Deductive Reasoning

In the 17th century, Hobbes stated that we reason by addition and subtraction. Historians of logic note that Hobbes thought of reasoning as “a ‘species of computation’” but point out that “his writing contains in fact no attempt to work out such a project.” Though Leibniz mentions the plus/minus character of the positive and negative copulas, neither he nor Hobbes say anything about a plus/minus character of other common logical words that drive our deductive judgments, words like ‘some’, ‘all’, ‘if’, (...) and ‘and’, each of which actually turns out to have an oppositive, character that allows us, “in our silent reasoning,” to ignore its literal meaning and to reckon with it as one reckons with a plus or a minus operator in elementary algebra or arithmetic. These ‘logical constants’ of natural language figure crucially in our everyday reasoning. Because Hobbes and Leibniz did not identify them as the plus and minus words we reason with, their insight into what goes on in ‘ratiocination’ did not provide a guide for a research program that could develop a +/- logic that actually describes how we reason deductively. I will argue that such a +/- logic provides a way back from modern predicate logic—the logic of quantifiers and bound variables that is now ‘standard logic’—to an Aristotelian term logic of natural language that had been the millennial standard logic. (shrink)

This essay advances and develops a dynamic conception of inference rules and uses it to reexamine a long-standing problem about logical inference raised by Lewis Carroll’s regress.

This paper tries to do three things. First, it tries to make it plausible that correct rules of reasoning do not always preserve justification: in other words, if you begin with a justified attitude, and reason correctly from that premise, it can nevertheless happen that you’ll nevertheless arrive at an unjustified attitude. Attempts to show that such cases in fact involve following an incorrect rule of reasoning cannot be vindicated. Second, it also argues that correct rules of reasoning do not (...) even correspond to permissions of “structural rationality”: it is not always structurally permissible to base an attitude on other attitudes from which it follows by correct reasoning. Third, from these observations it tries to build a somewhat positive account of the correctness of rules of reasoning as a more sui generis notion irreducible to either justification or structural rationality. This account vindicates an important unity of theoretical and practical reasoning as well as a qualified version of the thesis that deductive logic supplies correct rules of reasoning. (shrink)

Abstract Introduction Logically valid deductive arguments are clear examples of abstract recursive computational proce‐ dures on propositions or on probabilities. However, it is not known if the cortical time‐consuming inferential pro‐ cesses in which logical arguments are eventually realized in the brain are in fact physically different from other kinds of inferential processes. Methods In order to determine whether an electrical EEG discernible pattern of logical deduction exists or not, a new experimental paradigm is proposed contrasting logically valid and invalid (...) inferences with exactly the same content (same premises and same relational variables) and distinct logical complexity (propositional truth‐functional operators). Electroencephalographic signals from 19 subjects (24.2 ± 3.3 years) were acquired in a two‐condition para‐ digm (100 trials for each condition). After the initial general analysis, a trial‐by‐trial approach in beta‐2 band allowed to uncover not only evoked but also phase asynchronous activity between trials. Results showed that (i) deductive inferences with the same content evoked the same response pattern in logically valid and invalid conditions, (ii) mean response time in logically valid inferences is 61.54% higher, (iii) logically valid inferences are subjected to an early (400 ms) and a late reprocessing (600 ms) verified by two distinct beta‐2 activa‐ tions (p‐value < 0,01, Wilcoxon signed rank test). Conclusion We found evidence of a subtle but measurable electrical trait of logical validity. Results put forward the hypothesis that some logically valid deductions are recursive or computational cortical events. Keywords Beta‐2 band, Evoked potentials, Induced potentials, Deductive inference, Logical validity, Cortical bases of logical reasoning. (shrink)

Complex human reasoning involves minimal abilities to extract conclusions implied in the available information. These abilities are considered “deductive” because they exemplify certain abstract relations among propositions or probabilities called deductive arguments. However, the electrophysiological dynamics which supports such complex cognitive pro- cesses has not been addressed yet. In this work we consider typically deductive logico- probabilistically valid inferences and aim to verify or refute their electrophysiological functional connectivity differences from invalid inferences with the same content (same relational variables, same (...) stimuli, same relevant and salient features). We recorded the brain electrophysiological activity of 20 participants (age 1⁄4 20.35 ± 3.23) by means of an MEG system during two consecutive reasoning tasks: a search task (invalid condition) without any specific deductive rules to follow, and a logically valid deductive task (valid condition) with explicit deductive rules as instructions. We calculated the functional connectivity (FC) for each condition and conducted a seed-based analysis in a set of cortical regions of interest. Finally, we used a cluster-based permutation test to compare the dif- ferences between logically valid and invalid conditions in terms of FC. As a first novel result we found higher FC for valid condition in beta band between regions of interest and left prefrontal, temporal, parietal, and cingulate structures. FC analysis allows a second novel result which is the definition of a propositional network with operculo-cingular, parietal and medial nodes, specifically including disputed medial deductive “core” areas. The experiment discloses measurable cortical processes which do not depend on content but on truth-functional propositional operators. These experimental novelties may contribute to understand the cortical bases of deductive processes. (shrink)

