Inference

Leonard Savage famously contravened his own theory when first confronting the Allais Paradox, but then convinced himself that he had made an error. We examine the formal structure of Savage’s ‘error-correcting’ reasoning in the light of (i) behavioural economists’ claims to identify the latent preferences of individuals who violate conventional rationality requirements and (ii) John Broome’s critique of arguments which presuppose that rationality requirements can be achieved through reasoning. We argue that Savage’s reasoning is not vulnerable to Broome’s critique, but (...) does not provide support for the view that behavioural scientists can identify and counteract errors in people’s choices. (shrink)

Rationalization through reduction of cognitive dissonance does not have the function of representational exchange. Instead, cognitive dissonance is part of the “psychological immune system” and functions to protect the self-concept against evidence of incompetence, immorality, and instability. The irrational forms of attitude change that protect the self-concept in dissonance reduction are useful primarily for maintaining motivation.

This article investigates what constitutes good reason, in particular in scientific communication. I will start out with a general description of what scientists do and will identify the good argument as an integral part of all science. Employing some simple examples, I will then move on to derive some necessary conditions for the goodness of an argument. Along the way, I will introduce various basic concepts in logic and briefly talk about the nature of human knowledge. I will conclude by (...) relating my discussion of good reasoning in science to critical thinking in general and explain why I believe that critical thinking is at the heart of a well-functioning liberal democracy. (shrink)

Many contemporary epistemologists take rational inference to be a conscious action performed by the thinker (Boghossian 2014; 2018; Valaris 2014; Malmgren 2018). It is tempting to think that rational evaluability requires responsibility, which in turn requires conscious action. In that case, unconscious cognition involves merely associative or otherwise arational processing. This paper argues instead for deep rationalism: unconscious inference often exhibits the same rational status and richly structured logical character as conscious inference. The central case study is rationalization, in which (...) people shift their attitudes in logically structured, reason-responsive ways in response to evidence of their own incompetence or immorality. These attitude shifts are irrational in a way that reflects on the thinker. Thus rationally evaluable inference extends downward into the unconscious. Many take the sole aim of belief to be truth (Velleman 2000) or knowledge (Williamson 2000), but the prevalence of rationalization suggests that belief updating often aims instead at preserving our positive conceptions of ourselves—that is, belief updating is part of a psychological immune system (Gilbert 2006; Mandelbaum 2019). This paper argues that the psychological immune system comprises a suite of distinct cognitive mechanisms, some (ir)rational and some arational, which are united by a common function of avoiding the maladaptive predomination of negative affect and maintaining stable motivation. Other aspects of the psychological immune system include (i) a domain-general positive bias in evaluative attitudes and (ii) “terror management,” i.e., the systematic strengthening of meaning-conferring beliefs to avoid death anxiety. The multiplicity of processes underlying the psychological immune system point toward an irrational but adaptive function of cognition to keep us motivated in a world rife with negativity and death. (shrink)

This article provides a conceptual account of causal understanding by connecting current psychological research on time and causality with philosophical debates on the causal asymmetry. I argue that causal relations are viewed as asymmetric because they are understood in temporal terms. I investigate evidence from causal learning and reasoning in both children and adults: causal perception, the temporal priority principle, and the use of temporal cues for causal inference. While this account does not suffice for correct inferences of causal structure, (...) I show it to serve as a preliminary understanding of causal concepts as asymmetric, that later incorporates other types of evidence. This approach supplies causal models with an asymmetric concept of causation that underlies hypotheses about causal structure, as I will illustrate from the framework of the knowledge-based causal induction model. I further argue for an integrating perspective, showing how the understanding of causes as preceding their effects underlies both psychological models and philosophical debates over time and the causal asymmetry, particularly regarding problem cases such as simultaneous causation or backwards causation, and the conceptual connection between causation and action. (shrink)

My replies to Errol Lord, Adam Pautz, and Peter Railton's commentaries on The Rationality of Perception (2017).

