"This book is interesting and well-written. The research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages. Anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book." MAA Reviews "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with (...) basic syllogisms and deductions." CHOICE connect "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with basic syllogisms and deductions." CHOICE Connect For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results. Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents. Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy. (shrink)

"The Art of Logical Thinking" is a book written by William Walker Atkinson, an American attorney, merchant, publisher, and author in the late 19th and early 20th centuries. The book was first published in 1909 under the pseudonym Theron Q. Dumont, one of Atkinson's many pen names. The primary focus of "The Art of Logical Thinking" is to provide readers with insights into developing and refining their logical thinking abilities. Atkinson explores various aspects of logical reasoning and (...) critical thinking, aiming to guide readers in making better decisions, solving problems, and approaching issues with a more rational mindset. Key topics covered in the book include: The Nature of Thought: Atkinson delves into the fundamentals of thought processes, examining how ideas are formed and how the mind operates in its thinking capacity. Logical Analysis: The book provides techniques for breaking down complex problems into smaller, more manageable components, facilitating a systematic and logical approach to problem-solving. Deductive and Inductive Reasoning: Atkinson discusses both deductive and inductive reasoning, explaining their principles and applications. Deductive reasoning involves drawing specific conclusions from general principles, while inductive reasoning involves deriving general principles from specific observations. (shrink)

The present study proposes a valorization of the work of professor and philosopher Ioan Biriş. The statistics of his books and studies, their distribution by areas of interest, and especially the ideas in his work confirm the need for philosophy in the Romanian cultural life. As a whole, his philosophical endeavor is based on the concept of totality. Thus in the Hegelian spirit, Ioan Biriş successfully convinces us that the logical may exceed the limits of formal exercise and become the (...) organon of philosophy. In this capacity, the logical may operate on the real and valorize the multiple relationships between identity and difference. His books Filosofia și logica științelor sociale, Totalitate, sistem, holon, Rolul imaginarului în cunoașterea științifică, Istorie şi cultură, as well as a series of studies among which let me mention: “L’identité symbolique et la logique partitive des valeurs spirituelles”, “On the logic of religious terms”, “Le rapport identite-difference et la conjonction collective. Aspects logiques”, clearly prove the author’s capacity to integrate existential, religious, cognitive and axiological issues into a unitary vision. As Noica would say, he succeeded to enter the spirit’s life thorough the intellect’s gate. (shrink)

This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its ‘pyramidal’ graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the (...) central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid. Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of ‘false’ contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Argues that Americans must improve their understanding of probability and logic.

We are considered to be highly evolved conscious beings, but if we look at ourselves, do we actually feel that we are there; wise men or Homo sapiens as we call ourselves? In today’s world, reward based conditioning forms our contemporary culture that deeply defines how we look at life and how we intuitively perceive our consciousness. Presently, acquisitions are our priority and we behave as narcissistic conditioned puppets and let governments and corporations rule our lives. We are hypocrites that (...) can see, but behave blind; blinded within the realms of our short-termed thrills, joys and beliefs. Augmenting logical questioning and logical conditioning is the only way we can come out of this state that cannot be done individually, it has to be a collective effort. This paper is an attempt to understand our very own evolved consciousness and its relation to the current world with the true meaning of our existence, where we seek to understand it from a logical sense. (shrink)

This paper contains a preliminary investigation of an experimental, first-order logic with identity which encodes as an inference rule the faulty reasoning which Von Domarus (1944) suggested underwrote much of the bizarre thinking seen in certain forms of schizophrenia. I begin with a discussion of the "Von Domarus thesis," note its fate under statistical testing, and remark on its continued explanatory power in the hands of certain psychiatrists. I next discuss a proof calculus which contains a rule representing Von (...) Domarus reasoning — the phrenetic calculus — and present several nonstandard theorems which are provable in this system. In an appendix the phrenetic calculus is proven to be absolutely consistent, but unsound, yet complete. After a brief aside which addresses certain caveats and restrictions required in order to avoid rendering the calculus trivial, I close with a discussion of three of the nonstandard theorems, each of which are consistent in interesting ways with known schizophrenic cognitive deficits. (shrink)

Pollock argues that theories of ideal rationality are largely irrelevant to the decision making of real agents. Thinking about Acting aims to provide a theory of "real rationality.".