Drawing on the epistemology of logic literature on anti-exceptionalism about logic, we set out to investigate the following metaphilosophical questions empirically: Is philosophy special? Are its methods (dis)continuous with science? More specifically, we test the following metaphilosophical hypotheses empirically: philosophical deductivism, philosophical inductivism, and philosophical abductivism. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we searched through a large corpus of philosophical texts mined from the JSTOR database (N = 435,703) to find patterns of (...) argumentation. The results of our quantitative, corpus-based study suggest that deductive arguments are significantly more common than abductive arguments and inductive arguments in philosophical texts overall, but they are gradually and steadily giving way to non-deductive (i.e. inductive and abductive) arguments in academic philosophy. (shrink)

An influential way of distinguishing inferential from non-inferential processes appeals to representational states: an agent infers a conclusion from some premises only if she represents those premises as supporting that conclusion. By contrast, when some premises merely cause an agent to believe the conclusion, there is no relevant representational state. While promising, the appeal to representational states invites a regress problem, first famously articulated by Lewis Carroll. This paper develops a novel account of inference that invokes representational states without succumbing (...) to regress. The key move is to reject the tempting idea that the relevant representational states are causally prior to inferences. I argue, instead, that an inference constitutes the relevant representational state. To infer is thus—in the very drawing of the conclusion—to represent the premises as supporting the conclusion, and thereby to commit to that support relation. (shrink)

Choices confront us with questions. How we act depends on our answers to those questions. So the way our beliefs guide our choices is not just a function of their informational content, but also depends systematically on the questions those beliefs address. This paper gives a precise account of the interplay between choices, questions and beliefs, and harnesses this account to obtain a principled approach to the problem of deduction. The result is a novel theory of belief-guided action that explains (...) and predicts the decisions of agents who, like ourselves, fail to be logically omniscient: that is, of agents whose beliefs may not be deductively closed, or even consistent. (Winner of the 2021 Isaac Levi Prize.). (shrink)

How is moral knowledge possible? This paper defends the anti-Humean thesis that we can acquire moral knowledge by deduction from wholly non-moral premises. According to Hume’s Law, as it has become known, we cannot deduce an ‘ought’ from an ‘is’, since it is “altogether inconceivable how this new relation can be a deduction from others, which are entirely different from it” (Hume, 1739, 3.1.1). This paper explores the prospects for a deductive theory of moral knowledge that rejects Hume’s Law.

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.

Just as Quine and others have argued for a deflationism about the property of truth, Sinan Dogramaci has argued for a deflationism about rationality. Specifically, Dogramaci claims that we have no reason to think that the basic, deductive, epistemic rules we call “rational” have any sort of “unifying property.” A “unifying property” is a property that is necessary, sufficient, and explanatorily illuminating. My goal in this paper is to undermine Dogramaci’s argument for this radical position. I do this by first (...) outlining Dogramaci’s distinctive view on the function of our epistemically evaluative terms. This view, called epistemic communism, has it that the function of terms like “rational” is to support the coordination of our community on a single set of epistemic rules. I offer a reconstruction of Dogramaci’s argument from epistemic communism to deflationism about rationality. I next raise an objection to Dogramaci’s argument: different sets of epistemic rules do not equally support the coordinative function. Dogramaci has a response to this objection, but I argue that this response is less than satisfactory. I illustrate that this response is unsatisfactory by employing work by David Enoch and Joshua Schechter. After pushing my objection to Dogramaci’s argument, I develop, on Dogramaci’s behalf, an objection to my non-deflationary attempt to undermine his argument. In the final section of the paper, I reply to this objection offered on Dogramaci’s behalf and conclude that whether we are epistemic communists or not, we need not accept deflationism. (shrink)