Coordination in thought is the treatment of beliefs by the believer as being about the same thing. Such treatment can be indirect, via an identity belief, or direct. Direct coordination presents a problem concerning how this treatment is justified. Dickie (2015) accounts for the justification of coordination in terms of aptness to a motivational state: coordination serves to fulfil a need to represent things outside the mind. I argue that this account gets the problem coordination presents wrong, and so does (...) not present an adequate solution. While the material of that account may be reconfigured to provide a more promising proposal, I argue that this depends on a specious psychology of belief, and will anyway end up being circular. I propose an account that, while similar in some ways, improves on both the official and reconfigured Dickie-style accounts, and points to some broader conclusions about the nature of rational cognition. (shrink)

It is often supposed one can draw a distinction, among the assumptions on which an inference rests, between certain background assumptions and certain more salient, or foregrounded, assumptions. Yet what may such a fore-v-background structure, or such structures, consist it? In particular, how do they relate to consciousness? According to a ‘Boring View’, such structures can be captured by specifying, for the various assumptions of the inference, whether they are phenomenally conscious, or access conscious, or else how easily available they (...) are to such consciousness. According to an ‘Interesting View’, there are fore-v-background structures over and above such classifications. The chapter gestures at reasons for thinking that an Interesting View at least merits exploration. The paper discusses some recent contributions to such a view in analytical philosophy; some remarks in Husserl on what he dubbed the horizonal dimension of acts of consciousness; and psychological work on the role of gist or schema representations in perception and memory. It is proposed that background assumptions can figure in consciousness by being as it were condensed into a consciously, though inattentively, entertained notion of their overall thematic gist, where this thematic gist gives the drift of a possible elucidation of how or why such-and-such salient grounds mean that so-and-so conclusion holds. (shrink)

Inference to the Best Explanation is usually employed in the Scientific Realism debates. As far as particular scientific theories are concerned, its most ready usage seems to be that of a theory of confirmation. There are however more uses of IBE, namely as an epistemological theory of testimony and as a means of categorising and justifying the sources of evidence. In this paper, I will present, develop and exemplify IBE as a theory of the quality of evidence - taking examples (...) from medicine and showing that IBE can thereby provide the epistemological underpinning and justify the criteria of grading quality of mechanistic evidence that have been recently provided in the Clarke et al. paper on how evidence of medical mechanisms is to be construed alongside population studies. (shrink)

Some believe that all arguments make an implicit “inference claim” that the conclusion is inferable from the premises (e.g., Bermejo-Luque, Grennan, the Groarkes, Hitchcock, Scriven). I try to show that this is confused. An act of arguing arises because an inference can be attributed to us, not a meta-level “inference claim” that would make the argument self-referential and regressive. I develop six (other) possible explanations of the popularity of the doctrine that similarly identify confusions.

The set of entities that serves as the domain for our discourse about the mind is metaphysically heterogenous. It includes processes, events, properties, modes, and states. In the latter part of the twentieth century, philosophers started to suppose that a philosophical theory of the mind should be primarily concerned with the explanation of mental states. Those states could then be mentioned in the explanations that would need to be given for mental entities of other sorts. If, for example, we had (...) a prior explanation of belief states, those states could figure in our subsequent explanation of inferences: inferences, on this approach, are to be identified with certain processes of belief revision. This states-first approach was not favoured by earlier theorists of the mind, who tended to suppose that mental events and processes are explanatorily more basic than mental states. The current states-first approach faces insuperable difficulties, which the earlier approach avoids. (shrink)

Unconscious logical inference seems to rely on the syntactic structures of mental representations (Quilty-Dunn & Mandelbaum 2018). Other transitions, such as transitions using iconic representations and associative transitions, are harder to assimilate to syntax-based theories. Here we tackle these difficulties head on in the interest of a fuller taxonomy of mental transitions. Along the way we discuss how icons can be compositional without having constituent structure, and expand and defend the “symmetry condition” on Associationism (the idea that associative links and (...) transitions are perfectly symmetric). In the end, we show how a BIT (“bare inferential transition”) theory can cohabitate with these other non-inferential mental transitions. (shrink)

