Michael Titelbaum

This essay asks a new question: When someone with a firm understanding of basic operations nevertheless remains ignorant of a complex logical or mathematical truth, precisely what kind of information are they missing? I introduce “catenary truths,” a significant component of this non-omniscient shortfall. Traditional epistemologies of the a priori don't extend to catenary knowledge, so I offer a novel proposal for how we acquire catenary information. The proposal answers Benacerraf-inspired worries about access to abstracta by showing how processes of reasoning instantiate catenary truths. The proposal also sheds new light on whether logic is ampliative, how a calculation is like an experiment, higher-order doubts about deductive reasoning, the inconceivability of logically impossible worlds, and commonalities between mathematical and moral intuition.

Can self-locating beliefs be relevant to non-self-locating claims? Traditional Bayesian modeling techniques have trouble answering this question because their updating rule fails when applied to situations involving contextsensitivity. This essay develops a fully general framework for modeling stories involving context-sensitive claims. The key innovations are a revised conditionalization rule and a principle relating models of the same story with different modeling languages. The essay then applies the modeling framework to the Sleeping Beauty Problem, showing that when Beauty awakens her degree of belief in heads should be one-third. This demonstrates that it can be rational for an agent who gains only self-locating beliefs between two times to alter her degree of belief in a non-self-locating claim

This essay asks a new question: When someone with a firm understanding of basic operations nevertheless remains ignorant of a complex logical or mathematical truth, precisely what kind of information are they missing? I introduce “catenary truths,” a significant component of this non‐omniscient shortfall. Traditional epistemologies of the a priori don't extend to catenary knowledge, so I offer a novel proposal for how we acquire catenary information. The proposal answers Benacerraf‐inspired worries about access to abstracta by showing how processes of reasoning instantiate catenary truths. The proposal also sheds new light on whether logic is ampliative, how a calculation is like an experiment, higher‐order doubts about deductive reasoning, the inconceivability of logically impossible worlds, and commonalities between mathematical and moral intuition.

Self-locating beliefs are beliefs about one’s position or situation in the world, as opposed to beliefs about how the world is in itself. Section 1 of this entry introduces self-locating beliefs. Section 2 presents several distinct arguments that self-locating beliefs constitute a theoretically distinctive category. These arguments are driven by central examples from the literature; we categorize the examples by the arguments to which they contribute. (Some examples serve multiple strands of argument at once.) Section 3 examines positive proposals for modeling self-locating belief, focusing on the two most prominent proposals, due to Lewis and Perry. Section 4 discusses another, quite distinct phenomenon that motivates some discussions of self-locating belief: immunity to error through misidentification. Section 5 takes up issues arising in the philosophy of language—in particular in theories of communication. Section 6 discusses issues arising in decision theory and formal epistemology. We close with a brief taxonomy of objections to the claim that self-locating beliefs constitute a distinctive category.

Metaethicists have recently devoted a great deal of attention to questions about when a fact counts as a reason for or against a particular conclusion, and how such reasons interact. Chapter 9 asks a broader question: When a set of facts counts in favor of some conclusion, is that always because at least one of those facts is a reason for that conclusion? Examples are offered in which a set supports a conclusion without any fact in that set’s being a reason for. The chapter then assesses the significance of such examples for philosophical methodology, the ‘reasons-first’ program, and metanormative realism.

This chapter discusses responses to the author’s “Rationality’s Fixed Point (or: In Defense of Right Reason).” Among other things, the chapter: explains how the author understands rationality; explains why akrasia is irrational; intuitively overviews the argument from the Akratic Principle to the Fixed Point Thesis; explains why you can’t avoid this argument by distinguishing the rational from the reasonable, ideal rationality from everyday rationality, or substantive from structural norms; responds to the suggestion that misleading higher-order evidence creates rational dilemmas; explains why the Fixed Point Thesis doesn’t assume objectivist or externalist notions of rationality; dismisses complaints about agents who aren’t able to “figure out” what’s rational; then responds to an objection that peer disagreement undermines doxastic justification. Finally, the chapter modifies the author’s steadfast position on peer disagreement to take into account cases in which peer disagreement rationally affects an agent’s first-order opinions without affecting higher-order ones.

Different people reason differently, which means that sometimes they reach different conclusions from the same evidence. We maintain that this is not only natural, but rational. This chapter explores the epistemology of that state of affairs. First it canvasses arguments for and against the claim that rational methods of reasoning must always reach the same conclusions from the same evidence. Then it considers whether the acknowledgment that people have divergent rational reasoning methods should undermine one’s confidence in one’s own reasoning. Finally it explores how agents who employ distinct yet equally rational methods of reasoning should respond to interactions with the products of each others’ reasoning. The chapter finds that the epistemology of multiple reasoning methods has been misunderstood by a number of authors writing on epistemic permissiveness and peer disagreement.

This article defends the Fixed Point Thesis: that it is always a rational mistake to have false beliefs about the requirements of rationality. The Fixed Point Thesis is inspired by logical omniscience requirements in formal epistemology. It argues to the Fixed Point Thesis from the Akratic Principle: that rationality forbids having an attitude while believing that attitude is rationally forbidden. It then draws out surprising consequences of the Fixed Point Thesis, for instance that certain kinds of a priori justification are indefeasible and that misleading all-things-considered evidence about rational requirements is impossible. Finally, the Fixed Point Thesis is applied to defend the Right Reasons position on peer disagreement, according to which an agent who has drawn the correct conclusion from her evidence should retain belief in that conclusion even in the face of disagreeing peers.