Universal Generalization, if it is not the most poorly understood inference rule in natural deduction, then it is the least well explained or justified. The inference rule is, prima facie, quite ambitious: on the basis of a fact established of one thing, I may infer that the fact holds of every thing in the class to which the one belongs—a class which may contain indefinitely many things. How can such an inference be made with any confidence as to its validity (...) or ability to preserve truth from premise to conclusion? My goal in this paper is to explain how Universal Generalization works in a way that makes sense of its ability to preserve truth. In doing so, I shall review common accounts of Universal Generalization and explain why they are inadequate or are explanatorily unsatisfying. Happily, my account makes no ontological or epistemological presumptions and therefore should be compatible with whichever ontological or epistemological schemes the reader prefers. (shrink)

In Tractatus 5.132 Wittgenstein argues that inferential justification depends solely on the understanding of the premises and conclusion, and is not mediated by any further act. On this basis he argues that Frege’s and Russell’s rules of inference are “senseless” and “superfluous”. This line of argument is puzzling, since it is unclear that there could be any viable account of inference according to which no such mediation takes place. I show that Wittgenstein’s rejection of rules of inference can be motivated (...) by taking account of his holistic construal of the relation between inference and understanding. (shrink)

There are three theories in the epistemology of modality that have received sustained attention over the past 20 years: conceivability-theory, counterfactual-theory, and deduction-theory. In this paper we argue that all three face what we call the problem of modal epistemic friction. One consequence of the problem is that for any of the three accounts to yield modal knowledge, the account must provide an epistemology of essence. We discuss an attempt to fend off the problem within the context of the internalism (...) versus externalism debate about epistemic justification. We then investigate the effects that the PMEF has on reductive and non-reductive theories of the relation between essence and modality. (shrink)

A number of philosophers have recently proposed several alleged cases of “knowledge from falsehood,” i.e., cases of inferential knowledge epistemised by an inference with a false crucial premise. This paper examines such cases and argues against interpreting them as cases of knowledge from falsehood. Specifically, I argue that the inferences in play in such cases are in no position to epistemise their conclusions.

Jeśli można mówić o modzie w badaniach naukowych, to semantyka jest od prawie wieku niewątpliwie jedną z bardziej modnych dziedzin w nauce. Badają ją nie tylko logicy i filozofowie języka, lecz także kulturoznawcy, antropologowie, filologowie, kognitywiści czy informatycy. Niniejszy artykuł ma na celu zbadanie roli, jaką odgrywa semantyka w teorii argumentacji, a dokładniej — zarysowanie pewnego modelu argumentacji, który modyfikuje znaczenia terminów dla celów argumentacyjnych. Najpierw przedstawię kilka przykładowych argumentów semantycznych, analizując każdy z nich na tyle, aby wydobyć pewne subtelności (...) potrzebne do zbudowania modelu argumentu semantycznego. W ten sposób pokażę, jak nomen omen znaczący wpływ na argumentację ma znaczenie słów, a także na ile sposobów może ono wpływać na przebieg argumentacji. Na samym końcu zarysuję definicję argumentu semantycznego, która może wytyczyć kierunek dalszych badań nad semantyką w teorii argumentacji. (shrink)

There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such (...) as the psychology of reasoning and mathematics education. This introduction offers a snapshot of each trend and addresses how they intersect with some of the standard criticisms of experimental philosophy. It also briefly summarizes the specific contribution of the other chapters of this book. (shrink)

I address a type of circularity threat that arises for the view that we employ general basic logical principles in deductive reasoning. This type of threat has been used to argue that whatever knowing such principles is, it cannot be a fully cognitive or propositional state, otherwise deductive reasoning would not be possible. I look at two versions of the circularity threat and answer them in a way that both challenges the view that we need to apply general logical principles (...) in deductive reasoning and defuses the threat to a cognitivist account of knowing basic logical principles. (shrink)

We are justified in employing the rule of inference Modus Ponens (or one much like it) as basic in our reasoning. By contrast, we are not justified in employing a rule of inference that permits inferring to some difficult mathematical theorem from the relevant axioms in a single step. Such an inferential step is intuitively “too large” to count as justified. What accounts for this difference? In this paper, I canvass several possible explanations. I argue that the most promising approach (...) is to appeal to features like usefulness or indispensability to important or required cognitive projects. On the resulting view, whether an inferential step counts as large or small depends on the importance of the relevant rule of inference in our thought. (shrink)

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)

What is it to believe something might be the case? We develop a puzzle that creates difficulties for standard answers to this question. We go on to propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. After showing how our account solves the puzzle, we explore a surprising consequence: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical (...) implication. (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...) number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

