The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference , i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is (...) in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be "undone" by new information. (shrink)

Most human actions are complex, but some of them are basic. Which are these? In this paper, I address this question by invoking slips, a common kind of mistake. The proposal is this: an action is basic if and only if it is not possible to slip in performing it. The argument discusses some well-established results from the psychology of language production in the context of a philosophical theory of action. In the end, the proposed criterion is applied to discuss (...) some well-known theories of basic actions. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

One of the main goals of epistemologists is to provide a substantive and explanatory account of the conditions under which a belief has some desirable epistemic status (typically, justification or knowledge). According to the reliabilist approach to epistemology, any adequate account will need to mention the reliability of the process responsible for the belief, or truth-conducive considerations more generally. Historically, one major motivation for reliabilism—and one source of its enduring interest—is its naturalistic potential. According to reliabilists, epistemic properties can be (...) explained in terms of reliability, which in turn can be understood without reference to any unreduced epistemic notions, such as evidence or knowledge. This article begins by surveying some of the main forms of reliabilism, concentrating on process reliabilism as a theory of justification. It proceeds to review some of the main objections to reliabilism, and some of the responses that have been offered on the reliabilist’s behalf. After canvassing some recent developments in reliabilist epistemology, the article concludes by considering various cousins and spin-offs of reliabilist epistemology, including virtue reliabilism and various evidentialist-reliabilist hybrids. (shrink)

Pollock is developing, and testing computationally a theory of rationality. I endorse his claim that the structure of argument is not always linear, his replacement of the deductive-inductive distinction with a deductive-defeasible distinction, and hi s distinction between rebutting defeaters, and undercutting defeaters. I question the absence of pragmatic constraints in his acceptance rule, an absence which fits ill with his criterion of interruptibility, that it is reasonable to act on the conclusions drawn at any point. I also wonder about (...) building a model of a rational agent in which there is no place for interpersonal argumentative discussion. (shrink)

Abstract. This paper is concerned with the mental processes involved in intentional communication. I describe an agent's cognitive architecture as the set of cognitive dynamics (i.e., sequences of mental states with contents) she may entertain. I then describe intentional communication as one such specific dynamics, arguing against the prevailing view that communication consists in playing a role in a socially shared script. The cognitive capabilities needed for such dynamics are midreading (i.e., the ability to reason upon another individual's mental states), (...) and communicative planning (i.e., the ability to dynamically represent and act in a communicative situation). (shrink)

I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief Closure. After (...) recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too. (shrink)

The paper attempts to rationalize cooperation in the one-shot prisoners' dilemma (PD). It starts by introducing (and preliminarily investigating) a new kind of equilibrium (differing from Aumann's correlated equilibria) according to which the players' actions may be correlated (sect. 2). In PD the Pareto-optimal among these equilibria is joint cooperation. Since these equilibria seem to contradict causal preconceptions, the paper continues with a standard analysis of the causal structure of decision situations (sect. 3). The analysis then raises to a reflexive (...) point of view according to which the agent integrates his own present and future decision situations into the causal picture of his situation (sect. 4). This reflexive structure is first applied to the toxin puzzle and then to Newcomb's problem, showing a way to rationalize drinking the toxin and taking only one box with-out assuming causal mystery (sect. 5). The latter result is finally extended to a rationalization of cooperation in PD (sect. 6). (shrink)

Bayesian Epistemology is a general framework for thinking about agents who have beliefs that come in degrees. Theories in this framework give accounts of rational belief and rational belief change, which share two key features: (i) rational belief states are represented with probability functions, and (ii) rational belief change results from the acquisition of evidence. This dissertation focuses specifically on the second feature. I pose the Evidence Question: What is it to have evidence? Before addressing this question we must have (...) an understanding of Bayesian Epistemology. The first chapter argues that we should understand Bayesian Epistemology as giving us theories that are evaluative and not action-guiding. I reach this verdict after considering the popular ‘ought’-implies-‘can’ objection to Bayesian Epistemology. The second chapter argues that it is important for theories in Bayesian Epistemology to answer the Evidence Question, and distinguishes between internalist and externalist answers. The third and fourth chapters present and defend a specific answer to the Evidence Question. The account is inspired by reliabilist accounts of justification, and attempts to understand what it is to have evidence by appealing solely to considerations of reliability. Chapter 3 explains how to understand reliability, and how the account fits with Bayesian Epistemology, in particular, the requirement that an agent’s evidence receive probability 1. Chapter 4 responds to objections, which maintain that the account gives the wrong verdict in a variety of situations including skeptical scenarios, lottery cases, scientific cases, and cases involving inference. After slight modifications, I argue that my account has the resources to answer the objections. The fifth chapter considers the possibility of losing evidence. I show how my account can model these cases. To do so, however, we require a modification to Conditionalization, the orthodox principle governing belief change. I present such a modification. The sixth and seventh chapters propose a new understanding of Dutch Book Arguments, historically important arguments for Bayesian principles. The proposal shows that the Dutch Book Arguments for implausible principles are defective, while the ones for plausible principles are not. The final chapter is a conclusion. (shrink)

