The paper is concerned with the psychological relevance of a logical model for deductive reasoning. We propose a new way to analyze logical reasoning in a deductive version of the Mastermind game implemented within a popular Dutch online educational learning system (Math Garden). Our main goal is to derive predictions about the difficulty of Deductive Mastermind tasks. By means of a logical analysis we derive the number of steps needed for solving these tasks (a proxy (...) for working memory load). Our model is based on the analytic tableaux method, known from proof theory. We associate the difficulty of Deductive Mastermind game-items with the size of the corresponding logical trees obtained by the tableaux method. We derive empirical hypotheses from this model. A large group of students (over 37 thousand children, 5–12 years of age) played the Deductive Mastermind game, which gave empirical difficulty ratings of all 321 game-items. The results show that our logical approach predicts these item ratings well, which supports the psychological relevance of our model. (shrink)

No fictional character is more renowned for his powers of thought and observation than Sherlock Holmes. But is his extraordinary intellect merely a gift of fiction, or can we learn to cultivate these abilities ourselves, to improve our lives at work and at home? We can, says psychologist and journalist Maria Konnikova, and in Mastermind she shows us how. Beginning with the "brain attic"--Holmes's metaphor for how we store information and organize knowledge--Konnikova unpacks the mental strategies that lead to (...) clearer thinking and deeper insights. Drawing on twenty-first-century neuroscience and psychology, Mastermind explores Holmes's unique methods of ever-present mindfulness, astute observation, and logical deduction. In doing so, it shows how each of us, with some self-awareness and a little practice, can employ these same methods to sharpen our perceptions, solve difficult problems, and enhance our creative powers. For Holmes aficionados and casual readers alike, Konnikova reveals how the world's most keen-eyed detective can serve as an unparalleled guide to upgrading the mind. (shrink)

Innovative understanding or explanation stems almost exclusively from analogical reasoning. Induction systematizes the familiar; deduction casts it into formal relationship. Reasoning by analogy brings to bear on the familiar a new perspective derived from another realm of inquiry. Models are fruits from the tree of analogical knowledge.

Two experiments examined the role of conditional reasoning in the logical deduction game, Mastermind . An analysis suggested that Modus Tollens (MT) reasoning could be used to determine the code structure, for example, in determining if any of the colours in the code are repeated. Consistent with this analysis, Experiment 1 showed that only MT errors are correlated with the number of hypotheses advanced in Mastermind . A subsequent analysis showed that conditional reasoning such as Affirming the Consequent (...) (AC) and Denying the Antecedent (DA) could lead to particularly damaging inferences only when the code was four different colours. When that was known before play, Experiment 2 showed that AC errors, but not MT errors, were significantly correlated with Mastermind hypotheses advanced. A stepwise multiple regression analysis supported these findings: When the solvers knew they were playing a four-colour code, there was a slight diminution in the variance explained by MT errors, and a significant increase in the variance explained by AC errors. An analysis of the number of different possible codes that could be consistent with hypotheses actually played showed that the number of such codes is far fewer when the code consists of four different colours than when its structure is not known. This analysis suggests that reasoners are therefore unlikely to discover many alternative causes for the feedback given when the code consists of four different colours, and it is under these conditions that humans are most likely to engage in AC reasoning. (shrink)