ABSTRACTThis paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions, transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit taking, we posit (...) rich inferential transitions, which are transitions that the subject is disposed to endorse. (shrink)

In this paper I deal with epistemological issues that stem from the hypothesis that reasoning is not only a means of transmitting knowledge from premise-beliefs to conclusion-beliefs, but also a primary source of knowledge in its own right. The idea is that one can gain new knowledge on the basis of suppositional reasoning. After making some preliminary distinctions, I argue that there are no good reasons to think that purported examples of knowledge grounded on pure reasoning are just examples of (...) premise-based inferences in disguise. Next, I establish what kinds of true propositions can to a first approximation be known on the basis of pure reasoning. Finally, I argue that beliefs that are competently formed on the basis of suppositional reasoning satisfy both externalist and internalist criteria of justification. (shrink)

Hay doble pulsión en el centro de la discusión del razonamiento deductivo. Una conduce aparentemente a la abstracción y dominios arbitrarios, mientras que la otra conduce a la concreción y la dependencia del contenido. El objetivo de esta investigación es diseñar, aplicar y validar un instrumento de evaluación que nos permita corroborar si el razonamiento deductivo maneja reglas lógicas o contenidos. La muestra de estudio se compuso de 80 participantes (edad 18-77 años). El test consta de 60 ítems categorizados en: (...) formalidad, integrabilidad, complejidad y modalidad. Los resultados ponen de manifiesto la fiabilidad del test de razonamiento deductivo con un alpha de Cronbach. 775 y con un índice de validación. 850 para el índice de inteligencia no verbal (INV) del RIAS. Cómo conclusión inferimos que el razonador deductivo no dispone de un cuerpo preciso de reglas generales deductivas, sino que usa colecciones de reglas heurísticas cada vez menos abstractas. (shrink)

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...) for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

If a conclusion was reached that creatures without a language capability exhibit some form of a capability for logic, this would shed a new light on the relationship between logic, language, and thought. Recent experimental attempts to test whether some animals, as well as pre-linguistic human infants, are capable of exclusionary reasoning are taken to support exactly that conclusion. The paper discusses the analyses and conclusions of two such studies: Call’s (2004) two cups task, and Mody and Carey’s (2016) four (...) cups task. My paper exposes hidden assumptions within these analyses, which enable the authors to settle on the explanation which assigns logical capabilities to the participants of the studies, as opposed to the explanations which do not. The paper then demonstrates that the competing explanations of the experimental results are theoretically underdeveloped, rendering them unclear in their predictions concerning the behavior of cognitive subjects, and thus difficult to distinguish by use of experiments. Additionally, it is questioned whether the explanations are rivals at all, i.e. whether they compete to explain the cognitive processes of the same level. The contribution of the paper is conceptual. Its aim is to clear up the concepts involved in these analyses, in order to avoid oversimplified or premature conclusions about the cognitive abilities of pre- and non-linguistic creatures. It is also meant to show that the theoretical space surrounding the issues involved might be much more diverse and unknown than many of these studies imply. (shrink)

It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure. But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter argues that single-premise closure succumbs to risk (...) aggregation outright. For he thinks that there could be a long sequence of competent single-premise deductions such that, even though we are justified in believing the initial premise of the sequence, intutively, we are not justified in believing the final conclusion. This intuition, Schechter thinks, vitiates single-premise closure. In this paper, I defend single-premise closure against the arguments offered by Lasonen-Aarnio and Schechter. (shrink)

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...) deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives. (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.

The new paradigm in the psychology of reasoning draws on Bayesian formal frameworks, and some advocates of the new paradigm think of these formal frameworks as providing a computational-level theory of rational human inference. I argue that Bayesian theories should not be seen as providing a computational-level theory of rational human inference, where by “Bayesian theories” I mean theories that claim that all rational credal states are probabilistically coherent and that rational adjustments of degrees of belief in the light of (...) new evidence must be in accordance with some sort of conditionalization. The problems with the view I am criticizing can best be seen when we look at chains of inferences, rather than single-step inferences. Chains of inferences have been neglected almost entirely within the new paradigm. (shrink)

In this paper, I argue that, other things being equal, simpler arguments are better. In other words, I argue that, other things being equal, it is rational to prefer simpler arguments over less simple ones. I sketch three arguments in support of this claim: an argument from mathematical proofs, an argument from scientific theories, and an argument from the conjunction rule.