Tyler Burge first introduced his distinction between epistemic entitlement and epistemic justification in ‘Content Preservation’ in 1993. He has since deployed the distinction in over twenty papers, changing his formulation around 2009. His distinction and its basis, however, is not well understood in the literature. This chapter distinguishes two uses of ‘entitlement’ in Burge, and then focuses on his distinction between justification and entitlement, two forms of warrant, where warrants consists in the exercise of a reliable belief-forming competence. Since he (...) draws the distinction in terms of reasons, this chapter brings his account of reasons altogether in one place. The chapter introduces a decision-procedure for classifying warrants as justifications or entitlements. The distinction between justification and entitlement is not the same as the inferential vs. non-inferential distinction. The chapter distinguishes inference from processing, thinking, reasoning, and critically reasoning. Burge’s new formulation of the distinction was driven by the recognition of non-accessible modular reasons. Three kinds of access are distinguished. (shrink)

Under what conditions is a belief inferentially justified? A partial answer is found in Justification from Justification : a belief is inferentially justified only if all of the beliefs from which it is essentially inferred are justified. After reviewing some important features of JFJ, I offer a counterexample to it. Then I outline a positive suggestion for how to think about inferentially justified beliefs while still retaining a basing condition. I end by concluding that epistemologists need a model of inferentially (...) justified belief that is more permissive and more complex than JFJ. (shrink)

According to the perceptual view of language comprehension, listeners typically recover high-level linguistic properties such as utterance meaning without inferential work. The perceptual view is subject to the Objection from Context: since utterance meaning is massively context-sensitive, and context-sensitivity requires cognitive inference, the perceptual view is false. In recent work, Berit Brogaard provides a challenging reply to this objection. She argues that in language comprehension context-sensitivity is typically exercised not through inferences, but rather through top-down perceptual modulations or perceptual learning. (...) This paper provides a complete formulation of the Objection from Context and evaluates Brogaard's reply to it. Drawing on conceptual considerations and empirical examples, we argue that the exercise of context-sensitivity in language comprehension does, in fact, typically involve inference. (shrink)

ABSTRACTIn order to explain the effects found in the heuristics and biases literature, dual-process theories of reasoning claim that human reasoning is of two kinds: Type-1 processing is fast, automatic, and associative, while Type-2 reasoning is slow, controlled, and rule based. If human reasoning is so divided, it would have important consequences for morality, epistemology, and philosophy of mind. Although dual-process theorists have typically argued for their position by way of an inference to the best explanation, they have generally failed (...) to consider alternative hypotheses. Worse still, it is unclear how we might test dual-process theories. In this article, I offer a one-system theory, which I call the Sound-Board Account of Reasoning, according to which there is one reasoning system which is flexible, allowing the properties used to distinguished Type-1 and Type-2 reasoning to cross-cut one another. I empirically distinguish my theory from the two dominant versions of dual-process theory (parallel... (shrink)

In Lehrer’s case of the superstitious lawyer, a lawyer possesses conclusive evidence for his client’s innocence, and he appreciates that the evidence is conclusive, but the evidence is causally inert with respect to his belief in his client’s innocence. This case has divided epistemologists ever since Lehrer originally proposed it in his argument against causal analyses of knowledge. Some have taken the claim that the lawyer bases his belief on the evidence as a data point for our theories to accommodate, (...) while others have denied that the lawyer has knowledge, or that he bases his belief on the evidence. In this paper, we move the dialectic forward by way of arguing that the superstitious lawyer genuinely infers his client’s innocence from the evidence. To show that the lawyer’s inference is genuine, we argue in defense of a version of a doxastic construal of the ‘taking’ condition on inference. We also provide a pared-down superstitious lawyer-style case, which displays the key features of the original case without including its complicated and distracting features. But interestingly, although we argue that the lawyer’s belief is based on his good evidence, and is also plausibly doxastically justified, we do not argue that the lawyer knows that his client is innocent. (shrink)

This new volume addresses the central questions which surround the process of reasoning. This emerging topic of analytic philosophy intersects with numerous other areas of philosophy, such as epistemology, philosophy of mind, philosophy of language, and metaethics, and also psychological work on reasoning.