Introduction: Another Diction The hack. The salesman. The fired cop. The drifter. The betrayed criminal. Each of these constitutes a novel literary invention; each gives a new sense to the investigative character. They are not modifications of the classical model, stamped with the rational imprimatur of Sherlock Holmes, C. Auguste Dupin, or Joseph Rouletabille – there is no line of filiation from these to Vachss’s Burke, Pelecanos’s Nick Stefanos, or Himes’s Coffin Ed Johnson and Grave Digger Jones. Even Lacan’s powerful (...) psychoanalytic reading of Poe’s “The Purloined Letter” reveals Dupin to be a genius only in a game whose dialectical structure is given in advance. Although the subjects that come to occupy this structure only acquire determination through the assumption of their places, the dynamic form of the dialectic is itself “foreclosed” by the phallus whose circulation organizes the system. Dupin understands the circulation of the signifier only because this circulation is the figure of the law. Rejecting the phallocentric rationality of the mastermind, the new figurations of Vachss, Pelecanos, Himes, and others retain only in order to parody the grand orchestration of reason – their language is slang not deduction. They are not detectives but “dicks”: a name that incorporates within its reduction an empirical transformation of the transcendental. In fact, it is a transformation of the very sense of inquiry that requires this new type of conceptual personae in order to traverse its contours. The philosophical project of Gilles Deleuze – which he characterizes as a “transcendental empiricism” – is directed toward freeing thought from its determination by the philosophical traditions that constitute its history. Such a freeing would allow for a philosophical conceptualization of present events that are no longer able to be adequately conceptualized by that history. The distinctive character of Deleuze’s project comes from his insistence on the discontinuity between the tradition of thought and the new formulations that it is called upon to generate. For Deleuze, the philosopher is the one who asks about the generation of new concepts and thereby places herself in a double bind. On the one hand, the philosopher is historically conditioned, thrown into a tradition whose tools present a limited number of possible conceptual resolutions of a particular event. On the other hand, this conditional determination of philosophical thought is repeated, perpetually, so that the philosopher is always a parody of herself: solving the question of the determination of a present event by resolving the question of the determinability of the present by the past. This situation of parody is the limit of thinking; it is where thinking develops according to the vicissitudes of history. (shrink)

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near (...) perfect predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (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)

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)

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)

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

Seldom does human reasoning fit the standards of deduction. Yet logicians have tended to use the strict standards of deductive validity for assessing all inferences. _Within Reason_ develops instead a way of assessing arguments and inferences that is directly appropriate to the non-deductive forms people regularly use. It uses analogy, and argument from analogy, to provide a thread that unites various forms: raising objections, inductions of various sorts, arguments to explanation, and arguments to action. The discussion is developed (...) progressively, at each stage building on the skills learned previously. And at each stage the book suggetss ways of assessing the strength of reasoning. Most of the examples are taken from the great texts of the Western tradition. In the exercises that form an integral part of each chapter an even broader range of writing is presented, offering instructors an extraordinary variety of texts at various levels ot assign to their students. The thesis implicit in the book is that induction, arguments to explanation and arguments to action are all sophisticated forms of arguments from analogy. Burbidge is concerned not simply to warn against the misuse of non-deductive reasoning but also to develop a more positive theory that allows us both to better udnerstand the workings of non-deductive reasoning, and to better employ it. (shrink)

We show that a finitely generated protoalgebraic strict universal Horn class that is filter-distributive is finitely based. Equivalently, every protoalgebraic and filter-distributive multidimensional deductive system determined by a finite set of finite matrices can be presented by finitely many axioms and rules.

We show that a finitely generated protoalgebraic strict universal Horn class that is filter-distributive is finitely based. Equivalently, every protoalgebraic and filter-distributive multidimensional deductive system determined by a finite set of finite matrices can be presented by finitely many axioms and rules.

Classical temples in ancient Greece show two deterministic illusionistic principles of architecture, which govern their functional design: geometric proportionalism and a set of illusion-strengthening rules in the proportionalism's stochastic margin. Animal morphology, in its mechanistic-deductive revival, applies just one architectural principle, which is not always satisfactory. Whether a Greek Classical situation occurs in the architecture of living structure is to be investigated by extreme testing with deductive methods.Three deductive methods for explanation of living structure in animal morphology (...) are proposed: the parts, the compromise, and the transformation deduction. The methods are based upon the systems concept for an organism, the flow chart for a functionalistic picture, and the network chart for a structuralistic picture, whereas the optimal design serves as the architectural principle for living structure. These methods show clearly the high explanatory power of deductive methods in morphology, but they also make one open end most explicit: neutral issues do exist. (shrink)

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages.

Hempel and Oppenheim have stated in Part III of their paper “Studies in the Logic of Explanation” [2] a set of conditions for deductive explanation. However, their analysis has come under damaging systematic criticisms in a recent paper by Eberle, Kaplan and Montague [1], The principal aim of the present paper is to review the Hempel-Oppenheim analysis and propose a strengthened version of it that avoids the recent criticisms.