One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often not considered explicitly, but rather taken to be a collection of all unclear or troubling cases. However, current philosophy makes a strong point for taking indecision itself to be a proper object of consideration. This paper aims at revealing parallels between (...) the findings concerning indecision in philosophy and the treatment of indecision in argumentation theory. By investigating what philosophical forms and norms of indecision are involved in argumentation theory, we can improve our understanding of the different uncertain evidential situations in argumentation theory. (shrink)

Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) and offers a list of unsolved problems that are in need of investigation. (shrink)

The Nature and Status of Critical Questions in Argumentation Schemes.

Revision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision operation should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those distinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in a (...) dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors. (shrink)

The notions of inference and default are used in pragmatics with different meanings, resulting in theoretical disputes that emphasize the differences between the various pragmatic approaches. This paper is aimed at showing how the terminological and theoretical differences concerning the two aforementioned terms result from taking into account inference and default from different points of view and levels of analysis. Such differences risk making a dialogue between the theories extremely difficult. However, at a functional level of analysis the different theories, (...) definitions, and approaches to interpretation can be compared and integrated. At this level, the standardization of pragmatic inferences can be regarded as the development of a specific type of presumptions, used to draw prima-facie interpretations. (shrink)

It's natural to think that the principles expressed by the statements "Promises ought to be kept" and "We ought to help those in need" are defeasible. But how are we to make sense of this defeasibility? On one proposal, moral principles have hedges or built-in unless clauses specifying the conditions under which the principle doesn't apply. On another, such principles are contributory and, thus, do not specify which actions ought to be carried out, but only what counts in favor or (...) against them. Drawing on a defeasible logic framework, this paper sets up three models: one model for each proposal, as well as a third model capturing a mixed view on principles that combines them. It then explores the structural connections between the three models and establishes some equivalence results, suggesting that the seemingly different views captured by the models are closer than standardly thought. (shrink)

Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...) problematic if the arguments involve conditionals. I present a measure of argument strength that allows for dealing explicitly with uncertain conditionals in the premise set. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

The most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem of logical omnipotence, which highlights (...) the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence. (shrink)

Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

This essay addresses the collapse/incoherence problem for normative frameworks that contain both fundamental values and rules for promoting those values. The problem is that in some cases, we would bring about more of the fundamental value by violating the framework’s rules than by following them. In such cases, if the framework requires us to follow the rules anyway, then it appears to be incoherent; but if it allows us to make exceptions to the rules, then the framework “collapses” into one (...) that doesn’t make use of rules in the first place. The chapter begins with an examination of happiness and truth as fundamental values in Mill’s work, which lead into parallel versions of the collapse/incoherence problem in ethics and epistemology. It then sets out the collapse problem for rule-consequentialist approaches in ethics, truth-directed accounts of justification in epistemology, and epistemological approaches to argument cogency. The chapter closes with discussion of two potential solutions to the problem. (shrink)

This paper is concerned with the deconstruction of defeasible argument schemes. It will be claimed that one of the central elements of all defeasible argument schemes is the rule of similarity which demands that one must ascribe similar propositions to essentially similar entities in order to be treated as reasonable. This rule is presented as interculturally valid and of such central importance that it could even been used as a defining quality of defeasible argumentation.

