Eliminations and Reductions I

This chapter examines and argues against attempts to eliminate the category of structural rationality or reduce it to substantive rationality. Together with the following chapter—which argues against eliminations and reductions of the converse kind—it thereby provides a positive case for dualism about rationality, according to which both kinds of rationality are genuine and neither is reducible to the other. On the way, it also argues that there are cases where being substantively rational does not suffice for being structurally rational, and examines the preface paradox and cases of misleading higher-order evidence.

Justification and the knowledge-connection

I will present a novel account of justification in terms of knowledge on which one is justified in believing p just in case one could know that p. My main aim is to unravel some of the formal properties that justification has in virtue of its connection to knowledge. Assuming that safety is at least a necessary condition for knowledge, I show that justification (1) doesn’t iterate trivially; (2) isn’t a luminous condition; (3) is closed under a certain kind of multi-premise closure principle, but; (4) surprisingly one can nevertheless believe with justification a set of claims that’s jointly inconsistent. This last feature allows for a rather satisfying solution to the preface paradox. Finally, I contrast my account with other knowledge-first accounts of justification.

How to Believe Long Conjunctions of Beliefs: Probability, Quasi-Dogmatism and Contextualism

According to the so-called Lockean thesis, a rational agent believes a proposition just in case its probability is sufficiently high, i.e., greater than some suitably fixed threshold. The Preface paradox is usually taken to show that the Lockean thesis is untenable, if one also assumes that rational agents should believe the conjunction of their own beliefs: high probability and rational belief are in a sense incompatible. In this paper, we show that this is not the case in general. More precisely, we consider two methods of computing how probable must each of a series of propositions be in order to rationally believe their conjunction under the Lockean thesis. The price one has to pay for the proposed solutions to the paradox is what we call “quasi-dogmatism”: the view that a rational agent should believe only those propositions which are “nearly certain” in a suitably defined sense.

Context-sensitivity and the Preface Paradox for credence

It’s intuitively plausible to suppose that there are many things that we can be rationally certain of, at least in many contexts. The present paper argues that, given this principle of Abundancy, there is a Preface Paradox for (rational) credence. Section 1 gives a statement of the paradox, discusses its relation to its familiar counterpart for (rational) belief, and points out the congeniality between Abundancy and broadly contextualist trends in epistemology. This leads to the question whether considerations of context-sensitivity might lend themselves to solving the Preface for credence. Sections 2 and 3 scrutinize two approaches in this spirit—one mimicking Hawthorne’s (2002) Semantic Contextualist approach to an epistemic version of the Preface, the other one analogous to Clarke’s (2015) Sensitivist approach to the doxastic version—arguing that neither approach succeeds as it stands.

Applications

To earn their keep, theories of justification must be shown to have fruitful applications and to provide the means to address well-known puzzles and paradoxes. It is argued that the present account of justification does very well on this score. Not only does it prove amenable to the idea that standards for knowledge and justification may shift, it allows for an explanation of why they shift in tandem. It lends itself to a justificationist conception of the rules that may guide the formation of beliefs, to the extent that these beliefs aspire to be knowledgeable. The present account moreover affords principled solutions to the preface paradox, the lottery paradox, the related but distinct lottery puzzle, and a more recent sceptical challenge targeting doxastic justification.

Knowledge is closed under analytic content

I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true and that q is an analytic part of p, then S knows that q. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox.

Prefaces, Sorites and Guides to Reasoning

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the sorites? This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of ‘verities’. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain.

Hysteresis Hypotheses

This chapter assimilates the Sorites Paradox and the Preface Paradox, drawing parallels between reasoning with uncertainty and reasoning with vague concepts (a theme that Dorothy Edgington has explored). It discusses experiments in which subjects are taken along soritical series of coloured patches, displaying so-called reverse hysteresis in their responses. The chapter offers an explanation of why reverse hysteresis is rational there. It presents a variant of the Preface Paradox—the Progressive Preface Paradox—that is analogous to the Sorites Paradox and its associated experiments, and it offers an analogous explanation of why reverse hysteresis is again rational. The explanation’s central idea is that ‘belief’ is context-dependent.

Attributing Knowledge

The word “know” is revealed as vague, applicable to fallible agents, factive, and criterion-transcendent. It is invariant in its meaning across contexts and invariant relative to different agents. Only purely epistemic properties affect its correct application—not the interests of agents or those who attribute the word to agents. These properties enable “know” to be applied correctly—as it routinely is—to cognitive agents ranging from sophisticated human knowers, who engage in substantial metacognition, to various animals, who know much less and do much less, if any, metacognition, to nonconscious mechanical devices such as drones, robots, and the like. These properties of the word “know” suffice to explain the usage phenomena that contextualists and subject-sensitive invariantists invoke to place pressure on an understanding of the word that treats its application as involving no interests of agents, or others. It is also shown that the factivity and the fallibilist-compatibility of the word “know” explain Moorean paradoxes, the preface paradox, and the lottery paradox. A fallibility-sensitive failure of knowledge closure is given along with a similar failure of rational-belief closure. The latter explains why rational agents can nevertheless believe A and B, where A and B contradict each other. A substantial discussion of various kinds of metacognition is given—as well as a discussion of the metacognition literature in cognitive ethology. An appendix offers a new resolution of the hangman paradox, one that turns neither on a failure of knowledge closure nor on a failure of KK.