Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...) by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

Corcoran, J. 2007. Psychologism. American Philosophy: an Encyclopedia. Eds. John Lachs and Robert Talisse. New York: Routledge. Pages 628-9. -/- Psychologism with respect to a given branch of knowledge, in the broadest neutral sense, is the view that the branch is ultimately reducible to, or at least is essentially dependent on, psychology. The parallel with logicism is incomplete. Logicism with respect to a given branch of knowledge is the view that the branch is ultimately reducible to logic. Every branch of (...) knowledge depends on logic. Psychologism is found in several fields including history, political science, economics, ethics, epistemology, linguistics, aesthetics, mathematics, and logic. Logicism is found mainly in branches of mathematics: number theory, analysis, and, more rarely, geometry. Although the ambiguous term ‘psychologism’ has senses with entirely descriptive connotations, it is widely used in senses that are derogatory. No writers with any appreciation of this point will label their own views as psychologistic. It is usually used pejoratively by people who disapprove of psychologism. The term ‘scientism’ is similar in that it too has both pejorative and descriptive senses but its descriptive senses are rarely used any more. It is almost a law of linguistics that the negative connotations tend to drive out the neutral and the positive. Dictionaries sometimes mark both words with a usage label such as “Usually disparaging”. In this article, the word is used descriptively mainly because there are many psychologistic views that are perfectly respectable and even endorsed by people who would be offended to have their views labeled psychologism. A person who subscribes to logicism is called a logicist, but there is no standard word for a person who subscribes to psychologism. ‘Psychologist’, which is not suitable, occurs in this sense. ‘Psychologician’, with stress on the second syllable as in ‘psychologist’, has been proposed. In the last century, some of the most prominent forms of psychologism pertained to logic; the rest of this article treats only such forms. Psychologism in logic is very “natural”. After all, logic studies reasoning, which is done by the mind, whose nature and functioning is studied in psychology—using the word ‘psychology’ in its broadest etymological sense. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

The word pro-tasis is etymologically a near equivalent of pre-mise, pro-position, and ante-cedent—all having positional, relational connotations now totally absent in contemporary use of proposition. Taking protasis for premise, Aristotle’s statement (24a16) -/- A protasis is a sentence affirming or denying something of something…. -/- is not a definition of premise—intensionally: the relational feature is absent. Likewise, it is not a general definition of proposition—extensionally: it is too narrow. This paper explores recent literature on these issues.

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...) problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. (shrink)

This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...

Reprint of the original, first published in 1869.

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...) is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

Aristotle's theory of truth, which has been the most influential account of the concept of truth from Antiquity onwards, spans several areas of philosophy: philosophy of language, logic, ontology and epistemology. In this 2004 book, Paolo Crivelli discusses all the main aspects of Aristotle's views on truth and falsehood. He analyses in detail the main relevant passages, addresses some well-known problems of Aristotelian semantics, and assesses Aristotle's theory from the point of view of modern analytic philosophy. In the process he (...) discusses most of the literature on Aristotle's semantic theory to have appeared in the last two centuries. His book vindicates and clarifies the often repeated claim that Aristotle's is a correspondence theory of truth. It will be of interest to a wide range of readers working in both ancient philosophy and modern philosophy of language. (shrink)

This article examines the development of Russell's treatment of propositions, in relation to the topic of psychologism. In the first section, we outline the concept of psychologism, and show how it can arise in relation to theories of the nature of propositions. Following this, we note the anti-psychologistic elements of Russell's thought dating back to his idealist roots. From there, we sketch the development of Russell's theory of the proposition through a number of its key transitions. We show that Russell, (...) in responding to a variety of different problems relating to the proposition, chose to resolve these problems in ways that continually made concessions to psychologism. (shrink)

Another striking deviation with regard to philosophical tradition consists in the fact that contemporary schools in the philosophy of mathematics, with the exception again of Brouwer's intuitionism, hardly ever refer to mathematical thought.

HISTORICAL INTRODUCTION Although many of the details of the development of logic in the Middle Ages remain to be filled in, it is well known that between ...

By what process of development he came to this opinion, though in itself an important and interesting question, is logically irrelevant to the inquiry how far the opinion itself is correct ; and among his opinions, when these have been ascertained, it becomes desirable to prune away such as seem inconsistent with his main doctrines, before those doctrines themselves are subjected to a critical scrutiny. Philosophic truth and falsehood, in short, rather than historical fact, are what primarily demand our attention (...) in this inquiry. (shrink)

This book traces the development of formal logic from its origins in ancient Greece to the present day. The authors first discuss the work of logicians from Aristotle to Frege, showing how they were influenced by the philosophical or mathematical ideas of their time. They then examine developments in the present century.

The two works reprinted in this volume are a unique fusion of logical thought and inimitable whimsy. Written by the 19th-century mathematician who also gave us "Alive in Wonderland", they are among the most entertaining logical works ever written, and contain some of the most thought-provoking puzzles ever devised.

The _Encyclopedia of American Philosophy_ provides coverage of the major figures, concepts, historical periods and traditions in American philosophical thought. Containing over 600 entries written by scholars who are experts in the field, this _Encyclopedia_ is the first of its kind. It is a scholarly reference work that is accessible to the ordinary reader by explaining complex ideas in simple terms and providing ample cross-references to facilitate further study. The _Encyclopedia of American Philosophy_ contains a thorough analytical index and will (...) serve as a standard, comprehensive reference work for universities and colleges. Topics covered include: Great philosophers: Emerson, Dewey, James, Royce, Peirce, Santayana Subjects: Pragmatism, Progress, the Future, Knowledge, Democracy, Growth, Truth Influences on American Philosophy: Hegel, Aristotle, Plato, British Enlightenment, Reformation Self-Assessments: Joe Margolis, Donald Davidson, Susan Haack, Peter Hare, John McDermott, Stanley Cavell Ethics: Value, Pleasure, Happiness, Duty, Judgment, Growth Political Philosophy: Declaration of Independence, Democracy, Freedom, Liberalism, Community, Identity. (shrink)

Although a succession of fashions swept the American philosophical scene, C. J. Ducasse was throughout his long career an effective practitioner of analytic philosophy in the classic tradition. As he explained in 1924 "[i]t is only with truths about such questions as the meaning of the term 'true', or 'real', or 'good', and the like . . . that philosophy is concerned. " Such truths are to be discovered inductively by comparing and analyzing concrete cases of the admittedly proper u/le (...) . . . The pressing problems of philosophy are thus in my view primarily problems of def'mition, and moreover, problems of framing def'mitions which must be in formal terms, under penalty of not being otherwise understandable by or acceptable to one or another philosophical school, since the formal elements of thought and tp. ey only are common to all schools. These def'mitions, of course are not to be arbitrary; their relation to the facts of admittedly meaningful linguistic usage is the same as exists between any scientific hypothesis and the facts which it attempts to 1 construe. (shrink)