David Christensen - Putting Logic in Its Place: Formal Constraints on Rational Belief
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What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way -- either one believes a proposition, or one doesnt. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that ones beliefs be logically consistent, and that one believe the logical consequences of ones beliefs. A less popular picture sees belief as a graded phenomenon. This picture (explored more by decision-theorists and philosophers of science thatn by mainstream epistemologists) invites the use of probabilistic coherence to constrain rational belief. But this latter project has often involved defining graded beliefs in terms of preferences, which may seem to change the subject away from epistemic rationality.Putting Logic in its Place explores the relations between these two ways of seeing beliefs. It argues that the binary conception, although it fits nicely with much of our commonsense thought and talk about belief, cannot in the end support the traditional deductive constraints on rational belief. Binary beliefs that obeyed these constraints could not answer to anything like our intuitive notion of epistemic rationality, and would end up having to be divorced from central aspects of our cognitive, practical, and emotional lives.But this does not mean that logic plays no role in rationality. Probabilistic coherence should be viewed as using standard logic to constrain rational graded belief. This probabilistic constraint helps explain the appeal of the traditional deductive constraints, and even underlies the force of rationally persuasive deductive arguments. Graded belief cannot be defined in terms of preferences. But probabilistic coherence may be defended without positing definitional connections between beliefs and preferences. Like the traditional deductive constraints, coherence is a logical ideal that humans cannot fully attain. Nevertheless, it furnishes a compelling way of understanding a key dimension of epistemic rationality.
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Christensen, David , Department of Philosophy, University of Vermont
Putting Logic in its Place
Formal Constraints on Rational Belief
Publication date 2004 (this edition)
Print ISBN-10: 0-19-926325-6
Print ISBN-13: 978-0-19-926325-7
doi:10.1093/0199263256.001.0001
Print ISBN-10: 0-19-926325-6
Print ISBN-13: 978-0-19-926325-7
doi:10.1093/0199263256.001.0001
Abstract: Are rational beliefs constrained by formal logic? This book argues that if beliefs are seen in a binary way (either one believes a proposition or one doesn't), then the standard constraints of 'deductive cogency' (i.e. deductive consistency and deductive closure) are incompatible with epistemic rationality. If, however, beliefs are seen as graded, or coming in degrees, a probabilistic constraint (based on standard logic) is imposed by ideal rationality. This constraint, probabilistic coherence, explains both the appeal of the standard deductive constraints and the power of deductive arguments. Moreover, it can be defended without taking degrees of belief (as many decision-theoretic philosophers have) to be somehow defined or constituted by preferences. Although probabilistic coherence is humanly unattainable, this does not undermine its normative status as a constraint in a suitably idealized understanding of epistemic rationality.
Keywords: belief,deductive cogency,degrees of belief,epistemic,idealization,logic,preferences,probabilistic coherence,probability,rationality
Keywords: belief,deductive cogency,degrees of belief,epistemic,idealization,logic,preferences,probabilistic coherence,probability,rationality
PUTTING LOGIC IN ITS PLACE
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end p.ii
Putting Logic in its Place
Formal Constraints on Rational Belief
University of Vermont
Clarendon Press . Oxford
end p.iii
Great Clarendon Street, Oxford ox2 6 dp
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David Phiroze Christensen 2004
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end p.iv
For my parents,
Roshan Bharucha Christensen
and
James Roger Christensen
end p.v
end p.vi
PREFACE
W hen people talk informally about belief, "rational" and "logical" are often used almost synonymously. And even those who think carefully and precisely about rational belief often take logic to play an important role in determining which beliefs are rational. Explaining the importance of logic to students, philosophers often say things like, "Rational beliefs must be logically consistent with one another," or "If you believe the premises of a valid argument, then, if you are rational, you must believe the conclusion." This book aims to show that logic does indeed play an important role in characterizing ideally rational belief, but that its role is quite different from what it is often assumed to be.
The first chapter sets up parameters for the book's approach: it will focus on epistemic (rather than pragmatic) rationality; it will look at conditions on simultaneous rational beliefs (rather than on rational changes of belief); and it will concentrate on global rationality conditions for an agent's whole system of beliefs (rather than on local conditions for the rationality of particular beliefs). These choices are designed to focus the inquiry where formal logic is most likely to be useful in characterizing ideal rationality.
The second chapter ties the book's central question to a choice between two basic conceptions of belief. The standard binary model sees belief as an all-or-nothing state: either you believe P, or you don't. The graded model sees belief as coming in degrees. The two conceptions invite very different formal rationality conditions. Rational binary beliefs are often held to be subject to deductive cogency, which requires that an agent's beliefs form a logically consistent set which includes all the logical consequences of what the agent believes. Graded beliefs are often held to be subject to
end p.vii
probabilistic coherence: the requirement that they obey the axioms of probability theory. Chapter 2 argues that probability theory is best seen not as a new logic for graded belief, but as a way of applying standard deductive logic to graded belief. It explores different ways of understanding the relation between binary and graded belief, concluding that the way one sees this relation has important implications for the questions of whether and how beliefs are subject to formal rationality constraints.
The third and fourth chapters argue that ideally rational binary belief is not subject to deductive cogency. Chapter 3 begins with the "Preface Paradox," which poses a well-known challenge to deductive cogency requirements. The chapter examines and rejects attempts to avoid the problem by understanding cogency requirements in weakened ways. It then develops an extended version of a preface case which shows how the intuitively irrational beliefs required by deductive cogency will in certain cases cascade into massive irrationality. This highlights the problem's severity and illuminates what's absurd about the beliefs required by deductive cogency. The chapter then shows that situations with Preface Paradox structure occur commonly in ordinary life. Finally, it examines and rejects attempts to defend deductive constraints by explaining away our troublesome intuitions in preface cases and in related cases involving the "Lottery Paradox."
Chapter 4 takes on a deeper sort of response to preface and lottery cases. It has been argued that the fundamental purposes of binary belief require deductive cogency. The chapter examines and rejects several arguments of this sort, the strongest being that if deductive cogency were not rationally required, deductive arguments would have no rational force. The chapter develops and defends an alternative explanation of the epistemic importance of deductive arguments, rooted in a probabilistic coherence constraint on graded belief, and in the relation that rational binary belief would bear to rational graded belief on any plausible account. The chapter ends with a discussion of whether binary belief has any epistemic importance; it argues that although our binary way of
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