Lockean Thesis Research Articles

The epistemic and the deontic preface paradox

Abstract This paper generalizes the preface paradox beyond the conjunctive aggregation of beliefs and constructs an analogous paradox for deontic reasoning. The analysis of the deontic case suggests a systematic restriction of intuitive rules for reasoning with obligations. This proposal can be transferred to the epistemic case: It avoids the preface and the lottery paradox and saves one of the two directions of the Lockean Thesis (i.e. high credence is sufficient, but not necessary for rational belief). The resulting account compares favorably to competing proposals; in particular, we can formulate the rules of correct doxastic reasoning without reference to probabilistic features of the involved propositions.

Four Approaches to Supposition

Suppositions can be introduced in either the indicative or subjunctive mood. There are also two types of judgments that may be initiated by suppositions of either sort: qualitative (binary) judgments and quantitative (numerical) ones. The former are judgments about whether a given proposition is acceptable and the latter are about how acceptable it is. We systematically explicate the relationships between canonical representatives of each of the four available types of theories. For the qualitative accounts, our representative theories of indicative and subjunctive supposition are based on the belief change operations given by AGM revision and KM update respectively; for the quantitative ones, we consider those given by conditionalization and imaging. This choice is motivated by the familiar approach of understanding supposition as ‘provisional belief revision’ wherein one temporarily treats the supposition as true and forms judgments by making appropriate changes to their other opinions. To compare the numerical judgments recommended by the quantitative theories with the binary ones recommended by the qualitative accounts, we appeal to a suitably adapted version of the Lockean thesis. Ultimately, we establish a number of new results that we interpret as vindicating the often-repeated claim that conditionalization is a probabilistic version of revision, while imaging is a probabilistic version of update.

Cut-off points for the rational believer

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle.Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”).As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises.In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions.One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox.

A Probabilistic Semantics for Belief Logic

Belief logic is one of the most important branches of philosophical logic. The standard approach for characterizing belief is based on the so-called possible worlds model within which the problem of logical omniscience is considered a significant defect. We present an alternative semantics for belief logic based on a probabilistic model, which formalizes the so-called Lockean thesis in philosophical literature. The Lockean thesis states that a person believes a proposition whenever they see that the probability of the proposition has reached or exceeded a prespecified threshold. We give a complete deductive system for probabilistic belief logic as well as detailed comparisons to existing frameworks of belief logic.

Lockean Beliefs, Dutch Books, and Scoring Systems

On the Lockean thesis one ought to believe a proposition if and only if one assigns it a credence at or above a threshold (Foley in Am Philos Q 29(2):111–124, 1992). The Lockean thesis, thus, provides a way of characterizing sets of all-or-nothing beliefs. Here we give two independent characterizations of the sets of beliefs satisfying the Lockean thesis. One is in terms of betting dispositions associated with full beliefs and one is in terms of an accuracy scoring system for full beliefs. These characterizations are parallel to, but not merely derivative from, the more familiar Dutch Book (de Finetti in Theory of probability, vol 1, Wiley, London, 1974) and accuracy (Joyce in Philos Sci 65(4):575–603, 1998) arguments for probabilism.

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.

What Does Decision Theory Have to Do with Wanting?

AbstractDecision theory and folk psychology purport to represent the same phenomena: our belief-like and desire- and preference-like states. They also purport to do the same work with these representations: explain and predict our actions. But they use different concepts. Can we account for the concepts of one with the other’s? If not, we’d have two competing representations and systems of prediction and explanation, a dubious dualism. Many might then reject one of the two pictures, yet neither can be jettisoned lightly. Folk psychology structures daily life, and decision theory pervades various scientific disciplines. I’m interested in accounting for two central folk psychological concepts—believing and wanting—with decision theory. Many have attempted this task for believing. (The Lockean Thesis says that such an account exists.) This paper concerns the parallel task for wanting. I give necessary and sufficient conditions, stated in terms of decision theory, for when you’re truly said to want. I propose an alternative to orthodox accounts that link wanting to preference (e.g. Stalnaker (1984), Lewis (1986)). My account explains the context-sensitivity of want ascriptions, makes sense of conflicting desires, and accommodates phenomena that motivate traditional theses on which ‘want’ has multiple senses (e.g. all-things-considered vs. pro tanto).

The Lockean Law of Restitution

This article argues—in contrast to the claims of right-libertarians—that the Lockean thesis of justice in property seems to entail much egalitarian property redistribution. It starts by outlining what the Lockean thesis of justice in property is. It then argues that a Lockean version of the law of restitution is a reasonable way to approach the problem of holdings which were not gained in line with Lockean justice. Furthermore, according to this law, property which has unknown rightful owners should ideally be redistributed in an egalitarian manner among everybody in the world. In addition, due to the history of Lockean injustice throughout the world (e.g., feudalism and colonialism), it appears that much property in the world should be redistributed in an egalitarian manner.

Probability, coherent belief and coherent belief changes

This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent’s credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing one’s belief state. This updating method fits the idea of the Lockean Thesis better than plain Bayesian conditionalisation, and it affords a flexible method for adding and withdrawing categorical beliefs. We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals, as well as the Levi and Harper identities. We take this to be a problem for the latter principles rather than for the idea of coherent belief change.

The joint aggregation of beliefs and degrees of belief

The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: (1) consistency and deductive closure for belief sets, (2) conformity to the axioms of probability for degrees of belief, and (3) the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints may be imposed on the aggregation of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief.

From probabilities to categorical beliefs: Going beyond toy models

According to the Lockean thesis (LT), a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to be non-skeptical. We compare these proposals with each other and with the LT, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is of how likely it is that one believes more than the things one is fully certain of.

