In this paper we deal with two types of reasoning: induction, and deduction First, we present a unified computational model of deductive reasoning through models, where deduction occurs in five phases: Construction, Integration, Conclusion, Falsification, and Response. Second, we make an attempt, to analyze induction through the same phases. Our aim is an explorative evaluation of the mental processes possibly shared by deductive and inductive reasoning.

As stressed by Perruchet & Vinter, the SOC model echoes Johnson-Laird's mental model theory. Indeed, the latter rejects rule-based processing and assumes that reasoning is achieved through the manipulation of conscious representations. However, the mental model theory as well as its modified versions resorts to the abstraction of complex schemas and some form of implicit logic that seems incompatible with the SOC approach.

Inconsistency-adaptive logics isolate the inconsistencies that are derivable from a premise set, and restrict the rules of Classical Logic only where inconsistencies are involved. From many inconsistent premise sets, disjunctions of contradictions are derivable no disjunct of which is itself derivable. Given such a disjunction, it is often justified to introduce new premises that state, with a certain degree of confidence, that some of the disjuncts are false. This is an important first step on the road to consistency: it narrows (...) down suspicion in inconsistent premise sets and hence locates the real problems among the possible ones. In this paper I present two approaches for handling such new premises in the context of the original premises. The first approach may apparently be combined with all paraconsistent logics. The second approach does not have the same generality, but is decidedly more elegant. (shrink)

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

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

In this paper, I challenge a widely presupposed principle in the epistemology of inference. The principle, (Validity Requirement), is this: S’s (purportedly deductive) reasoning, R, from warranted premise-beliefs provides (conditional) warrant for S’s belief in its conclusion only if R is valid. I argue against (Validity Requirement) from two prominent assumptions in the philosophy of mind: that the cognitive competencies that constitute reasoning are fallible, and that the attitudes operative in reasoning are anti-individualistically individuated. Indeed, my discussion will amount to (...) a defence of anti-individualism against a novel ‘slow-switch’ argument against it. This argument contra anti-individualism has it that given anti-individualism and certain auxiliary assumptions, A, a switched reasoner may, in certain slow-switch circumstances, C, reason invalidly by equivocating concepts. More specifically: (Valid 0): Peter is in circumstances C, and auxiliary assumptions, A, hold.(Valid 1): If Peter is in circumstances C, and auxiliary assumptions A hold, then (if the attitudes operative in Peter’s reasoning R are anti-individualistically individuated, then R is not valid). (Valid 2): Peter’s reasoning, R, generates warrant for the conclusion-belief. (Valid 3): Peter’s reasoning, R, generates warrant for the conclusion-belief only if the reasoning, R, is valid. (Valid 4): So, the attitudes operative in Peter’s reasoning R are not anti-individualistically individuated. The argument involves weaker premises than those of familiar slow-switch arguments against anti-individualism. In particular, it requires only that the reasoning be de facto valid. This assumption is much weaker than the requirement that the validity of the reasoning be ‘transparent’ to the reasoner. Indeed, (Valid 3) is simply an instance of (Validity Requirement). However, I argue that anti-individualism and (Valid 0)–(Valid 2) should be upheld at the expense of (Valid 3). In consequence, (Validity Requirement) stands in need of restriction. Thus, I argue for a surprising result in the epistemology of inference from widely accepted assumptions in the philosophy of mind. (shrink)

Much debate has surrounded "switching" scenarios in which a subject's reasoning is said to exhibit the fallacy of equivocation ( Burge 1988 ; Boghossian 1992, 1994 ). Peter Ludlow has argued that such scenarios are "epistemically prevalent" and, therefore, epistemically relevant alternatives ( Ludlow 1995a ). Since a distinctive feature of the cases in question is that the subject blamelessly engages in conceptual equivocation, we may label them 'equivocational switching cases'. Ludlow's influential argument occurs in a discussion about compatibilism with (...) regards to anti-individualism (or content externalism) and self-knowledge. However, the issue has wide-reaching consequences for many areas of epistemology. Arguably, the claim that equivocational switching cases are epistemically relevant may bear on the epistemology of inference, testimony, memory, group rationality and belief revision. Ludlow's argument proceeds from a now well-known "down to Earth" switching-case of a subject, Biff, who travels between the US and the UK. I argue that Ludlow's case-based argument fails to support the general claim that conceptual equivocational switching cases are prevalent and epistemically relevant. Thus, the discussion addresses the basis of some poorly understood issues regarding the epistemological consequences of anti-individualism. Simultaneously, the discussion is broadened from the narrow focus on self-knowledge. Finally, the critical discussion serves as the basis for some general reflections on epistemic relevance and the epistemic risks associated with conceptual equivocation. Specifically, I suggest that philosophy is an area where the risk of conceptual equivocation is extraordinarily high. (shrink)

It is often taken for granted by writers who propose--and, for that matter, by writers who oppose--'justifications' of inductions, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.