El libro se divide en seis secciones y un apéndice. La primera sección motiva la introducción de grados numéricos de convicción y explora algunas de sus posibles relaciones con otros estados psicológicos. La segunda sección explica restricciones racionales sugeridas para estos grados numéricos de convicción, a partir del cálculo de probabilidades. La tercera sección describe las principales aplicaciones de este formalismo (especialmente relevantes para la filosofía, pero también para otros ámbitos en las ciencias sociales y las humanidades). La cuarta sección describe los intentos más influyentes por justificar esta aproximación formal. La quinta sección resume los principales desafíos que enfrenta y algunas propuestas de solución. La sexta sección describe algunas aproximaciones formales alternativas. En el apéndice se describe un resultado original que contribuye a respaldar esta aproximación para modelar los grados de convicción. Este texto es una traducción del capítulo “Precise Credences”, de Michael G. Titelbaum, que se incluye en el Open Handbook of Formal Epistemology (páginas 1 a 55), editado por Richard Pettigrew y Jonathan Weisberg en 2019, bajo el sello de la PhilPapers Foundation. Fue publicado con una Licencia Internacional Creative Commons Attribution-NonCommercial-NoDerivatives 4.0. La presente traducción se publica con autorización del autor y de los editores.

Abstract. Richard Feldman’s Uniqueness Thesis holds that “a body of evidence justifies at most one proposition out of a competing set of proposi- tions”. The opposing position, permissivism, allows distinct rational agents to adopt differing attitudes towards a proposition given the same body of evidence. We assess various motivations that have been offered for Uniqueness, including: concerns about achieving consensus, a strong form of evidentialism, worries about epistemically arbitrary influences on belief, a focus on truth-conduciveness, and consequences for peer disagreement. We argue that each of these motivations either misunderstands the commitments of permissivism or is question-begging. Better understanding permissivism makes it a much more plausible position.

Different people reason differently, which means that sometimes they reach different conclusions from the same evidence. We maintain that this is not only natural, but rational. In this essay we explore the epistemology of that state of affairs. First we will canvass arguments for and against the claim that rational methods of reasoning must always reach the same conclusions from the same evidence. Then we will consider whether the acknowledgment that people have divergent rational reasoning methods should undermine one’s confidence in one’s own reasoning. Finally we will explore how agents who employ distinct yet equally rational methods of reasoning should respond to interactions with the products of each others’ reasoning. We find that the epistemology of multiple reasoning methods has been misunderstood by a number of authors writing on epistemic permissiveness and peer disagreement.

The Uniqueness Thesis holds, roughly speaking, that there is a unique rational response to any particular body of evidence. We first sketch some varieties of Uniqueness that appear in the literature. We then discuss some popular views that conflict with Uniqueness and others that require Uniqueness to be true. We then examine some arguments that have been presented in its favor and discuss why permissivists find them unconvincing. Last, we present some purported counterexamples that have been raised against Uniqueness and discuss some possible reasons why proponents of Uniqueness might find these similarly unconvincing

Metaethicists have recently devoted a great deal of attention to questions about when a fact counts as a reason for or against a particular conclusion, and how such reasons interact. Chapter 9 asks a broader question: When a set of facts counts in favor of some conclusion, is that always because at least one of those facts is a reason for that conclusion? Examples are offered in which a set supports a conclusion without any fact in that set’s being a reason for. The chapter then assesses the significance of such examples for philosophical methodology, the ‘reasons-first’ program, and metanormative realism.

This article defends the Fixed Point Thesis: that it is always a rational mistake to have false beliefs about the requirements of rationality. The Fixed Point Thesis is inspired by logical omniscience requirements in formal epistemology. It argues to the Fixed Point Thesis from the Akratic Principle: that rationality forbids having an attitude while believing that attitude is rationally forbidden. It then draws out surprising consequences of the Fixed Point Thesis, for instance that certain kinds of a priori justification are indefeasible and that misleading all-things-considered evidence about rational requirements is impossible. Finally, the Fixed Point Thesis is applied to defend the Right Reasons position on peer disagreement, according to which an agent who has drawn the correct conclusion from her evidence should retain belief in that conclusion even in the face of disagreeing peers.

Roger White argued for a principle of indifference. Hart and Titelbaum showed that White’s argument relied on an intuition about conditioning on biconditionals that, while widely shared, is incorrect. Hawthorne, Landes, Wallmann, and Williamson argue for a principle of indifference. Remarkably, their argument relies on the same faulty intuition. We explain their intuition, explain why it’s faulty, and show how it generates their principle of indifference. 1Introduction 2El Caminos and Indifference 2.1Overview 2.2Fins and antennas 2.3HLWW in the example 2.4The restrictiveness of Condition 2 2.5Summary 3The Specifics of HLWW s Argument 3.1Mapping their conditions to our equations 3.2HLWW’s responses to objections

The Sleeping Beauty Problem attracts so much attention because it connects to a wide variety of unresolved issues in formal epistemology, decision theory, and the philosophy of science. The problem raises unanswered questions concerning relative frequencies, objective chances, the relation between self-locating and non-self-locating information, the relation between self-location and updating, Dutch Books, accuracy arguments, memory loss, indifference principles, the existence of multiple universes, and many-worlds interpretations of quantum mechanics. After stating the problem, this article surveys its connections to all of these areas