In this chapter, we begin by sketching in the broadest possible strokes the ideas behind two formal systems that have been introduced with to goal of explicating the ways in which reasons interact to support the actions and conclusions they do. The first of these is the theory of defeasible reasoning developed in the seminal work of Pollock; the second is a more recent theory due to Horty, which adapts and develops the default logic introduced by Reiter to provide an (...) account of reasons. However, the implementations are complex enough, in both cases, to prevent anything more than this sketch. And we would not want to give the impression that we think that work on the logic of reasons must follow the path mapped out in either of these theories—indeed, we feel that the field is wide open. In the remainder of the chapter, therefore, will concentrate on a number of issues bearing on the logic of reasons that are either not treated in the work of Pollock and Horty, or whose treatment there is, we feel, either inadequate or incomplete. These are: first, the question of whether it is necessary to understand logical interactions among reasons themselves, rather than simply between reasons and the actions or conclusions they support, and if so, what principles might govern these interactions; second, priority relations among reasons and the notion of reason accrual; and third, some problems posed by undercutting defeat. (shrink)

The notions of defeasibility and defeasible reasoning have generated a great deal of interest in various research communities. Here I want to focus on their use in logic and argumentation studies. I will approach these topics from the perspective of an informal logician who finds himself struggling with some issues that surround the idea of and the deployment of the concept of defeasibility. My intention is to make those struggles as clear as I can.

Este artículo presenta un análisis comparativo de los modelos de argumentación basados en las nociones de probabilidad subjetiva y de razonamiento plausible. Se hacen explícitos los “parecidos de familia” entre probabilidad y plausibilidad, y se examinan las diferencias en las prescripciones invocadas para la evaluación de tres tipos de falacias informales: apelación a la autoridad, a la popularidad y petición de principio. Se concluye que el razonamiento plausible, como Rescher y Walton lo describen, no proporciona una alternativa sólida a la (...) probabilidad como modelo normativo o descriptivo de la evaluación de argumentos. (shrink)

The Toulmin diagram layout is very familiar and widely used, particularly in the teaching of critical thinking skills. The conventional box-and-arrow diagram is equally familiar and widespread. Translation between the two throws up a number of interesting challenges. Some of these challenges represent slightly different ways of looking at old and deep theoretical questions. Others are diagrammatic versions of questions that have already been addressed in artificial intelligence models of argument. But there are further questions that are posed as a (...) specific result of examining the diagram inter-translation problem. These three classes of problems are discussed. To the first class are addressed solutions based on engineering pragmatism; to the second class are addressed solutions drawn from the appropriate literature; and to the third class, fuller exploration is offered justifying the approaches taken in developing solutions that offer both pragmatic utility and theoretical interest. Finally, these solutions are explored briefly in the context of the Araucaria system, showing the ways in which analysts can tackle arguments either using one diagrammatic style or another, or even a combination of the two. (shrink)

This paper pictures emotions as able to provide reasons for action in so far as the beliefs and desires which make up reasons for action are constitutive elements of emotions themselves. It claims that the states of the world which prompt emotional attitudes “justify” them in so far as they render the beliefs constitutive of those attitudes true. Finally, it addresses the question what can make the desires or valuings ingredient to emotions appropriate to their objects.

The concept of conductive argument weight was developed by Carl Wellman and later by Trudy Govier. This concept has received renewed attention recently from another informal logician, Robert C. Pinto. Argument weight has also been addressed in recent years by theorists in AI & Law. I argue from a non-technical perspective that some aspects of AI & Law’s approach to argument weight can be usefully applied to the issues addressed by Pinto. I also relate some of these issues to the (...) work of argument theorist Harald Wohlrapp. (shrink)

This paper uses the language of formal dialectics to explore how argumentation schemes and their critical questions can be characterized as an extension to traditional dialectical systems. The aim is to construct a dialectical system in which the set of locutions is extended to include scheme-based moves the set of structural rules describes the roles that critical questioning can play; and the set of commitment rules distinguishes between exceptions and assumptions.

This paper considers how the terms ‘objection,’ ‘rebuttal,’ ‘attack,’ ‘refutation,’ ‘rebutting defeater’ and ‘undercutting defeater’ are used in writings on argumentation and artificial intelligence. The central focus is on the term ‘rebuttal.’ A provisional classification system is proposed that provides a normative structure within which the terms can be clarified, distinguished from each other, and more precisely defined.

The paper compares the uses of “critical question” in recent publications on the topic, contrasting explicit definitions where they exist and reconstructing implicit definitions where possible, and suggests a taxonomy of different “critical questions” as they are used in argumentative evaluation and criticism. In distinguishing different meanings of “critical question” horizontally between authors and vertically within the analysis, it strives to make a contribution to the ongoing work on the systematization of argumentative criticism.