Inference

Inferential Internalists accept the Principle of Inferential Justification (PIJ), according to which one has justification for believing P on the basis of E only if one has justification for believing that E makes probable P. Richard Fumerton has defended PIJ by appeal to examples, and recently Adam Leite has argued that this principle is supported by considerations regarding the nature of responsible belief. In this paper, I defend a form of externalism against both arguments. This form of externalism recognizes what (...) I call the phenomenon of reflective defeat: if one is justified in not believing that E makes probable P, then this defeats whatever justification one has for believing P upon the basis of E. I argue that this modified version of externalism has the virtue of accommodating the intuitions that motivate internalism, without the cost of the vicious regress that makes internalism so unattractive. (shrink)

In this essay we argue that reasoning can sometimes generate epistemic justification, rather than merely transmitting justification that the subject already possesses to new beliefs. We also suggest a way to account for it in terms of the relationship between epistemic normative requirements, justification and cognitive capacities.

Knowledge can be transmitted by a valid deductive inference. If I know that p, and I know that if p then q, then I can infer that q, and I can thereby come to know that q. What feature of a valid deductive inference enables it to transmit knowledge? In some cases, it is a proof of validity that grounds the transmission of knowledge. If the subject can prove that her inference follows a valid rule, then her inference transmits knowledge. (...) However, this only pushes the question back to the inference that was made in this proof. What feature of that inference enables it to transmit knowledge? A vicious regress looms here. Every proof requires a valid inference, and every valid inference must follow at least one rule of inference. So every proof must follow at least one rule of inference. Therefore not every valid inference that transmits knowledge can acquire this power through a proof, on pain of vicious infinite regress. So it must be possible to transmit knowledge by making an inference that follows an underived rule. A deductive inference that follows an underived rule is what I will call a basic deductive inference. It must be possible to transmit knowledge by making a basic deductive inference. But how is this possible? What feature of a basic deductive inference gives it this power to transmit knowledge? (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)

Here we challenge the orthodoxy according to which abduction is an a posteriori mode of inference. We start by providing a case study illustrating how abduction can justify a philosophical claim not justifiable by empirical evidence alone. While many grant abduction's epistemic value, nearly all assume that abductive justification is a posteriori, on grounds that our belief in abduction's epistemic value depends on empirical evidence about how the world contingently is. Contra this assumption, we argue, first, that our belief in (...) abduction’s epistemic value is not and could not be justified a posteriori, and second, that attention to the roles experience plays in abductive justification supports taking abduction to be an a priori mode of inference. We close by highlighting how our strategy for establishing the a priority of abduction positively contrasts with strategies in Bonjour (1998), Swinburne (2001), and Peacocke (2004) aiming to establish the a priority of certain ampliative modes of inference or abductive principles. (shrink)

The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ‘blind but blameless’ reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible.

Epistemic relativism has the contemporary academy in its grip. Not merely in the United States, but seemingly everywhere, most scholars working in the humanities and the social sciences seem to subscribe to some form of it. Even where the label is repudiated, the view is embraced. Sometimes the relativism in question concerns truth, sometimes justification. The core impulse appears to be a relativism about knowledge. The suspicion is widespread that what counts as knowledge in one cultural, or broadly ideological, setting (...) need not count as knowledge in another. (shrink)

The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to (...) enlarge his knowledge, and this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance. (shrink)

A surge of empirical research demonstrating flexible cognition in animals and young infants has raised interest in the possibility of rational decision-making in the absence of language. A venerable position, which I here call “Classical Inferentialism”, holds that nonlinguistic agents are incapable of rational inferences. Against this position, I defend a model of nonlinguistic inferences that shows how they could be practically rational. This model vindicates the Lockean idea that we can intuitively grasp rational connections between thoughts by developing the (...) Davidsonian idea that practical inferences are at bottom categorization judgments. From this perspective, we can see how similarity-based categorization processes widely studied in human and animal psychology might count as practically rational. The solution involves a novel hybrid of internalism and externalism: intuitive inferences are psychologically rational (in the explanatory sense) given the intensional sensitivity of the similarity assessment to the internal structure of the agent's reasons for acting, but epistemically rational (in the justificatory sense) given an ecological fit between the features matched by that assessment and the structure of the agent's environment. The essay concludes by exploring empirical results that show how nonlinguistic agents can be sensitive to these similarity assessments in a way that grants them control over their opaque judgments. (shrink)

