Compares and contrasts Philip Kitcher's Ideal Agent account of mathematics with the constructibility view of this work. Raises a variety of doubts about the cogency of Kitcher's account and points out several weaknesses in the account.

Penelope Maddy has attempted to develop a form of realism in mathematics that is not plagued by the sort of epistemological problems that beset traditional Platonism. Maddy advances the radical doctrine that we can and do causally interact with sets. We can see them, feel them, smell them, and even taste them. This chapter raises a series of objections to Maddy's version of realism.

Concerns an attempted refutation of nominalism put forward by John Burgess in the form of a dilemma argument. Argues that Burgess's argument is based upon a false dilemma.

The PEIRCE EDITION contains large sections of previously unpublished material in addition to selected published works. Each volume includes a brief historical and biographical introduction, extensive editorial and textual notes, and a full chronological list of all of Peirce’s writings, published and unpublished, during the period covered.

"For anyone seriously interested in Peirce, or in nineteenth-century American philosophy, or in American intellectual history, or in philosophy in general, or in semiotics and its philosophical import, these volumes should be required reading." —Murray G. Murphey, Semiotica.

Focuses on Hartry Field's Instrumentalism. The ‘Conservation Theorems’, upon which Field bases so much of his form of Instrumentalism, are examined in detail, as is Field's attempt to ‘nominalize’ physics. Doubts are raised about the adequacy of Field's views of mathematics and physics, and a detailed comparison with the Constructibility Theory is presented.

Since the constructibility quantifiers, used in the mathematical system to be developed, will all assert the constructibility of open sentences, an explanation is given of the kinds of open sentences that will be asserted to be constructible. Each of these open sentences will be assigned to a specific ‘level’, depending on the kind of objects or open sentences that can satisfy it, thus providing the basis for the Simple Type Theoretical characteristic of the system to be developed. The satisfaction relation (...) under discussion will be taken to be a primitive of the system. The relevance of Quine's objections to modality for this system is taken up. (shrink)

Concerns the ‘problem of existence’ in mathematics: the problem of how to understand existence assertions in mathematics. The problem can best be understood by considering how Mathematical Platonists have understood such existence assertions. These philosophers have taken the existential theorems of mathematics as literally asserting the existence of mathematical objects. They have then attempted to account for the epistemological and metaphysical implications of such a position by putting forward arguments that supposedly show how humans can come to know of the (...) existence of mathematical objects. The reasoning of the most prominent philosophers in this Literalist tradition, Quine and Gödel, are critically discussed. By way of contrast, an alternative position, Heyting's Intuitionism, is examined. (shrink)

The fundamentals of cardinality theory are laid out within the framework of the Constructibility Theory. Finite cardinality theory is developed along the lines described by Frege in his Foundations of Arithmetic, and applications of theory are discussed.

Briefly sketches a standard form of the development of analysis within the Constructibility Theory. Then develops an axiomatized theory of lengths, in terms of which a system of rational and real numbers is specified. These developments are used to provide the basis for a theory of functions of real and complex variables.

The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here are those of Stewart Shapiro and Michael Resnik. A number of difficulties with these two views are detailed and it is explained how the Constructibility Theory is not troubled by the problems that Structuralism was explicitly developed to resolve.

Sketches the basic idea for the approach taken. A mathematical system is to be developed in which the existential theorems of traditional mathematics are to be replaced by constructibility theorems: where, in traditional mathematics, it is asserted that such and such exists, it will be asserted in this system that something or other can be constructed. Thus, constructibility quantifiers are introduced in this chapter as logical constants of formal systems. The logic of the constructibility quantifier is explained in each case (...) via possible worlds semantics, which is used as a didactic or heuristic device. (shrink)

The promised mathematical system—the Constructibility Theory—is presented as an axiomatized deductive theory formalized in a many‐sorted first‐order logical language. The axioms of the theory are specified and a justification for each of the axioms is given. Objections to the theory are considered.

The author explores recent cases involving Church closure, cancellation of historical figures, instructional materials in public schools, display of religious symbols on public land, and his current work defending the First Amendment rights of Christian bakers.

A compilation of selected papers presented at the 1989 Charles S. Pierce International Congress Interest in Charles Sanders Peirce (1839-1914) is today worldwide. Ernest Nagel of Columbia University wrote in 1959 that "there is a fair consensus among historians of ideas that Charles Sanders Peirce remains the most original, versatile, and comprehensive philosophical mind this country has yet produced." The breadth of topics discussed in the present volume suggests that this is as true today as it was (...) in 1959. Papers concerning Peirce's philosophy of science were given at the Harvard Congress by representatives from Italy, France, Sweden, Finland, Korea, India, Denmark, Greece, Brazil, Belgium, Spain, Germany, and the United States. The Charles S. Peirce Sesquicentennial International Congress opened at Harvard University on September 5, 1989, and concluded on the 10th—Peirce's birthday. The Congress was host to approximately 450 scholars from 26 different nations. The present volume is a compilation of selected papers presented at that Congress. The philosophy of science and its logic are themes in the work of Charles Peirce that have been of greatest interest to scholars. Peirce was himself a physical scientist. He worked as an assistant at the Harvard Astronomical Observatory from 1869 to 1872 and made a series of astronomical observations there from 1872 to 1875. Solon I. Bailey says of these observations, "The first attempt at the Harvard Observatory to determine the form of the Milky Way, or the galactic system, was made by Charles S. Peirce....The investigation was of a pioneer nature, founded on scant data." Peirce also made major contributions in fields as diverse as mathematical logic and psychology. C. I. Lewis has remarked that "the head and font of mathematical logic are found in the calculus of propositional functions as developed by Peirce and Schroeder." Peirce subsequently invented, almost from whole cloth, semiotics - the science of the meaning of signs. Ogden and Richards, the British critics, say that "by far the most elaborate and determined attempt to give an account of signs and their meanings is that of the American logician C. S. Peirce, from whom William James took the idea and the term Pragmatism, and whose Algebra of Dyadic Relations was developed by Schroeder.". (shrink)

Peirceana provides a forum for the best current work on Peirce worldwide. Besides monographs, the series will publish thematically unified anthologies and edited volumes with a defined topical focus and untranslated English selections of Peirce's writings.