Current conceptions of the nature of human reasoning make it no longer tenable to assess children's inference by reference to the norms of logical inference. Alternatively, the complexity of the mental models employed in children's inferences can be analysed. This approach is applied to transitive inference, class inclusion, categorical induction, theory of mind, oddity, categorical syllogisms, analogy, and reasoning deficits. It is argued that a coherent account of children's reasoning emerges in that there is correspondence between tasks at the same (...) level of complexity across different domains, and that the inferences of younger children, while impressive and important, are consistently simpler than those of older children. (shrink)

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)

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)

The confusion/non-consequential thinking explanation proposed by Newstead, Girotto, and Legrenzi (1995) for poor performance on Wason's THOG problem (a hypothetico-deductive reasoning task) was examined in three experiments with 300 participants. In general, as the cognitive complexity of the problem and the possibility of non-consequential thinking were reduced, correct performance increased. Significant but weak facilitation (33-40% correct) was found in Experiment 1 for THOG classification instructions that did not include the indeterminate response option. Substantial facilitation (up to 75% correct) was obtained (...) in Experiment 2 with O'Brien et al.'s (1990) one-other-THOG classification instruction. In Experiment 3, a revised version of O'Brien et al.'s pre-test problem format also led to substantial facilitation, even with the use of the standard three-choice THOG classification instruction. These findings are discussed in terms of Newstead et al.'s theoretical proposal and possible attentional factors. (shrink)

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural (...) language is what determines both its logical properties and its logical relations to other sentences. The logical form of a sentence of natural language is typically represented in a theory of logical form by a well-formed formula in a ‘logically pure’ language whose only meaningful symbols are expressions with fixed, distinctly logical meanings (e.g., quantifiers). Thus, the logical forms of the sentences in the above argument would be represented in a theory based on pure predicate logic by the formulas ‘∀x(Fx ⊃ Gx)’, ‘Fy’, and ‘Gy’, respectively, where ‘F’, ‘G’, and ‘y’ are all free variables. The argument’s intuitive validity is then explained in virtue of the fact that the logical forms of the premises formally entail the logical form of the conclusion. The primary goal of a theory of logical form is to explain as broad a range of such intuitive logical phenomena as possible in terms of the logical forms that it assigns to sentences of natural language. (shrink)

Using the matching bias example, the aim of the present studies was to show that adults' reasoning biases are due to faulty executive inhibition programming. In the first study, the subjects were trained on Wason's classical card selection task; half were given training in how to inhibit the perceptual matching bias (experimental group) and half in logic without the inhibition component (control group). On the pre- and post-tests, their performance was assessed on the Evans conditional rule falsification task (with a (...) negation in the antecedent of the rule), a task that also involves matching bias. In addition, subjects were tested for perceptual field dependence/independence using the Embedded Figures Test. The results brought out a specific inhibition training effect, as well as a clear-cut relationship in the experimental group between receptiveness to training and perceptual field independence. In the second study, the training paradigm was the same except that on the pre- and post-tests, the negation was in the consequent of the conditional rule (in this case, the perceptual matching response corresponds to the logical response). The subjects succeeded on the pre-test, and the matching-bias inhibition training had a negative effect on post-test performance. This specific negative priming effect confirms the inhibitory impact of our experimental training and outlines the dissociation of inhibition and logical components. (shrink)