This paper addresses the extent to which quotidian cognition is like scientific inference by focusing on Jerry Fodor's famous analogy. I specifically consider and rebut a recent attempt made by Tim Fuller and Richard Samuels to deny the usefulness of Fodor's analogy. In so doing, I reveal some subtleties of Fodor's arguments overlooked by Fuller and Samuels and others. Recognizing these subtleties provides a richer appreciation of the analogy, allowing us to gain better traction on the issue concerning the extent (...) to which everyday cognition is like scientific inference. In the end, I propose that quotidian cognition is indeed like scientific inference, but not precisely in the way Fodor claims it is. (shrink)

A survey of contemporary philosophical and scientific literatures reveals that different authors employ the term ‘heuristic’ in ways that deviate from, and are sometimes inconsistent with, one another. Given its widespread use in philosophy and cognitive science generally, it is striking that there appears to be little concern for a clear account of what phenomena heuristics pick out or refer to. In response, I consider several accounts of ‘heuristic’, and I draw a number of distinctions between different sorts of heuristics (...) in order to make sense of various research programmes. I then develop a working characterization of ‘heuristic’ which is shown to be coherent and robust enough to serve as a kind within philosophy and cognitive science broadly. My intent is not to pursue a unified account of ‘heuristic’, but to highlight some features of certain kinds of heuristics that are important for theorizing about cognition in order to proceed with a science of the mind/brain. 1 Why We Need an Appropriate Characterization of ‘Heuristic’2 Inadequate Definitions2.1 A positive attempt2.2 Heuristics versus guaranteed correct outcomes3 A Taxonomy of Heuristics3.1 Stimulus-driven versus heuristic3.2 Perceptual versus cognitive heuristics3.3 Computational versus cognitive heuristics3.4 Methodological versus inferential heuristics3.5 Summary of distinctions4 Characterizing Cognitive Heuristics4.1 Heuristics as rules of thumb4.2 Beyond rules of thumb: exploiting information5 Concluding Remarks. (shrink)

NOTE: this is a substantial revision of a previously uploaded draft. Intuitions are often thought of as inputs to theoretical reasoning. For example, you might form a belief by taking an intuition at face value, or you might take your intuitions as starting points in the method of reflective equilibrium. The aim of this paper is to argue that in addition to these roles intuitions also play action-guiding roles. The argument proceeds by reflection on the transmission of justification through inference. (...) According to inferential internalists, in order to gain justification for believing the conclusion of an argument by inferring it from the premises in that argument one must “see” that the premises support the conclusion. I motivate this view and endorse the idea that one’s “seeing” such a support relation consists of one’s having an intuition. In a number of recent papers, Paul Boghossian has pressed a regress argument against inferential internalism inspired by Lewis Carroll’s dialogue “What the Tortoise Said to Achilles.” I develop a response to Bogossian’s argument according to which intuitions work like mental imperatives and inferences are mental actions performed by obeying them. After developing this response to Boghossian’s argument, I take up the question of what it is in virtue of which intuitions play a guidance role, when they do so. (shrink)

Standard definitions of validity are designed to preserve truth from the premises to the conclusion. However, it seems possible to construct arguments that contain sentences in the imperative mood. Such sentences are incapable of being true or false, so the standard definitions cannot capture the validity of these imperative arguments. Bernard Williams offers an argument that imperative inference is impossible: two imperatives will always have different permissive presuppositions, so a speaker will have to change his mind before uttering a second (...) imperative, and so imperatives cannot ever be accumulated into a set of premises. I offer four objections to Williams’ argument: (1) Permissive presuppositions are analogous to conversational implicature, and so should be ignored when formulating imperative arguments. (2) There are other valid argument forms, which Williams does not consider, that do not suffer from different permissive presuppositions. (3) There are explanations for the change in permissive presuppositions in Williams’ example other than a change of mind, so the different permissive presuppositions do not have to prevent accumulation. Finally, (4) Williams accepts enough logical relations between imperatives (contradiction and a form of negation) for a definition of a valid imperative inference to follow naturally. (shrink)

The problem I address is: how are cogent inferences possible? In § 1 I distinguish three senses in which we say that one is “compelled” by an inference: automatic, seductive-rhetorical and epistemic compulsion. Cogency is epistemic compulsion: a cogent inference compels us to accept its conclusion, if we accept its premises and we aim at truth. In §§ 2–3 I argue that cogency is intelligible if we consider an inference as a compound linguistic act in which several component acts are (...) related to one another by a commitment that the premises support the conclusion. Non-automatic inferences are primarily public acts in an intersubjective context. But cogency arises in special contexts described in § 4, epistemic contexts, where the participants care for truth, i.e. are intellectually virtuous. An inference is cogent in an epistemic context if it stands up to all the objections raised in the context. In § 5 I consider three different kinds of cogent inferences. In § 6 I argue that in all three cases cogency is fallible and propose a fallibilist variety of inferentialism. In § 7 I distinguish context of utterance and contexts of evaluation. Cogency is relative to epistemic contexts of evaluation. However, validity, i.e. stable cogency, is transcontextual. (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.