Foley's Threshold View of Belief and The Safety Condition on Knowledge

AbstractThis paper introduces a new argument against Richard Foley's threshold view of belief. Foley's view is based on the Lockean Thesis (LT) and the Rational Threshold Thesis (RTT). The former thesis is the claim that it is epistemically rational to believe a proposition if and only if it is epistemically rational to have a degree of confidence in that proposition sufficient for belief. The latter thesis is the claim that it is epistemically rational to believe a proposition if and only if it is epistemically rational to have a degree of confidence in that proposition that meets or exceeds a specified threshold. The argument introduced here shows that the views derived from the joint endorsement of the LT and the RTT violate the safety condition on knowledge in way that threatens the LT and/or the RTT.

La «Biblia filosófica» y la Reforma: el caso de John Locke

La transición de la Escritura como una obra sobrenatural a un mero texto es algo que tiene que ver con el movimiento reformado, sin embargo, no se puede atribuir como tal a la Reforma, sino sobre todo a la corriente filosófica ilustrada, nutrida de las convicciones que movilizó la Reforma. El artículo analiza esta corriente en uno de sus predecesores: John Locke. Su obra contribuyó a generar la «Biblia académica», como contrapuesta a la «Biblia escriturística». En la obra de Locke se pone de manifiesto una dialéctica entre el carácter sobrenatural de la Escritura y la consideración de la razón como revelación natural, que la conduce a numerosas aporías. De ahí que la bibliografía haya considerado a John Locke alternativamente calvinista, latitudinario, arminiano, sociniano o unitariano. El artículo presenta estas aporías y procura una evaluación de su aportación a la cuestión de la interpretación bíblica, que es indisociable de su fe, de su epistemología y de su teoría del lenguaje.

Two Approaches to Belief Revision

In this paper, we compare and contrast two methods for the revision of qualitative (viz., “full”) beliefs. The first (“Bayesian”) method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second (“Logical”) method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable (and mysterious) finding is that the inverse of the golden ratio emerges as a non-arbitrary bound on the Bayesian method’s free-parameter—the Lockean threshold. This “golden threshold” surfaces in two of our results and turns out to be crucial for understanding the relation between the two methods.

Impossibility Results for Rational Belief

AbstractThere are two ways of representing rational belief: qualitatively as yes‐or‐no belief, and quantitatively as degrees of belief. Standard rationality conditions are: (i) consistency and logical closure, for qualitative belief, (ii) satisfaction of the probability axioms, for quantitative belief, and (iii) a relationship between qualitative and quantitative beliefs in accordance with the Lockean thesis. In this paper, it is shown that these conditions are inconsistent with each of three further rationality conditions: fallibilism, open‐mindedness, and invariance under independent conceptual expansions. Restrictions of the Lockean thesis that have been suggested in the literature cannot remove the inconsistency. In the outlook we discuss two alternative ways of dealing with this problem: restricting conjunctive closure or going for a dual system account.

I-The Humean Thesis on Belief

This paper suggests a bridge principle for (rational) all-or-nothing belief and degrees of belief to the effect that belief corresponds to stably high degree of belief. Different ways of making this Humean thesis on belief precise are discussed, and one of them is shown to stand out by unifying the others. The resulting version of the thesis proves to be fruitful in entailing the logical closure of belief, the Lockean thesis on belief, and coherence between decision-making based on all-or-nothing beliefs and on degrees of belief.

The Stability Theory of Belief

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, I will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as I am going to argue in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc but that has various philosophical features that are plausible independently.

What is the Permissibility Solution a Solution of? – A Question for Kroedel

Kroedel (2012; 2013a; 2013b) has proposed a new solution, the permissibility solution, to the lottery paradox. The lottery paradox results from the Lockean thesis according to which one ought to believe a proposition just in case one’s degree of belief in it is sufficiently high. The permissibility solution replaces the Lockean thesis by the permissibility thesis according to which one is permitted to believe a proposition if one’s degree of belief in it is sufficiently high. This note shows that the epistemology of belief that results from the permissibility thesis and the epistemology of degrees of belief is empty in the sense that one need not believe anything, even if one’s degrees of belief are maximally bold. Since this result can also be achieved by simply dropping the Lockean thesis, or by replacing it with principles that are logically stronger than the permissibility thesis, the question arises what the permissibility solution is a solution of.

The Decision-Theoretic Lockean Thesis

Certain philosophers maintain that there is a ‘constitutive threshold for belief’: to believe that p just is to have a degree of confidence that p above a certain threshold. On the basis of this view, these philosophers defend what is known as ‘the Lockean Thesis’, according to which it is rational to believe that p just in case it is rational to have a degree of confidence that p above the constitutive threshold for belief. While not directly speaking to the controversy over the Lockean Thesis, this paper defends the general idea behind it—namely, the thesis that there is some threshold such that it is rational to believe that p if and only if it is rational to have a degree of confidence greater than that threshold. This paper identifies the threshold in question—not with the alleged constitutive threshold for belief—but with what I call ‘the practical threshold for rational belief’. Roughly, the thesis defended here is that it is rational to believe that p if and only if it is rational to have a degree of confidence that p that rationalizes engaging in certain types of practical reasoning.

Ultralarge lotteries: Analyzing the Lottery Paradox using non-standard analysis

A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that is intrinsically vague. We propose application of the language of relative analysis—a type of non-standard analysis—to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’ and satisfies a moderately weakened form of the Conjunction Principle. We also propose an adaptation of the model that is able to deal with beliefs that are less firm than ‘almost certainty’. The adapted version is also of interest for the epistemicist account of vagueness.