The First Riddle of Induction

What, exactly, is puzzling about induction? While the so-called problem of induction is normally introduced through David Hume’s famous argument, this essay shows how Sextus Empiricus gets to the heart of the matter. When properly understood, Sextus’ argument shows how the very power of inductive reasoning—its ability to move from particulars to universals—is at the same time what makes it “totter.” The argument has only been analyzed in any detail by the formal learning theorist Kevin Kelly, who uses the formal tools of computability theory and topology to mount a principled response. It is shown that this response depends on questionable assumptions and thus that they have not resolved Sextus’ riddle of induction.

Pyrrhonian Skepticism and Humean Skepticism

Richard Popkin famously argued that David Hume “maintained the only consistent Pyrrhonian point of view”; yet Hume explicitly rejected Pyrrhonism, as he understood it, in favor of a mitigated “Academic” skepticism. The keys to understanding Hume’s relationship to Pyrrhonism lie partly in his own historical understanding of it, but even more in his own distinctive and non-Pyrrhonian theories of belief and evidence, theories that allow him to employ common sense and reflection to correct what he regards as “excessive” skeptical doubts. Central to those theories, in turn, are his conceptions of causal reasoning and of the causal relation itself. Ultimately, it is on the topic of the nature of causation that Hume comes closest to a Pyrrhonian outlook.

Hypothetical Syllogisms and Infinite Regress

In his commentary on Aristotle’s De interpretatione, Ammonius puts forward an argument for the priority of categorical over hypothetical syllogisms. The argument relies on two of the Five Modes of Agrippa, the modes from infinite regress and from hypothesis. Much of the argument, however, remains unclear and open to doubt. The present chapter sheds new light on the argument by considering it against the backdrop of two related arguments given by Pseudo-Ammonius and Alexander of Aphrodisias in their commentaries on the Prior Analytics. The chapter argues that all three arguments originate in Theophrastus’ discussion of Aristotle’s treatment of syllogisms from a hypothesis. They rely on the view that stating a hypothetical proposition If P, then Q does not amount to the unqualified assertion of a conditional proposition, but rather to a conditional assertion of Q on the supposition that P.

Perceptual Variation and Relativism

There is variation in how people perceive colors and other secondary qualities. The challenge of perceptual variation is to say whose perceptions are accurate. According to Sextus, Protagoras’ response is that all of our perceptions might be accurate. As this response is traditionally developed, it is difficult to explain color illusion and color constancy. This difficulty is due to a widespread assumption called perceptual atomism. This chapter argues that, if we want to develop Protagoras’ response, we need to give up perceptual atomism. It ends with a brief sketch of an alternative called perceptual structuralism.

Value Disagreement, Action, and Commitment

The problem of disagreement is a well-known tool in the arsenal of various anti-realist and skeptical views. Persistent disagreement is supposed to be evidence that our moral judgments do not track a realm of objective values. This chapter is concerned with a different form of skepticism that one might try to ground on the fact of value disagreement: namely, “commitment skepticism.” According to the commitment skeptic, the fact of value disagreement should, at least under certain circumstances, lower our confidence in our evaluative judgments. But such lowering of confidence, if taken seriously, leaves us with no way to move from our judgments to actions. According to this skeptic, we have justification neither for our usual moral commitments, nor for any particular course of action based on these evaluative judgments. This chapter argues that Kant’s view about our awareness of the moral law provides an important way of resisting commitment skepticism.

Echoes of Sextus Empiricus in Nietzsche?

The essay considers two related questions: (a) whether Sextus was a philosophical influence on Nietzsche, and (b) whether there are significant connections between their philosophies. On the first question, it is notable that while Nietzsche cites Sextus Empiricus numerous times in his early scholarly works, it is always for purely antiquarian reasons; he never shows interest in Sextus as a philosopher in his own right. On the second question, a considerable philosophical overlap is identified, especially concerning the perspectival character of all human thinking, and the possibility of forms of knowledge and inquiry that do not aspire to any absolute status. One significant difference, however, concerns Nietzsche’s moral anti-realism. This appears to be inconsistent with the general emphasis on perspective that he shares with Sextus—although paradoxically, it also puts him in contact with another part of Sextus’ writing, Against the Ethicists, that is itself inconsistent with Sextus’ outlook elsewhere.

Incomplete Ignorance

One can neither inquire into what one knows nor into what one doesn’t know. The first leg of this problem has recently been called the Dogmatism Puzzle. If knowledge is incompatible with inquiry, the thought goes, knowledge breeds dogmatism. Call the second leg of the problem the Ignorance Puzzle. Inquiry starts from not knowing what one seeks to know, and yet it cannot simply start from ignorance. A compelling solution, we argue, jointly addresses the Dogmatism and Ignorance Puzzles. Inquirers, we propose, are in Incomplete Ignorance. They have proleptic concepts, which enable them to ask questions. We defend a minimalist account of the complement of questions. Questions, this chapter argues, call for an improvement of the inquirer’s cognitive state regarding the issue. Such improvement may psychologically close off further inquiry. But the inquirer’s cognitive state is not thereby epistemically closed. In principle, it permits further inquiry.

“The Skeptical Physitian”

This chapter makes the case that John Locke was influenced by the Pyrrhonian medical tradition, both in his own methods and commitments as a physician, and in the philosophical strategies he employed. Following Sextus Empiricus and other Pyrrhonian physicians, Locke rejects metaphysical accounts of the causal processes underlying diseases and their cures in favor of practical guidelines based on observation and experience. This approach leads Locke to explain madness as an intellectual disorder based on phenomenology and self-report, instead of in terms of the neurological processes posited by his contemporaries. Locke ultimately mobilizes this original account of madness as part of his skeptical attack on innatism, in which, analogous to his employment of Pyrrhonian strategies from cultural diversity, he argues that the commitments of dogmatists might just as well be mad as inborn. The possibility of mad ideas aping certain ones, he suggests, should give the nativist pause.

Wittgensteinian Epistemology, Epistemic Vertigo, and Pyrrhonian Skepticism

In On Certainty, Wittgenstein offers a radical conception of the structure of rational evaluation, such that all rational evaluations are essentially local in that they necessarily occur relative to arational hinge certainties. Support is canvassed for the following claims: (1) that a Wittgensteinian epistemology, while the antidote to a certain formulation of Cartesian skepticism, is entirely compatible, including in spirit, with Pyrrhonian skepticism; (2) that the philosophical quietism which provides the wider context for Wittgenstein’s epistemology is very much in keeping with the core nature of Pyrrhonian skeptical techniques; and (3) that a Wittgensteinian epistemology sits very well alongside a particular way of thinking about Pyrrhonian skepticism such that it is primarily directed at our specifically theoretical commitments. As we will see, a key element to understanding how the Wittgensteinian line against Cartesian skepticism can be allied to a Pyrrhonian skepticism is the notion of epistemic vertigo.

Variation and Change in Appearances

Consider sentence (1): The boat looks immense, yet it also looks small. Predications of “is immense” and “is small” applied to the same object appear to be contradictory, but (1) need not be contradictory. When do appearances conflict with each other, and how can this be marked in our judgments about appearance? In 1953, G. E. Moore argued that the possible truth of (1) shows that there must be multiple senses of “looks.” Moore’s example prefigures by thirty years a much-cited discussion by Christopher Peacocke about trees and apparent size with which Peacocke illustrates a contrast between sensational and representational properties of experience. This chapter argues that Moore’s argument for different senses of “looks” is unsound, and hence that we need a different explanation of how we mark the contrast between appearances which conflict and those which do not. The essay closes by offering such an account.