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, (...) whereas Hilbert dismisses elucidation and consequently treats the primitives as schematic. (shrink)

Almost every formal model of explanation thus far proposed has been demonstrated to be faulty. In this paper, a new model, proposed by Raimo Tuomela, is also demonstrated to be faulty. In particular, one condition of the model is shown to be too restrictive, and another condition of the model is shown to be too permissive.

A methodology is proposed as a tool for explanation of form in zoomorphology, in particular its design, diversity, and transformation. An alternate use of descriptive, inductive/comparative, and deductive methods is suggested. The basic concepts required are summarized. Following an extensive anatomical analysis a specific deductive methodology is developed, comprising three major parts: 1) Formal analysis of systems, using optimal design. 2) Transformation of an initial system's model by simulating modifications via maximizing the model for specific functional requirements. 3) (...) Testing by comparison of deduced modifications with real systems having the maximized functional capacity, trends in specific morphoclines, and empirical analogues from technology.The methodology produces a morpho-space of modifications that has the form of branching pathways. That pattern results from innovation, bifurcation, and radiation moments in the deduction. The morpho-space is converted in a mechano-space by including next to constructional characters those of operation and rolefulfilment. If the initial system is verified as the ancestor and the transformation-function is verified as the evolutionary theme of change, the explanation turns -in addition to a function anatomical one- also into an evolutionary one. The method is illustrated by reviewing some recent analyses about avian feeding: maximization of avian pecking for probing and filter feeding capacities. (shrink)

Background As more people are living longer, they become frail and are affected by multi-morbidity, resulting in increased demands from the ambulance service. Being vulnerable, older patients may have reduced decision-making capacity, despite still wanting to be involved in decision-making about their care. Their needs may be complex and difficult to assess, and do not always correspond with ambulance assessment protocols. When needing an ambulance, older patients encounter ambulance clinicians who are under high workloads and primarily consider themselves as emergency (...) medical care providers. This situates them in the struggle between differing expectations, and ethical conflicts may arise. To resolve these, providing ethical care, focussing on interpersonal relationships and using ethical competence is needed. However, it is not known whether ambulance clinicians possess the ethical competence required to provide ethical care. Thus, the aim of this study was to deductively explore their ethical competence when caring for older patients with reduced decision-making ability. Methods A qualitative deductive and exploratory design was used to analyse dyadic interviews with ambulance clinicians. A literature review, defining ethical competence as comprising ethical sensitivity, ethical knowledge, ethical reflection, ethical decision-making, ethical action and ethical behaviour, was used as a structured categorization matrix for the analysis. Results Ambulance clinicians possess ethical competence in terms of their ethical knowledge, highlighting the need for establishing an interpersonal relationship with the older patients. To establish this, they use ethical sensitivity to interpret the patients’ needs. Doing this, they are aware of their ethical behaviour, signifying how they must act respectfully and provide the necessary time for listening and interacting. Conclusions Ambulance clinicians fail to see their gut feeling as a professional ethical competence, which might hinder them from reacting to unethical ways of working. Further, they lack ethical reflection regarding the benefits and disadvantages of paternalism, which reduces their ability to perform ethical decision-making. Moreover, their ethical knowledge is hampered by an ageist approach to older patients, which also has consequences for their ethical action. Finally, ambulance clinicians show deficiencies regarding their ethical reflections, as they reflect merely on their own actions, rather than on their values. (shrink)

After presenting the major objections raised against standard formulations of the H-D method of theory testing, I identify what seems to be an important element of truth underlying the method. I then draw upon this element in an effort to develop a plausible formulation of the H-D method which avoids the various objections.

In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these (...) structures with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACSs A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

We show that the Boolean Prime Ideal Theorem () does not imply the Nielsen‐Schreier Theorem () in, thus strengthening the result of Kleppmann from “Nielsen‐Schreier and the Axiom of Choice” that the (strictly weaker than ) Ordering Principle () does not imply in. We also show that is false in Mostowski's Linearly Ordered Model of. The above two results also settle the corresponding open problems from Howard and Rubin's “Consequences of the Axiom of Choice”.