Metaphysical and absolute possibility

It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib without qualification.” And Stalnaker writes, “we can agree with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense.” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it

Justification and Explanation in Mathematics and Morality

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

Realism, Objectivity, and Evaluation

I discuss Benacerraf's epistemological challenge for realism about areas like mathematics, metalogic, and modality, and describe the pluralist response to it. I explain why normative pluralism is peculiarly unsatisfactory, and use this explanation to formulate a radicalization of Moore's Open Question Argument. According to the argument, the facts -- even the normative facts -- fail to settle the practical questions at the center of our normative lives. One lesson is that the concepts of realism and objectivity, which are widely identified, are actually in tension

Epistemic Non-Factualism and Methodology

I discuss methodology in epistemology. I argue that settling the facts, even the epistemic facts, fails to settle the questions of intellectual policy at the center of our epistemic lives. An upshot is that the standard methodology of analyzing concepts like knowledge, justification, rationality, and so on is misconceived. More generally, any epistemic method that seeks to issue in intellectual policy by settling the facts, whether by way of abductive theorizing or empirical investigation, no matter how reliable, is inapt. The argument is a radicalization of Moore’s Open Question Argument. I conclude by considering the ramifications of this conclusion for the debate surrounding “Modal Security”, a proposed necessary condition on undermining defeat

Objectivity and Evaluation

I this article, I introduce the notion of pluralism about an area, and use it to argue that the questions at the center of our normative lives are not settled by the facts -- even the normative facts. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the concept of objectivity, not realism, should take center stage

Objectivity in Ethics and Mathematics

How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry

The Primitive Thesis: Defending a Davidsonian Conception of Truth

In this dissertation I defend the claim, long held by Donald Davidson, that truth is a primitive concept that cannot be correctly or informatively defined in terms of more basic concepts. To this end I articulate the history of the primitive thesis in the 20th century, working through early Moore, Russell, and Frege, and provide improved interpretations of their reasons for advancing and (in the cases of Moore and Russell) eventually abandoning the primitive thesis. I show the importance of slingshot-style arguments in the work of Frege, Church, Davidson, and Gödel for resisting certain versions of the correspondence theory of truth. I argue that most slingshots fail to convincingly establish a collapsing conclusion, but that a Gödelian version of the slingshot is terminal to certain varieties of the correspondence theory of truth. I then provide a Davidsonian theory of truth and interpretation that is consistent with and makes use of the primitive thesis. Finally, I provide an account of predication, properties, and universals that I argue is both serviceable and consistent with Davidson’s overall program

What is Absolute Undecidability?†

It is often alleged that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical hypothesis is absolutely undecidable, then it is indeterminate. I shall argue that on no understanding of absolute undecidability could one hope to establish all of (a)–(c). However, I will identify one understanding of absolute undecidability on which one might hope to establish both (a) and (c) to the exclusion of (b). This suggests that a new style of mathematical antirealism deserves attention—one that does not depend on familiar epistemological or ontological concerns. The key idea behind this view is that typical mathematical hypotheses are indeterminate because they are relevantly similar to CH

Improving Trust in Deep Neural Networks with Nearest Neighbors

Deep neural networks are used increasingly for perception and decision-making in UAVs. For example, they can be used to recognize objects from images and decide what actions the vehicle should take. While deep neural networks can perform very well at complex tasks, their decisions may be unintuitive to a human operator. When a human disagrees with a neural network prediction, due to the black box nature of deep neural networks, it can be unclear whether the system knows something the human does not or whether the system is malfunctioning. This uncertainty is problematic when it comes to ensuring safety. As a result, it is important to develop technologies for explaining neural network decisions for trust and safety. This paper explores a modification to the deep neural network classification layer to produce both a predicted label and an explanation to support its prediction. Specifically, at test time, we replace the final output layer of the neural network classifier by a k-nearest neighbor classifier. The nearest neighbor classifier produces 1) a predicted label through voting and 2) the nearest neighbors involved in the prediction, which represent the most similar examples from the training dataset. Because prediction and explanation are derived from the same underlying process, this approach guarantees that the explanations are always relevant to the predictions. We demonstrate the approach on a convolutional neural network for a UAV image classification task. We perform experiments using a forest trail image dataset and show empirically that the hybrid classifier can produce intuitive explanations without loss of predictive performance compared to the original neural network. We also show how the approach can be used to help identify potential issues in the network and training process