Online research in philosophy

Logic is viewed by many as inseparable from rationality, and James' 'rejection of logic' in A Pluralistic Universe may be the most flagrantly 'irrational' strand in his philosophy. Nevertheless, when viewed in the context of the psychological naturalism developed in The Principles of Psychology, James' 'rejection of logic' can seem both plausible and, crucially, rational. James' rejection of conceptual logic is deeply connected to his naturalism about concepts, and his belief that there is no reason to think that an intellect "built up of practical interests" need develop concepts that accurately mirror the structure of reality. James position is, then, not so much that we should give up logic, but rather that (given the practical rather than theoretical nature of our concepts) we should give up the assumption that we are rationally obligated to accept all the apparent logical consequences of all the claims that we accept.

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such view.

This logic book puts critical-thinking skills into a context that you'll remember and use throughout your life.

Logic, it is often held, is primarily concerned with reasoning; and the conviction that logic and reasoning are two sides of the same coin nowadays usually equates with the conviction that logic spells out some directives for the "right" maintenance of beliefs. In this paper I put forward an alternative view, based on seeing rules of logic rules as constitutive rules, not instructing us how to reason, but rather providing us with certain vehicles or in terms of which to reason. This also emphasizes the social nature of beliefs: they are entities forged in a social mold, formed by rules originating from social argumentative practices. Because of this fact, I suggest, trying to understand logic by means of studying (rules of) the kinematics of beliefs of a solitary individual is essentially misguided.

Although Kant envisaged a prominent role for logic in the argumentative structure of his Critique of pure reason, logicians and philosophers have generally judged Kant's logic negatively. What Kant called `general' or `formal' logic has been dismissed as a fairly arbitrary subsystem of first order logic, and what he called `transcendental logic' is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant's `transcendental logic' is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first order logic. The main technical application of the formalism developed here is a formal proof that Kant's Table of Judgements in §9 of the Critique of pure reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant's 'general' logic is after all a distinguished subsystem of first order logic, namely what is known as geometric logic.

This book deals with questions everyone should become acquainted with when studying logic. It, however, has nothing in common with current introductions to logic, which are actually introductions to a particular logic paradigm, mathematical logic. There is nothing wrong with this, except that at present such paradigm is a problematic one. For mathematical logic, on the one hand, is inadequate for the use for which it was originally designed – to give mathematics the most secure foundation – and, on the other hand, has found no crucial alternative use. This fact is almost invariably passed over in silence in current introductions to logic. This is as it could be expected, for people working within a given paradigm tend to consider it as the only possible one and cannot conceive of any alternative. But to read only such introductions will give a rather narrow view of the subject. In this book mathematical logic is presented as being not ‘The Logic’ but rather a particular logic paradigm, with some basic limitations. An alternative logic paradigm is outlined, meant to remove such limitations, in which logic is supposed to be a logic of discovery and justification a part of discovery. With respect to mathematical logic, the alternative paradigm involves a different view of the relation of logic with nature. Logic is a continuation of the problem solving procedures with which biological evolution has endowed humans and all organisms generally. The alternative paradigm also involves a different view of the relation of logic with method. Method is the source of logic. To implement the alternative paradigm, a number of basic discovery procedures are discussed. By their very nature, discovery procedures do not form a closed set, given once for all, but rather an open set, which can always be expanded. Those considered in this book, however, are especially important. This book is not intended to replace any introduction to mathematical logic but rather to be read parallel to it. Its aim is, on the one hand, to put mathematical logic into perspective, on the other hand, to show that an alternative paradigm is possible and to outline it. I hope it will give the reader a better feel of what logic really is.

Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.

Imagine a dog tracing a scent to a crossroads, sniffing all but one of the exits, and then proceeding down the last without further examination. According to Sextus Empiricus, Chrysippus argued that the dog effectively employs disjunctive syllogism, concluding that since the quarry left no trace on the other paths, it must have taken the last. The story has been retold many times, with at least four different morals: (1) dogs use logic, so they are as clever as humans; (2) dogs use logic, so using logic is nothing special; (3) dogs reason well enough without logic; (4) dogs reason better for not having logic. This paper traces the history of Chrysippus's dog, from antiquity up to its discussion by relevance logicians in the twentieth century.

The formal systems of logic have ordinarily been regarded as independent of biology, but recent developments in evolutionary theory suggest that biology and logic may be intimately interrelated. In this book, Cooper outlines a theory of rationality in which logical law emerges as an intrinsic aspect of evolutionary biology. This biological perspective on logic, though at present unorthodox, could change traditional ideas about the reasoning process. Cooper examines the connections between logic and evolutionary biology and illustrates how logical rules are derived directly from evolutionary principles, and therefore have no independent status of their own. Laws of decision theory, utility theory, induction, and deduction are reinterpreted as natural consequences of evolutionary processes. Cooper's connection of logical law to evolutionary theory results in a unified foundation for an evolutionary science of reason.