doi.org/10.1093/ar.

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)

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)

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.

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.

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)

Nozick analyzes fundamental issues, such as the identity of the self, knowledge and skepticism, free will, the foundations of ethics, and the meaning of life.

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.

In The Myth of Morality, Richard Joyce argues that moral discourse is hopelessly flawed. At the heart of ordinary moral judgements is a notion of moral inescapability, or practical authority, which, upon investigation, cannot be reasonably defended. Joyce argues that natural selection is to blame, in that it has provided us with a tendency to invest the world with values that it does not contain, and demands that it does not make. Should we therefore do away with morality, as we (...) did away with other faulty notions such as witches? Possibly not. We may be able to carry on with morality as a 'useful fiction' - allowing it to have a regulative influence on our lives and decisions, perhaps even playing a central role - while not committing ourselves to believing or asserting falsehoods, and thus not being subject to accusations of 'error'. (shrink)

In this important new book Nagel, one of the most distinguished philosophers writing in English today, presents a sustained defence of reason against the attacks of subjectivism. He offers systematic rebuttals of relativistic claims with respect to language, logic, science, and ethics.

All contentious moral issues--from gay marriage to abortion and affirmative action--raise difficult questions about the justification of moral beliefs. How can we be justified in holding on to our own moral beliefs while recognizing that other intelligent people feel quite differently and that many moral beliefs are distorted by self-interest and by corrupt cultures? Even when almost everyone agrees--e.g. that experimental surgery without consent is immoral--can we know that such beliefs are true? If so, how? These profound questions lead to (...) fundamental issues about the nature of morality, language, metaphysics, justification, and knowledge. They also have tremendous practical importance in handling controversial moral questions in health care ethics, politics, law, and education. Sinnott-Armstrong here provides an extensive overview of these difficult subjects, looking at a wide variety of questions, including: Are any moral beliefs true? Are any justified? What is justified belief? The second half of the book explores various moral theories that have grappled with these issues, such as naturalism, normativism, intuitionism, and coherentism, all of which are attempts to answer moral skepticism. Sinnott-Armstrong argues that all these approaches fail to rule out moral nihilism--the view that nothing is really morally wrong or right, bad or good. Then he develops his own novel theory,--"moderate Pyrrhonian moral skepticism"--which concludes that some moral beliefs can be justified out of a modest contrast class but no moral beliefs can be justified out of an extreme contrast class. While explaining this original position and criticizing alternatives, Sinnott-Armstrong provides a wide-ranging survey of the epistemology of moral beliefs. (shrink)

What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions.

An encyclopedia entry which covers various revisionary conceptions of which macroscopic objects there are, and the puzzles and arguments that motivate these conceptions: sorites arguments, the argument from vagueness, the puzzles of material constitution, arguments against indeterminate identity, arguments from arbitrariness, debunking arguments, the overdetermination argument, and the problem of the many.

In this essay, I draw on Haidt’s and Baron’s respective insights in the service of a bit of philosophical psychoanalysis. I will argue that deontological judgments tend to be driven by emotional responses, and that deontological philosophy, rather than being grounded in moral reasoning, is to a large extent3 an exercise in moral rationalization. This is in contrast to consequentialism, which, I will argue, arises from rather different psychological processes, ones that are more “cognitive,” and more likely to involve genuine (...) moral reasoning. These claims are strictly empirical, and I will defend them on the basis of the available evidence. Needless to say, my argument will be speculative and will not be conclusive. Beyond this, I will argue that if these empirical claims are true, they may have normative implications, casting doubt on deontology as a school of normative moral thought. (shrink)

Some things we can know just by thinking about them: for example, that identity is transitive, that Gettier’s Smith does not know that the man who will get the job has ten coins in his pockets, that the ratio between two and six holds also between one and three, that it is wrong to wantonly torture innocent sentient beings, and various other things that simply strikeus, intuitively, as true when we consider them. The question is how : how can we (...) know things just by thinking about them? (shrink)