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (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)

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)

Some philosophers have recently argued that there are no diachronic norms of epistemic rationality, that is, that there are no norms regarding how you should change your attitudes over time. I argue that this is wrong on the grounds that there are norms governing reasoning.

I argue that the accounts of inference recently presented (in this journal) by Paul Boghossian, John Broome, and Crispin Wright are unsatisfactory. I proceed in two steps: First, in Sects. 1 and 2, I argue that we should not accept what Boghossian calls the “Taking Condition on inference” as a condition of adequacy for accounts of inference. I present a different condition of adequacy and argue that it is superior to the one offered by Boghossian. More precisely, I point out (...) that there is an analog of Moore’s Paradox for inference; and I suggest that explaining this phenomenon is a condition of adequacy for accounts of inference. Boghossian’s Taking Condition derives its plausibility from the fact that it apparently explains the analog of Moore’s Paradox. Second, in Sect. 3, I show that neither Boghossian’s, nor Broome’s, nor Wright’s account of inference meets my condition of adequacy. I distinguish two kinds of mistake one is likely to make if one does not focus on my condition of adequacy; and I argue that all three—Boghossian, Broome, and Wright—make at least one of these mistakes. (shrink)

The thesis aims at a methodological reflection of logical reconstruction and tries to develop this method in detail, especially with regard to the reconstruction of natural language arguments. First, the groundwork for the thesis is laid by presenting and, where necessary, adapting its foundations with regard to the philosophy of language and the theory of argument. Subsequently, logical reconstruction, especially the logical reconstruction of arguments, is presented as a hermeneutic method and as a tool for the application of (formal) logic (...) and argumentation theory to natural language arguments. Logical reconstruction is presented as a special type of exegetical interpretation by paraphrase that is subject to (adapted) hermeneutic maxims and presumption rules that govern exegetical interpretation in general. However, in contrast to the interpretation of texts by natural language paraphrases, logical reconstruction leads to interpretantia that are logically explicit formal language texts and can be analyzed using formal methods and meta-theoretical concepts that are not directly applicable to natural language texts. By providing explicit and precise records of different readings, logical reconstruction can thus help to clarify (and maybe even solve) persistent interpretation controversies. Through an adaptation and specification of hermeneutic maxims and presumption rules, the thesis aims at providing suitable means for the systematic guidance and evaluation of logical reconstructions of argumentative texts. As a genuinely interpretative undertaking, logical reconstruction will be distinguished from the non-interpretative enterprise of formalization and from the development of theories of logical form, which provide a framework in which formalization and reconstruction take place. As exegetical interpretations, logical reconstructions of texts that are not readily formalizable can still be assessed with respect to their hermeneutic quality. The hermeneutic method of logical reconstruction can thus widen the scope for the application of logic and argumentation theory, because it allows us to use formal methods for the analysis and assessment of "difficult" natural language texts in a non-arbitrary, albeit indirect way. The last part of the thesis presents a manual for the logical reconstruction of natural language arguments, whose application is illustrated step by step. (shrink)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

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)

In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...) the paper, I then argue, on the basis of epistemic communism, for a view about rationality itself. I set up the argument in section 2 by saying what a theory of rational deduction is supposed to do. I claim that such a theory would provide a necessary, sufficient, and explanatorily unifying condition for being a rational rule for inferring deductive consequences. I argue in section 3 that, given epistemic communism and the conventionality that it entails, there is no such theory. Nothing explains why certain rules for deductive reasoning are rational. (shrink)

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.

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)

Deductive reasoning is the kind of reasoning in which, roughly, the truth of the input propositions (the premises) logically guarantees the truth of the output proposition (the conclusion), provided that no mistake has been made in the reasoning. The premises may be propositions that the reasoner believes or assumptions that the reasoner is exploring. Deductive reasoning contrasts with inductive reasoning, the kind of reasoning in which the truth of the premises need not guarantee the truth of the conclusion.

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...) one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty in (...) known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (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)

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)

The definitions of ‘deduction’ found in virtually every introductory logic textbook would encourage us to believe that the inductive/deductive distinction is a distinction among kinds of arguments and that the extension of ‘deduction’ is a determinate class of arguments. In this paper, we argue that that this approach is mistaken. Specifically, we defend the claim that typical definitions of ‘deduction’ operative in attempts to get at the induction/deduction distinction are either too narrow or insufficiently precise. We conclude by presenting a (...) deflationary understanding of the inductive/deductive distinction; in our view, its content is nothing over and above the answers to two fundamental sorts of questions central to critical thinking. (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)