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

I object to Markos Valaris’s thesis that reasoning requires a belief that your conclusion follows from your premisses. My counter-examples highlight the important but neglected role of suppositional reasoning in the basis of so much of what we know.

In this paper, I explore a question about deductive reasoning: why am I in a position to immediately infer some deductive consequences of what I know, but not others? I show why the question cannot be answered in the most natural ways of answering it, in particular in Descartes’s way of answering it. I then go on to introduce a new approach to answering the question, an approach inspired by Hume’s view of inductive reasoning.

Consider: -/- The Evidence Question: When, and under what conditions does an agent have proposition E as evidence (at t)? -/- Timothy Williamson's (2000) answer to this question is the well-known E = K thesis: -/- E = K: E is a member of S's evidence set at t iff S knows E at t. -/- I will argue that this answer is inconsistent with the version of Bayesianism that Williamson advocates. This is because E = K allows an agent (...) to garner evidence via inductive inference whereas standard Bayesian views disallow such a thing. Since Williamson's version of Bayesianism shares the key features with the standard Bayesian view, there is an inconsistency. (shrink)

In this paper, we develop an account of the justification thinkers have for employing certain basic belief-forming methods. The guiding idea is inspired by Reichenbach's work on induction. There are certain projects in which thinkers are rationally required to engage. Thinkers are epistemically justified in employing any belief-forming method such that "if it doesn't work, nothing will" for successfully engaging in such a project. We present a detailed account based on this intuitive thought and address objections to it. We conclude (...) by commenting on the implications that our account may have for other important epistemological issues and debates. (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)

We examine the role of working memory's central executive in the mental model explanation of propositional reasoning by using two working memory measures: the classical “reading span” test by Daneman and Carpenter (1980) and a new measure. This new “reasoning span” measure requires individuals to solve very simple anaphora problems, and store and remember the word solution in a growing series of inferential problems. We present one experiment in which we check the involvement of the central executive in conditional and (...) disjunctive inference tasks and compare predictions of the new reasoning span test with those of the classical reading span test. The results of the experiment confirm that reasoning responses, which according to mental model theory require high cognitive work, are predicted by working memory measures. Results also show that some reasoning responses are probably obtained by means of superficial biases or strategies that do not load working memory. The reasoning span test, which involves the central executive to a greater degree, predicts reasoning performance better than the reading span test. The significance and possibilities of the new measure in studying reasoning are discussed. (shrink)

I pursue an answer to the psychological question “what is it for S to presuppose that p?” I will not attempt a general answer. Rather, I will explore a particular kind of presuppositions that are constituted by the mental act of reasoning: Inferential presuppositions. Indeed, I will consider a specific kind of inferential presuppositions—one that is constituted by a specific reasoning competence: The univocality competence. Roughly, this is the competence that reliably governs the univocal thought-components’ operation as univocal in a (...) line of reasoning. I will argue that the exercise of this reasoning competence constitutes certain inferential presuppositions. More specifically, I outline a conception of an inferential presupposition as a non-attitudinal but genuinely psychological and rationally committing relation that holds between a reasoner and a proposition. Thus, inferential presuppositions may be distinguished from tacit or standing attitudes that function as premise-beliefs in reasoning. Likewise inferential presuppositions may be distinguished from other kinds of presuppositions. In conclusion, I note some features of inferential presuppositions that bear on the epistemology of inference. (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)

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)

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)

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)

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)

I Imperative Sentences It has often been taken for granted by logicians that there is a class of sentences which is the proper subject-matter of logic, ...

Change in View offers an entirely original approach to the philosophical study of reasoning by identifying principles of reasoning with principles for revising one's beliefs and intentions and not with principles of logic. This crucial observation leads to a number of important and interesting consequences that impinge on psychology and artificial intelligence as well as on various branches of philosophy, from epistemology to ethics and action theory. Gilbert Harman is Professor of Philosophy at Princeton University. A Bradford Book.

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.