The objective of this book is to produce a theory of rational decision making for realistically resource-bounded agents. My interest is not in “What should I do if I were an ideal agent?”, but rather, “What should I do given that I am who I am, with all my actual cognitive limitations?” The book has three parts. Part One addresses the question of where the values come from that agents use in rational decision making. The most comon view among philosophers (...) is that they are based on preferences, but I argue that this is computationally impossible. I propose an alternative theory somewhat reminiscent of Bentham, and explore how human beings actually arrive at values and how they use them in decision making. Part Two investigates the knowledge of probability that is required for decision-theoretic reasoning. I argue that subjective probability makes no sense as applied to realistic agents. I sketch a theory of objective probability to put in its place. Then I use that to define a variety of causal probability and argue that this is the kind of probability presupposed by rational decision making. So what is to be defended is a variety of causal decision theory. Part Three explores how these values and probabilities are to be used in decision making. In chapter eight, it is argued first that actions cannot be evaluated in terms of their expected values as ordinarily defined, because that does not take account of the fact that a cognizer may be unable to perform an action, and may even be unable to try to perform it. An alternative notion of “expected utility” is defined to be used in place of expected values. In chapter nine it is argued that individual actions cannot be the proper objects of decision-theoretic evaluation. We must instead choose plans, and select actions indirectly on the grounds that they are prescribed by the plans we adopt. However, our objective cannot be to find plans with maximal expected utilities. Plans cannot be meaningfully compared in that way. (shrink)

John Pollock aims to construct a theory of rational decision making for real agents--not ideal agents. Pollock argues that theories of ideal rationality are largely irrelevant to the decision making of real agents. Thinking about Acting aims to provide a theory of "real rationality.".

The paper discusses Berkeley's classical critique of Locke's theory of generating concepts by abstraction, rebuts it, and shows that endorses Lockean abstractionism concerning the formation of empirical concepts.

One of the many research projects of Jaakko Hintikka was entitled “Logical tools for human thinking and their history”. This is in fact an apt summary of the lifetime work of this master logician who developed several new methods and systems in mathematical and philosophical logic, among them distributive normal forms, model sets, possible-worlds semantics, epistemic logic, doxastic logic, inductive logic, semantic information, game-theoretical semantics, interrogative approach to inquiry, and independence-friendly logic. He applied them to study problems in philosophy (...) of language, formal epistemology, and philosophy of science. He combined systematic work with novel interpretations of important historical figures like Aristotle, Leibniz, Kant, Peirce, and Wittgenstein. Hintikka was one of the most cited analytic philosophers, and he influenced logic and philosophy also as a successful teacher and the long-time editor of the journal Synthese. (shrink)

This is a review of the book by E.G. Dragalina-Chyornaya “Informal notes on logical form". The review discusses the structure and the main ideas of the book. The review focuses on the author's arguments in favor of the dynamic regulatory model of logic and provides a critical analysis of them.

This book review describes and evaluates John Pollock's view about rational decision-making.

Combining two thoughts into a compound mental representation is a central feature of our verbal and non-verbal logical abilities. We here approach this issue by focusing on the contingency that while natural languages have typically lexicalised only two of the possible 16 binary connectives from formal logic to express compound thoughts—namely, the coordinatorsandandor—some of the remainder appear to be entertainable in a non-verbal, conceptual representational system—alanguage of thought—and this suggests a theoretical split between the “lexicalisation” of the connectives and the (...) “learnability” of invented words corresponding to unlexicalised connectives. In avisual worldexperiment aimed at tracking comprehension-related as well as reasoning-related aspects of the capacity to represent compound thoughts, we found that participants are capable of learning and interpreting a made-up word standing for logic's NAND operator, a result that indicates that unlexicalised logical connectives are not only conceptually available, but can also be mapped onto new function words, as in the case of coordinators, or connectives, a class of words that do not usually admit new coinages. (shrink)

