Deductive Reasoning

The conclusion of a valid deductive argument is contained in its premises, but the deductive argument can still be informative if the arguer is trying to find the missing premises that together with the accepted premises will ensure the truth of the conclusion. Necessarily true conditionals have a deductive-like character so their consequents are contained in their antecedents. These conditionals can be informative, so we need to find the missing antecedent that makes the connection between the antecedent and the consequent. (...) So where is it? (shrink)

Lycan (2010: 617) maintained that if we know about a deductive argument P1, P2…, ∴C that it is valid, this shows that a set containing the premises and the negation of conclusion is internally inconsistent {P1, P2,…, ~C}. Using a similar reasoning, we should conclude that an invalid deductive argument shows that a set containing the premises and the negation of conclusion is internally consistent. This implies that premises and conclusion of any deductive argument are truth-apt. Since it is uncontroversial (...) that the argument that motivates the liar paradox is deductive, it follows that the liar sentences are truth-apt. The reason is obvious: if a sentence can’t be true, it can’t be a part of a consistent or inconsistent set, by definition. Consequently, the liar paradox cannot be solved by arguing that liar sentences are truth-valueless. (shrink)

The modus ponens can be interpreted as an answer to a circularity charge, but this strategy is only feasible if the additional conditional premise is interpreted as a claim to a material implication. Here’s how it works.

An argument is deductive when the arguer believes the truth of the premises necessitates the truth of the conclusion. A deductive argument is valid when the arguer’s claim is true, i.e., when there are no possible worlds whether the premises are true and the conclusion is false. But in order to evaluate this claim in an accurate manner we need to consider three qualifications that have been repeatedly ignored in the literature, namely, consistency in the attribution of truth values, world (...) consistency, and the inclusion of the reasons offered by the arguer in support of the premises. These apparently innocuous restrictions have significant and far-reaching implications. (shrink)

In a typical modus ponens the reasoner will (a) assert that a premise materially implies a conclusion in a given world; (b) assert this premise and (c) infer the conclusion. But this restricted modus ponens has little in common with the unrestricted textbook modus ponens, since the latter claims that there are no possible worlds where: (a’) a premise materially implies a conclusion, (b’) that premise is true and (c’) the conclusion is false. It is clear that this textbook modus (...) ponens cannot be a real argumentative form since the same inference cannot be repeated across all possible worlds by one reasoner. What is wrong? (shrink)

Logic textbooks advertise that they can teach how to spot a valid argument by its logical form alone. They also boast having collections with the most basic valid argumentative forms people of flesh and blood can use in deductive matters. Think about this for a moment. These are bold statements. If they were accurate, logic textbook authors would be in higher demand than software engineers and no one would be able to make contributions to theoretical physics without ever taking a (...) logic class. Of course, none of that is true. Their basic argumentative forms are nowhere to be seen in real-life argumentation and people will carry on their cognitive business without ever putting their hands on a logic textbook. I believe philosophers overpromise and underdeliver due to a subtle, but profound confusion they make about their own object of study. They take metalogical principles such as hypothetical syllogism for real forms of the arguments that are used in natural language. I try to connect these principles with real-life argumentation by interpreting their ‘premises’ as background assumptions and their ‘conclusions’ as either arguments or categorical assertions. This is not enough to save face for two reasons. First, the arguer’s assumptions should count as additional premises, but they will involve numerous arguments and the resulting formal interpretation will be too cumbersome to be practical. Second, we can’t determine the validity of an argument by formal means except when the conclusion repeats the premise, the premise is contradictory or the conclusion is tautological. These limitations are usually ignored due to the prevalent but questionable assumption that conditionals are connectives and not claims to implication. But conditionals can be elegantly explained as claims to implication in a variety of modal ranges that are all classical in nature. Consequently, the substantial validity of a deductive argument can only be determined in an informal manner and requires an extensive investigation of the nature of the subject. I conclude the article with some observations about the need to rethink the role of logic, its cognitive importance, and its teaching. Logic is important because it allows us to understand the nature of logical consequence and not because it is supposed to be useful for other deductive endeavours. I also make some observations about the need to rethink informal logic. Similarly to baby logic conventions involving formal logic, the textbook fallacies have no uncontroversial corresponding examples in real-life argumentation and are better interpreted as a list of epistemic vices that any honest epistemic agent should avoid. In this sense, informal logic has been misunderstood as a poor cousin of formal logic for decades, when it should be viewed as a speciality of virtue epistemology. (shrink)