Many hold that theoretical reasoning aims at truth. In this paper, I ask what it is for reasoning to be thus aim-directed. Standard answers to this question explain reasoning’s aim-directedness in terms of intentions, dispositions, or rule-following. I argue that, while these views contain important insights, they are not satisfactory. As an alternative, I introduce and defend a novel account: reasoning aims at truth in virtue of being the exercise of a distinctive kind of cognitive power, one that, unlike ordinary (...) dispositions, is capable of fully explaining its own exercises. I argue that this account is able to avoid the difficulties plaguing standard accounts of the relevant sort of mental teleology. (shrink)

The paper considers contemporary models of presumption in terms of their ability to contribute to a working theory of presumption for argumentation. Beginning with the Whatelian model, we consider its contemporary developments and alternatives, as proposed by Sidgwick, Kauffeld, Cronkhite, Rescher, Walton, Freeman, Ullmann-Margalit, and Hansen. Based on these accounts, we present a picture of presumptions characterized by their nature, function, foundation and force. On our account, presumption is a modal status that is attached to a claim and has the (...) effect of shifting, in a dialogue, a burden of proof set at a local level. Presumptions can be analysed and evaluated inferentially as components of rule-based structures. Presumptions are defeasible, and the force of a presumption is a function of its normative foundation. This picture seeks to provide a framework to guide the development of specific theories of presumption. (shrink)

The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper 'Blind Reasoning'. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as 'Boche' are examined (...) and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

This is a response to Paul Boghossian’s paper: What is inference?. The paper and the abstract originate from a symposium at the Pacific Division Meeting of the APA in San Diego in April 2011. John Broome was a co-commentator.

Pronpongo una nueva manera de concebir la aceptación de proposiciones y su relación con la creencia y la inferencia. Argumento además que adoptar esta propuesta nos permite resolver de manera relativamente sencilla algunas paradojas aparentemente tan disímbolas cómo la del prefacio, la lotería y el sorites. Según esta propuesta, el error detrás de la paradoja sorítica es pensar que quién cree que hay una línea divisoria entre lo que cae dentro de la extensión de un término y lo que cae (...) fuera de él debe creer también de algún lugar que ahí se encuentra dicha línea divisoria. Espero convencerlos de que no es así, y que por lo tanto, nuestros juicios de sentido común no nos llevan a ninguna contradicción. (shrink)

Argument mapping is a way of diagramming the logical structure of an argument to explicitly and concisely represent reasoning. The use of argument mapping in critical thinking instruction has increased dramatically in recent decades. This paper overviews the innovation and provides a procedural approach for new teaches wanting to use argument mapping in the classroom. A brief history of argument mapping is provided at the end of this paper.

This paper argues that Moore's specifist defence of critical thinking as ‘diverse modes of thought in the disciplines’, which appeared in Higher Education Research & Development, 30(3), 2011, is flawed as it entrenches relativist attitudes toward the important skill of critical thinking. The paper outlines the critical thinking debate, distinguishes between ‘top-down’, ‘bottom-up’ and ‘relativist’ approaches and locates Moore's account therein. It uses examples from one discipline-specific area, namely, the discipline of Literature, to show that the generalist approach to critical (...) thinking does not ‘leave something out’ and outlines why teaching ‘generic’ critical thinking skills is central to tertiary education, teaching and learning, and employment opportunities for students. The paper also defends the assessment of critical thinking skills. (shrink)

This paper is in two parts. Part I outlines three traditional approaches to the teaching of critical thinking: the normative, cognitive psychology, and educational approaches. Each of these approaches is discussed in relation to the influences of various methods of critical thinking instruction. The paper contrasts these approaches with what I call the “visualisation” approach. This approach is explained with reference to computer-aided argument mapping (CAAM) which uses dedicated computer software to represent inferences between premise and conclusions. The paper presents (...) a detailed account of the CAAM methodology, and theoretical justification for its use, illustrating this with the argument mapping software Rationale™. A number of Rationale™ design conventions and logical principles are outlined including the principle of abstraction, the MECE principle, and the “Holding Hands” and “Rabbit Rule” heuristics. Part II of this paper outlines the growing empirical evidence for the effectiveness of CAAM as a method of teaching critical thinking. (shrink)