Oaksford & Chater (O&C) rely on a data fitting approach to show that a Bayesian model captures the core reasoning data better than its logicist rivals. The problem is that O&C's modeling has focused exclusively on response output data. I argue that this exclusive focus is biasing their conclusions. Recent studies that focused on the processes that resulted in the response selection are more positive for the role of logic.

This chapter intervenes in recent debates in Kant scholarship about the possibility of a general logical alien. Such an alien is a thinker whose laws of thinking violate ours. She is third-personal as she is radically unlike us. Proponents of the constitutive reading of Kant’s conception of general logic accordingly suggest that Kant rules out the possibility of such an alien as unthinkable. I add to this an often-overlooked element in Kant’s thinking: there is reason to think that (...) he grants—and in fact presupposes—the possibility of a transcendental logical alien. Such an alien is a knower whose laws of experience purport to violate ours. She is first-personal as she is radically like us. In other words, she is us, insofar as we are alienated from ourselves and our experience. I go on to draw an analogy between her, a dogmatist, and another transcendental alien, an evil agent. Just as a dogmatist is alienated from her (our) experiential laws, an evil agent is alienated from her (our) moral law. These forms of theoretical and practical self-conceit require self-knowledge in the form of a critique of speculative or practical reason. In bringing this point out, I aim to shift from the question of whether logical laws constitute our thinking to the question of whether grasping our experiential and moral laws as our laws constitutes our reason. (shrink)

Critical Thinking is a comprehensive introduction to the essential skills of good reasoning, refined and updated through seven editions published over more than two decades. This concise edition offers a succinct presentation of the essential elements of reasoning that retains the rigor and sophistication of the original text. The authors provide a thorough treatment of such central topics as deductive and inductive reasoning, logical fallacies, how to recognize and avoid ambiguity, and how to distinguish what is relevant from what (...) is not. A companion website provides a range of interesting supplements, including interactive review materials, supplemental readings, and writing tips. (shrink)

Thought and its subject-matter, by J. Dewey.--Thought and its subject-matter: the antecedents of thought, by J. Dewey.--Thought and its subject-matter: the datum of thinking, by J. Dewey.--Thought and its subject-matter: the content and object of thought, by J. Dewey.-- Bosanquet's theory of judgment, by H. B. Thompson.--Typical stages in the development of judgement, by S. F. McLennan.--The nature of hypothesis, by M. L. Ashley.--Image and idea in logic, by W. C. Gore.--The logic of the pre-Socratic philosophy, by W.A. Heidel.--Valuation (...) as a logical process, by H. W. Strart.--Some logical aspects of purpose, by A. W. Moore. (shrink)

This chapter contains sections titled: Nothing and Negativity from a Logical Point of View Hegel's Conceptions of Nothing and Negativity Heidegger's Criticism Conclusion.

'There is much food for thought in McGinn's discussions and each chapter is rich with a series of considerations for thinking that the currently received views on the various topics have some serious difficulties that need confronting... For those interested in metaphysics and the philosophy of logic, this book will stimulate much further thought' -Mind 'The sweep of the book is broad and the pace is brisk... There is much material here to provide the basis for many a deep (...) philosophical discussion' -Mind 'Lucid and provocative little book... clear, direct and well argued' -Times Higher Education SupplementIdentity, existence, predication, necessity, and truth are fundamental philosophical concerns. Colin McGinn treats them both philosophically and logically, aiming for maximum clarity and minimum pointless formalism. He contends that there are real logical properties that challenge naturalistic metaphysical outlooks. These concepts are not definable, though we can say a good deal about how they work. The aim of Logical Properties is to bring philosophy back to philosophical logic. (shrink)