From certain sorts of premise, individuals reliably infer invalid conclusions. Two Experiments investigated a possible cause for these illusory inference: Reasoners fail to think about what is false. In Experiment 1, 24 undergraduates drew illusory and control inferences from premises based on exclusive disjunctions (“or else”). In one block, participants were instructed to falsify the premises of each illusory and control inference before making the inference. In the other block, participants did not receive these instructions. There were more correct answers (...) for illusory disjunctions whose premises had been falsified than there were for illusory disjunctions that had not been falsified. A second Experiment introduced illusory inferences in a real world context that accentuated falsification of premises. Accuracy also improved. Knowledge of how to falsify premises and to consider their implications for true premises transferred to a new problem introduced at the end of the Experiment without the falsification instruction. The participants' ratings of the difficulty of the inferences showed that they did not err simply because illusory inferences are perceived to be more difficult than control problems. The model theory predicts these results because it postulates that the limitations of working memory preclude the representation of false information. (shrink)

This book examines two questions: Do people make use of abstract rules such as logical and statistical rules when making inferences in everyday life? Can such abstract rules be changed by training? Contrary to the spirit of reductionist theories from behaviorism to connectionism, there is ample evidence that people do make use of abstract rules of inference -- including rules of logic, statistics, causal deduction, and cost-benefit analysis. Such rules, moreover, are easily alterable by instruction as it occurs in classrooms (...) and in brief laboratory training sessions. The fact that purely formal training can alter them and that those taught in one content domain can "escape" to a quite different domain for which they are also highly applicable shows that the rules are highly abstract. The major implication for cognitive science is that people are capable of operating with abstract rules even for concrete, mundane tasks; therefore, any realistic model of human inferential capacity must reflect this fact. The major implication for education is that people can be far more broadly influenced by training than is generally supposed. At high levels of formality and abstraction, relatively brief training can alter the nature of problem-solving for an infinite number of content domains. (shrink)

There has long been a history of studies investigating how people (“ordinary people”) perform on tasks that involve deductive reasoning. The upshot of these studies is that people characteristically perform some deductive tasks well but others badly. For instance, studies show that people will typically perform MP (“modus ponens”: from ‘If A then B’ and ‘A’, infer ‘B’) and bi-conditional MP (from: ‘A if and only if B’ and ‘A’, infer ‘B’) correctly when invited to make the inference and additionally (...) can discover of their own accord when such inferences are appropriate. On the other hand, the same studies show that people typically perform MT (“modus tollens”: from ‘If A then B’ and ‘not-B’, infer ‘not-A’) and biconditional MT badly. They not only do not recognize when it is appropriate to draw such inferences, but also they will balk at doing them even when they are told that they can make it. Related to these shortcomings seems to be the inability of people to understand that contrapositives are equivalent (that ‘If A then B’ is equivalent to ‘If not-B then not-A’). [Studies of people’s deductive inference-drawing abilities have a long history, involving many studies in the early 20th century concerning Aristotelian syllogisms. But the current spate of studies draws much of its impetus from Wason (Wason, 1968; see also Wason & <span class='Hi'>Johnson</span>-Laird, 1972). ] The general conclusion seems to be that there are specific areas where “ordinary people” do not perform very logically. This conclusion will not come as a surprise to teachers of elementary logic, who have long thought that the majority of “ordinary people” are inherently illogical and need deep and forceful schooling in order to overcome this flaw. (shrink)

Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals). -/- This contribution consists of two parts. In the first part we discuss general features of reasoning systems including consequence relations, how uncertainty may enter argument forms, probability intervals, and probabilistic informativeness. These concepts are of (...) central importance for the psychological task analysis. In the second part we report new experimental data on the paradoxes of the material conditional, the probabilistic modus ponens, the complement task, and data on the probabilistic truth table task. The results of the experiments provide evidence for the hypothesis that people represent indicative conditionals by conditional probability assertions. (shrink)

In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard first (...) courses in logic can be used for testing arguments with strict implications, strict equivalences and other operators which may represent connectives from natural language. (shrink)

The mental model theory predicts that reasoners normally represent what is true, but not what is false. One consequence is that reasoners should make "illusory" inferences, which are compelling but invalid. Three experiments confirmed the existence of such illusions based on disjunctions of disjunctions. They also established a successful antidote to them: Reasoners are much less likely to succumb to illusions if the inferences concern disjunctions of physical objects (alternative newspaper advertisements) rather disjunctions of the truth values of assertions. The (...) results shed light both on the cause of the illusions and on the current controversy among different theories of reasoning. (shrink)

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)

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.

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)

[Paul Boghossian] The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of 'blind but blameless' reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible. (...) /// [Timothy Williamson] The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper 'Blind Reasoning'. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as 'Boche' are examined and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)