Part I of this paper outlined the three standard approaches to the teaching of critical thinking: the normative (or philosophical), cognitive psychology, and educational taxonomy approaches. The paper contrasted these with the visualisation approach; in particular, computer-aided argument mapping (CAAM), and presented a detailed account of the CAAM methodology and a theoretical justification for its use. This part develops further support for CAAM. A case is made that CAAM improves critical thinking because it minimises the cognitive burden of prose and (...) the demands that arguments in prose typically place on memory. CAAM also has greater usability, complements the imperfect human cognitive system, and adopts a logic of semi-formality which is both natural and intuitive. The paper claims that CAAM is an important advance given that traditional stand-alone critical thinking courses do not teach critical thinking as well as they as they are assumed to do. It is also important given that tertiary education fails to deliver improvements in critical thinking gains for too many students. The paper outlines results from a number of empirical studies that demonstrate that CAAM yields robust gains in critical thinking as measured by independent tests. Students themselves also believe CAAM to be beneficial as noted in coded responses to surveys. I conclude the paper by comparing the traditional approaches to the teaching of critical thinking to the visualisation approach. I argue that CAAM should taken seriously in the context of contemporary educational practices. (shrink)

In recent years, academics and educators have begun to use software mapping tools for a number of education-related purposes. Typically, the tools are used to help impart critical and analytical skills to students, to enable students to see relationships between concepts, and also as a method of assessment. The common feature of all these tools is the use of diagrammatic relationships of various kinds in preference to written or verbal descriptions. Pictures and structured diagrams are thought to be more comprehensible (...) than just words, and a clearer way to illustrate understanding of complex topics. Variants of these tools are available under different names: “concept mapping”, “mind mapping” and “argument mapping”. Sometimes these terms are used synonymously. However, as this paper will demonstrate, there are clear differences in each of these mapping tools. This paper offers an outline of the various types of tool available and their advantages and disadvantages. It argues that the choice of mapping tool largely depends on the purpose or aim for which the tool is used and that the tools may well be converging to offer educators as yet unrealised and potentially complementary functions. (shrink)

Computer-Assisted Argument Mapping (CAAM) is a new way of understanding arguments. While still embryonic in its development and application, CAAM is being used increasingly as a training and development tool in the professions and government. Inroads are also being made in its application within education. CAAM claims to be helpful in an educational context, as a tool for students in responding to assessment tasks. However, to date there is little evidence from students that this is the case. This paper outlines (...) the use of CAAM as an educational tool within an Economics and Commerce Faculty in a major Australian research university. Evaluation results are provided from students from a CAAM pilot within an upper-level Economics subject. Results indicate promising support for the use of CAAM and its potential for transferability within the disciplines. If shown to be valuable with further studies, CAAM could be included in capstone subjects, allowing computer technology to be utilised in the service of generic skill development. (shrink)

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will (...) run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

This volume reflects the development and theoretical foundation of a new paradigm for critical thinking based on inquiry. The field of critical thinking, as manifested in the Informal Logic movement, developed primarily as a response to the inadequacies of formalism to represent actual argumentative practice and to provide useful argumentative skills to students. Because of this, the primary focus of the field has been on informal arguments rather than formal reasoning. Yet the formalist history of the field is still evident (...) in its emphasis, with respect to both theory and pedagogy, on the structure and evaluation of individual, de-contextualized arguments. It is our view that such a view of critical thinking is excessively narrow and limited, failing to provide an understanding of argumentation as largely a matter of comparative evaluation of a variety of contending positions and arguments with the goal of reaching a reasoned judgment on an issue. As a consequence, traditional critical thinking instruction is problematic in failing to provide the reasoning skills that students need in order to accomplish this goal. Instead, the goal of critical thinking instruction has been seen largely as a defensive one: of learning to not fall prey to invalid, inadequate, or fallacious arguments. (shrink)