It is usually accepted that one of the properties of classical logic is monotonicity, which states that the validity of implication is not affected by the addition of new premises. In this piece, I will argue that this common notion is unjustified since it is motivated by a category mistake. The notion of monotonicity is primarily epistemic in character and can’t be meaningfully attributed to a system. This is acutely clear in the contrast of monotonicity with non-monotonicity, which we tend (...) to associate with defeasible inferences, where reasoners can abandon a previous inference based on new information. So non-monotonicity is actually the reasoners’ willingness to abandon a previous inference based on new information. Therefore, it can be a property of a system only in a manner of speaking. But since non-monotonicity is the reasoners’ willingness to abandon a previous inference based on new information, monotonicity should be understood in a similar epistemic fashion, namely, as the reasoners’ willingness to maintain a previous inference after newly discovered information. By analyzing the problem from this perspective, a classical inference can be considered non-monotonic if the reasoner is willing to retract her previous conclusions based on new information. (shrink)

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.

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)

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)

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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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 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)

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)

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)

The Neo-Moorean Deduction (I have a hand, so I am not a brain-in-a-vat) and the Zebra Deduction (the creature is a zebra, so isn’t a cleverly disguised mule) are notorious. Crispin Wright, Martin Davies, Fred Dretske, and Brian McLaughlin, among others, argue that these deductions are instances of transmission failure. That is, they argue that these deductions cannot transmit justification to their conclusions. I contend, however, that the notoriety of these deductions is undeserved. My strategy is to clarify, attack, defend, (...) and apply. I clarify what transmission and transmission failure really are, thereby exposing two questionable but quotidian assumptions. I attack existing views of transmission failure, especially those of Crispin Wright. I defend a permissive view of transmission failure, one which holds that deductions of a certain kind fail to transmit only because of premise circularity. Finally, I apply this account to the Neo-Moorean and Zebra Deductions and show that, given my permissive view, these deductions transmit in an intuitively acceptable way—at least if either a certain type of circularity is benign or a certain view of perceptual justification is false. (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)

It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. Because of the symmetry between (...) the principles, they come as a package: either both will have to be rejected or both will have to be revised. (shrink)

Is it possible to give a justification of our own practice of deductive inference? The purpose of this paper is to explain what such a justification might consist in and what its purpose could be. On the conception that we are going to pursue, to give a justification for a deductive practice means to explain in terms of an intuitively satisfactory notion of validity why the inferences that conform to the practice coincide with the valid ones. That is, a justification (...) should provide an analysis of the notion of validity and show that the inferences that conform to the practice are just the ones that are valid. Moreover, a complete justification should also explain the purpose, or point, of our inferential practice. We are first going to discuss the objection that any justification of our deductive practice must use deduction and therefore be circular. Then we will consider a particular model of justificatory explanation, building on Georg Kreisel’s concept of informal rigour. Finally, in the main part of the paper, we will discuss three ideas for defining the notion of validity: (i) the classical conception according to which the notion of (bivalent) truth is taken as basic and validity is defined in terms of the preservation of truth; (ii) the constructivist idea of starting instead with the notion of (a canonical) proof (or verification) and define validity in terms of this notion; (iii) the idea of taking the notions of rational acceptance and rejection as given and define an argument to be valid just in case it is irrational to simultaneously accept its premises and reject its conclusion (or conclusions, if we allow for multiple conclusions). Building on work by Dana Scott, we show that the last conception may be viewed as being, in a certain sense, equivalent to the first one. Finally, we discuss the so-called paradox of inference and the informativeness of deductive arguments. (shrink)

This paper argues that general skills and the varieties of subject-specific discourse are both important for teaching, learning and practising critical thinking. The former is important because it outlines the principles of good reasoning simpliciter (what constitutes sound reasoning patterns, invalid inferences, and so on). The latter is important because it outlines how the general principles are used and deployed in the service of ‘academic tribes’. Because critical thinking skills are—in part, at least—general skills, they can be applied to all (...) disciplines and subject-matter indiscriminately. General skills can help us assess reasoning independently of the vagaries of the linguistic discourse we express arguments in. The paper looks at the debate between the ‘specifists’—those who stress the importance of critical thinking understood as a subject-specific discourse—and the ‘generalists’—those that stress the importance of critical thinking understood independently of disciplinary context. The paper suggests that the ‘debate’ between the specifists and the generalists amounts to a fallacy of the false alternative, and presents a combinatory-‘infusion’ approach to critical thinking. (shrink)

There is ample justification for having analogical material in standardized tests for graduate school admission, perhaps especially for law school. We think that formal-analogy questions should compare different scenarios whose structure is the same in terms of the number of objects and the formal properties of their relations. The paper deals with this narrower question of how legitimately to have formal analogy test items, and the broader question of what constitutes a formal analogy in general.