Volume 8 of this landmark edition follows Peirce from May 1890 through July 1892—a period of turmoil as his career unraveled at the U.S. Coast and Geodetic Survey. The loss of his principal source of income meant the beginning of permanent penury and a lifelong struggle to find gainful employment. His key achievement during these years is his celebrated Monist metaphysical project, which consists of five classic articles on evolutionary cosmology. Also included are reviews and essays from The Nation in (...) which Peirce critiques Paul Carus, William James, Auguste Comte, Cesare Lombroso, and Karl Pearson, and takes part in a famous dispute between Francis E. Abbot and Josiah Royce. Peirce's short philosophical essays, studies in non-Euclidean geometry and number theory, and his only known experiment in prose fiction complete his production during these years. Peirce's 1883-1909 contributions to the Century Dictionary form the content of volume 7 which is forthcoming. (shrink)

"Highly recommended." —Choice "... an important event for the world of philosophy. For the first time we have available in an intelligible form the writings of one of the greatest philosophers of the past hundred years." —The Times Literary Supplement Volume 5 of this landmark edition covers an important transition in Peirce's life, marked by a rekindled enthusiasm for speculative philosophy. The writings include essays relating to his all-embracing theory of categories as well as papers on logic and mathematics.

Volume 6 of this landmark edition contains 66 writings mainly from the unsettled period in Peirce’s life just after he moved from New York to Milford, Pennsylvania, followed shortly afterward by the death of his mother. The writings in this volume reveal Peirce’s powerful mind probing into diverse issues, looking for an underlying unity, but, perhaps, also looking for direction.

The PEIRCE EDITION contains large sections of previously unpublished material in addition to selected published works. Each volume includes a brief historical and biographical introduction, extensive editorial and textual notes, and a full chronological list of all of Peirce’s writings, published and unpublished, during the period covered.

"The volumes are handsomely produced and carefully edited,... For the first time we have available in an intelligible form the writings of one of the greatest philosophers of the past hundred years... " —The Times Literary Supplement "... an extremely handsome and impressive book; it is an equally impressive piece of scholarship and editing." —Man and World.

v. 1-2. Principles of philosophy and Elements of logic.--v. 3-4. Exact logic (published papers) and The simplest mathematics.--v. 5-6. Pragmatism and pragmaticism and Scientific metaphysics.--v. 7. Science and philosophy.--v. 8. Reviews, correspondence and bibliography.

Arranged and integrated to reveal epistemology, phenomenology, theory of signs, other major topics.

This book presents a thorough overview of a model of human functioning based on the idea that behavior is goal-directed and regulated by feedback control processes. It describes feedback processes and their application to behavior, considers goals and the idea that goals are organized hierarchically, examines affect as deriving from a different kind of feedback process, and analyzes how success expectancies influence whether people keep trying to attain goals or disengage. Later sections consider a series of emerging themes, including dynamic (...) systems as a model for shifting among goals, catastrophe theory as a model for persistence, and the question of whether behavior is controlled or instead 'emerges'. Three chapters consider the implications of these various ideas for understanding maladaptive behavior, and the closing chapter asks whether goals are a necessity of life. Throughout, theory is presented in the context of diverse issues that link the theory to other literatures. (shrink)

This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

We propose a model of motivated skepticism that helps explain when and why citizens are biased information processors. Two experimental studies explore how citizens evaluate arguments about affirmative action and gun control, finding strong evidence of a prior attitude effect such that attitudinally congruent arguments are evaluated as stronger than attitudinally incongruent arguments. When reading pro and con arguments, participants (Ps) counterargue the contrary arguments and uncritically accept supporting arguments, evidence of a disconfirmation bias. We also find a confirmation bias—the (...) seeking out of confirmatory evidence—when Ps are free to self-select the source of the arguments they read. Both the confirmation and disconfirmation biases lead to attitude polarization—the strengthening of t2 over t1 attitudes—especially among those with the strongest priors and highest levels of political sophistication. We conclude with a discussion of the normative implications of these findings for rational behavior in a democracy. (shrink)

We propose a model of motivated skepticism that helps explain when and why citizens are biased information processors. Two experimental studies explore how citizens evaluate arguments about affirmative action and gun control, finding strong evidence of a prior attitude effect such that attitudinally congruent arguments are evaluated as stronger than attitudinally incongruent arguments. When reading pro and con arguments, participants (Ps) counterargue the contrary arguments and uncritically accept supporting arguments, evidence of a disconfirmation bias. We also find a confirmation bias—the (...) seeking out of confirmatory evidence—when Ps are free to self-select the source of the arguments they read. Both the confirmation and disconfirmation biases lead to attitude polarization—the strengthening of t2 over t1 attitudes—especially among those with the strongest priors and highest levels of political sophistication. We conclude with a discussion of the normative implications of these findings for rational behavior in a democracy. (shrink)