We are pleased to publish this WSIA edition of Trudy’s Govier’s seminal volume, Problems in Argument Analysis and Evaluation. Originally published in 1987 by Foris Publications, this was a pioneering work that played a major role in establishing argumentation theory as a discipline. Today, it is as relevant to the field as when it first appeared, with discussions of questions and issues that remain central to the study of argument. It has defined the main approaches to many of those issues (...) and guided the ways in which we might respond to them. From this foundation, it sets the stage for further investigations and emerging research. This is a second edition of the book that is corrected and updated by the author, with new prefaces to each chapter. (shrink)

Mathematical rigor is commonly formulated by mathematicians and philosophers using the notion of proof gap: a mathematical proof is rig­orous when there is no gaps in the mathematical reasoning of the proof. Any philosophical approach to mathematical rigor along this line requires then an account of what a proof gap is. However, the notion of proof gap makes sense only relatively to a given conception of valid mathematical reasoning, i.e., to a given conception of the validity of mathematical inference. A (...) proof gap can in particular be conceived as a failure in drawing a valid mathematical inference. The aim of this paper is to discuss two possible views of the validity of math­ematical inference with respect to their capacity to yield a plausible account of the intuitive notion(s) of proof gap present in mathematical practice. The first view is the one provided by the contemporary standards of mathematical rigor: a mathematical inference is valid if and only if its conclusion can be formally derived from its premises. We will argue that this conception does not lead to a plausible account of the intuitive notion(s) of proof gap. The second view is based on a new account of the validity of inference proposed by Prawitz: an inference is valid if and only if it consists in an operation that provides a ground for its conclusion given (previously obtained) grounds for its premises. We will first specify Prawitz's account to mathematical inference and we will then argue that the resulting ground-based account is able to capture various intuitive notions of proof gap as different types of failure in drawing valid mathematical inferences. We conclude that the ground-based account ap­pears of particular interest for the philosophy of mathematical practice, and we finally raise several challenges facing a full development of a ground-based account of the notions of mathematical rigor, proof gap and the validity of mathematical inference. (shrink)

The paper offers an account of inference. The account underwrites the idea that inference requires that the reasoner takes her premises to support her conclusion. I reject views according to which such ‘takings’ are intuitions or beliefs. I sketch an alternative view on which inferring consists in attaching what I call ‘inferential force’ to a structured collection of contents.

Poincaré and Prawitz have both developed an account of how one can acquire knowledge through reasoning by mathematical induction. Surprisingly, their two accounts are very close to each other: both consider that what underlies reasoning by mathematical induction is a certain chain of inferences by modus ponens ‘moving along’, so to speak, the well-ordered structure of the natural numbers. Yet, Poincaré’s central point is that such a chain of inferences is not sufficient to account for the knowledge acquisition of the (...) universal propositions that constitute the conclusions of inferences by mathematical induction, as this process would require to draw an infinite number of inferences. In this paper, we propose to examine Poincaré’s point—that we will call the closure issue—in the context of Prawitz’s framework where inferences are represented as operations on grounds. We shall see that the closure issue is a challenge that also faces Prawitz’s own account of mathematical induction and which points out to an epistemic gap that the chain of modus ponens cannot bridge. One way to address the challenge is to introduce suitable additional inferential operations that would allow to fill the gap. We will end the paper by sketching such a possible solution. (shrink)

We propose a dynamic-epistemic analysis of the different epistemic operations constitutive of the process of interrogative inquiry, as described by Hintikka’s Interrogative Model of Inquiry (IMI). We develop a dynamic logic of questions for representing interrogative steps, based on Hintikka’s treatment of questions in the IMI, along with a dynamic logic of inferences for representing deductive steps, based on the tableau method. We then merge these two systems into a dynamic logic of interrogative inquiry which articulates a joint treatment of (...) questions and inferences, providing thereby a unified framework representing the informational dynamics of interrogative inquiry. We provide sound and complete axiomatic systems for the three dynamic logics that we introduce, we compare our framework with existing approaches, and we finally propose several directions for further work. (shrink)

What is an inference? Logicians and philosophers have proposed various conceptions of inference. I shall first highlight seven features that contribute to distinguish these conceptions. I shall then compare three conceptions to see which of them best explains the special force that compels us to accept the conclusion of an inference, if we accept its premises.

