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)

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 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)

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

"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)

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)

Must you respect basic logical laws (BLL) – such as the law of non-contradiction – in order to think? Frege wrote that one must “acknowledge” BLL in order not to “abandon judgement altogether”. Some have argued that Frege therefore thought of logic as somehow ‘constitutive’ of thinking. However, some interpreters contend, due to his strong commitment to logic’s normative status, that Frege held the opposite view, namely the non-constitutivist view that (systematic) ‘illogical’ thinking is possible and that one (...) need not accept or follow BLL in order to think as such, although one must do so in order to think correctly. The aim of this paper is to investigate the interpretative landscape regarding Frege’s view on logic’s constitutive role for thinking and suggest, against the non-constitutivist readings, that he indeed was committed to some version of the constitutivity thesis, but that this commitment is not, as some constitutivist interpretations suggest, inconsistent with the idea that logic is normative for thinking. I will, instead, propose to read his view in a soft and agent-relative sense, according to which it is a necessary condition for the possibility of thinking that the agent in question is sensitive to and acknowledges BLL. (shrink)

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)

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 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)

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.

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.

RESUMEN Este trabajo pretende relacionar dos debates emparentados sobre cómo la lógica y el lenguaje influyen sobre el pensamiento. Existe un eje de discusión en relación a si hay una pluralidad de lógicas o un único sistema lógico como criterio de evaluación para cualquier contexto de razonamiento. En lingüística, el debate surgido a partir de las interpretaciones fuertes y débiles de la hipótesis Sapir-Whorf ha centralizado la discusión en torno al grado de influencia o determinación del lenguaje sobre el pensamiento. (...) Desde perspectivas y marcos teórico-conceptuales diferentes, lógica y lingüística delimitan y problematizan un campo de indagación y reflexión. El artículo, desde una mirada transdisciplinar, pretende dar cuenta y postular vasos comunicantes entre estos debates atendiendo a los matices de cada enfoque, así como proponer una hipótesis propia sobre la problemática planteada. ABSTRACT This paper aims to relate two debates about how logic and language influence thought. There is an axis of discussion about whether there exists a plurality of logic or a single logical system as an evaluation criterion for any reasoning context. In linguistics, the debate arising from the strong and weak interpretations of the Sapir-Whorf hypothesis has centralized the discussion around the degree of influence or determination of language on thought. From different perspectives and theoretical-conceptual frameworks, logic, and linguistics delimit and problematize a field of inquiry and reflection. The article, from a transdisciplinary perspective, intends to account for and postulate communicating vessels between these debates, considering the nuances of each approach. It also seeks to propose its own hypothesis on the problem raised. (shrink)

A philosopher sets forth and illustrates the principles of logical thinking and reasoning and considers the use of language as a vehicle of thought.

Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world’s (...) most significant philosophers is a remarkable attempt to establish a novel way of thinking. (shrink)

With the advent of classical logic we are continuing to observe an adherence to the laws of logic. Moreover, the system of classical logic exhibits a prominent role within analytic philosophy. Given that the laws of logic have persistently endured in actively defining classical logic and its preceding system of logic, it begs the question as to whether it actually proves to be consistent with Islam. To consider this inquiry in a broader manner; it would be an investigation into the (...) consistency between Islam and the logic which has been the predominant driving force of analytic philosophy. Despite the well documented engagement and novel contributions made in the field of logic by Arab and Islamic theologians/logicians, I think this question deserves examination not just in terms of classical logic but also from perspectives which go beyond classical logic, namely, non-classical logic. Doing so, would I believe, retain this inquiry within the purview of analytic philosophy despite the reference to non-classical logic. To be more specific, this question would be directed toward the Islamic theologian who espouses the system of classical logic in attempting to make sense of an absolute ineffable God of Islam. The inquiry would seek to determine if classical logic is consistent (amenable) in making sense of an absolute ineffable God of Islam. This would principally involve an analysis which determines whether the metaphysical assumptions of the laws of logic (more specifically the law of non-contradiction) are consistent in making sense of an absolute ineffable God of Islam. I shall argue that it is inconsistent. I shall establish my position on this matter by demonstrating why classical logic is inconsistent (not amenable) with an absolute ineffable God of Islam. Although, I am principally concerned with classical logic, my argument is as applicable to all earlier systems of logic as much as it is to classical logic. This is on the basis that both systems of logic, namely, all preceding systems and classical logic, consider the laws of logic as defining features. (shrink)

In the international bestseller, Thinking, Fast and Slow, Daniel Kahneman, the renowned psychologist and winner of the Nobel Prize in Economics, takes us on a groundbreaking tour of the mind and explains the two systems that drive the way we think. System 1 is fast, intuitive, and emotional; System 2 is slower, more deliberative, and more logical. The impact of overconfidence on corporate strategies, the difficulties of predicting what will make us happy in the future, the profound effect of (...) cognitive biases on everything from playing the stock market to planning our next vacation—each of these can be understood only by knowing how the two systems shape our judgments and decisions. -/- Engaging the reader in a lively conversation about how we think, Kahneman reveals where we can and cannot trust our intuitions and how we can tap into the benefits of slow thinking. He offers practical and enlightening insights into how choices are made in both our business and our personal lives—and how we can use different techniques to guard against the mental glitches that often get us into trouble. Winner of the National Academy of Sciences Best Book Award and the Los Angeles Times Book Prize and selected by The New York Times Book Review as one of the ten best books of 2011, Thinking, Fast and Slow is destined to be a classic. (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)

In this paper, we will explore two initiatives that focus on the importance of employing logical theories in educating people how to think and reason properly, one in Poland: The Lvov-Warsaw School; the other in North America: The Informal Logic Initiative. These two movements differ in the logical means and skills that they focus on. However, we believe that they share a common purpose: to educate students in logic and reasoning (logical education conceived as a process) so that they may (...) be able to apply their skills to analyze the issues in their society (logical culture as a result of logical education). The aim of the paper is to justify this claim by exploring research objectives and products that are common to both movements. (shrink)

'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)

Tarski's 1936 paper, “On the concept of logical consequence”, is a rather philosophical, non-technical paper that leaves room for conflicting interpretations. My purpose is to review some important issues that explicitly or implicitly constitute its themes. My discussion contains four sections: terminological and conceptual preliminaries, Tarski's definition of the concept of logical consequence, Tarski's discussion of omega-incomplete theories, and concluding remarks concerning the kind of conception that Tarski's definition was intended to explicate. The third section involves subsidiary issues, such as (...) Tarski's discussion concerning the distinction between material and formal consequence and the important question ofthe criterion for distinguishing between logical and non-logical terms.§1. Preliminaries. In this paper an argument is a two-part system composed of a set of propositions P and a single proposition c. The expression ‘c is a [logical] consequence of P’ is used with the same meaning as the expression ‘c is [logically] implied by P’. The expressions ‘is a logical consequence of’ and the converse ‘implies’ are relational. Often, I shall be talking in the same sense of validity of an argument. Validity is a property of arguments; an argument with premise-set P and conclusion c is valid if and only if P implies c; i.e., c is a logical consequence of P. Notice that this notion of argument is strictly ontic; it does not involve any agent that thinks, determines or establishes that a given proposition is or is not a consequence of a given set of propositions. (shrink)

There are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of thoughts (...) that violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant’s pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternative ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic. (shrink)