The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a (...) necessary prerequisite to first possess a clear picture of what the deviation of mathematical proof from formal proof consists in. The present work aims to contribute building such a picture by investigating the relation between the elementary steps of deduction constituting the two types of proofs—mathematical inference and logical inference. Many claims have been made in the literature regarding the relation between mathematical inference and logical inference, most of them stating that the former is lacking properties that are constitutive of the latter. Such differentiating claims are, however, usually put forward without a clear conception of the properties occurring in them, and are generally considered to be immediately justified by our direct acquaintance, or phenomenological experience, with the two types of inferences. The present study purports to advance our understanding of the relation between mathematical inference and logical inference by developing a detailed philosophical analysis of the differentiating claims, that is, an analysis of the meaning of the differentiating claims—through the properties that occur in them—as well as the reasons that support them. To this end, we provide at the outset a representative list of the different properties of logical inference that have occurred in the differentiating claims, and we notice that they all boil down to the three properties of formality, generality, and mechanicality. For each one of these properties, our analysis proceeds in two steps: we first provide precise conceptual characterizations of the different ways logical inference has been said to be formal, general, and mechanical, in the philosophical and logical literature on formal proof; we then examine why mathematical inference does not appear to be formal, general, and mechanical, for the different variations of these notions identified. Our study results in a precise conceptual apparatus for expressing and discussing the properties differentiating mathematical inference from logical inference, and provides a first inventory of the various reasons supporting the observations of those differences. The differentiating claims constitute thus a set of data that any philosophical account of mathematical inference and proof purporting to be more faithful to mathematical practice ought to be able to accommodate and explain. (shrink)

This textbook is not a textbook in the traditional sense. Here, what we have attempted is compile a set of assignments and exercise that may be used in critical thinking courses. To that end, we have tried to make these assignments as diverse as possible while leaving flexibility in their application within the classroom. Of course these assignments and exercises could certainly be used in other classes as well. Our view is that critical thinking courses work best when they are (...) presented as skills based learning opportunities. We hope that these assignments speak to that desire and can foster the kinds of critical thinking skills that are both engaging and fun Please feel free to contact us with comments and suggestions. We will strive to correct errors when pointed out, add necessary material, and make other additional and needed changes as they arise. Please check back for the most up to date version. Rebeka Ferreira and Anthony Ferrucci. (shrink)

According to McHugh and Way reasoning is a person-level attitude revision that is regulated by its constitutive aim of getting fitting attitudes. They claim that this account offers an explanation of what is wrong with reasoning in ways one believes to be bad and that this explanation is an alternative to an explanation that appeals to the so-called Taking Condition. I argue that their explanation is unsatisfying.

A summary of The Rationality of Perception, and my replies to symposium papers on it by Andy Clark and Christopher Peacocke.

It is sometimes suggested that there are two kinds of reasoning: inferential reasoning and non-inferential reasoning. However, it is not entirely clear what the difference between these two kinds of reasoning is. In this paper, I try to answer the question what this difference is. I first discuss three answers to this question that I argue are unsatisfactory. I then give a different answer to this question, and I argue that this answer is satisfactory. I end by showing that this (...) answer can help to resolve some disagreements in which the difference between inferential and noninferential reasoning plays a role. (shrink)

Robert Talisse charges as doomed the Berlinian effort to infer liberal politics from value pluralism, based on the observation that it unavoidably vio- lates Hume’s law and that the two in fact clash in their basic logic. In arriving at this diagnosis, however, Talisse relies on several problematic assumptions about practical reasoning as well as about value pluralism and liberalism. As a result, he fails to appreciate the practical nature of practical reasoning and also fails to see the negative aspects (...) of value pluralism and of liberalism. Once these misconceptions get straightened out there is an increased opportunity for the Berlinian inference to succeed. (shrink)