In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...) axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is ᵎ x ᵎ for some set ᵎ) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. (shrink)

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...) axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. (shrink)

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...) correspondence language, so both can express the same input–output behavior of processes. (shrink)

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...) correspondence language, so both can express the same input-output behavior of processes. (shrink)

Rapid individual cognitive phenotyping holds the potential to revolutionize domains as wide‐ranging as personalized learning, employment practices, and precision psychiatry. Going beyond limitations imposed by traditional lab‐based experiments, new efforts have been underway toward greater ecological validity and participant diversity to capture the full range of individual differences in cognitive abilities and behaviors across the general population. Building on this, we developed Skill Lab, a novel game‐based tool that simultaneously assesses a broad suite of cognitive abilities while providing an engaging (...) narrative. Skill Lab consists of six mini‐games as well as 14 established cognitive ability tasks. Using a popular citizen science platform (N = 10,725), we conducted a comprehensive validation in the wild of a game‐based cognitive assessment suite. Based on the game and validation task data, we constructed reliable models to simultaneously predict eight cognitive abilities based on the users’ in‐game behavior. Follow‐up validation tests revealed that the models can discriminate nuances contained within each separate cognitive ability as well as capture a shared main factor of generalized cognitive ability. Our game‐based measures are five times faster to complete than the equivalent task‐based measures and replicate previous findings on the decline of certain cognitive abilities with age in our large cross‐sectional population sample (N = 6369). Taken together, our results demonstrate the feasibility of rapid in‐the‐wild systematic assessment of cognitive abilities as a promising first step toward population‐scale benchmarking and individualized mental health diagnostics. (shrink)

We investigate the possibility to characterize (multi) functions that are Σ b i -definable with small i (i = 1, 2, 3) in fragments of bounded arithmetic T 2 in terms of natural search problems defined over polynomial-time structures. We obtain the following results: (1) A reformulation of known characterizations of (multi)functions that are Σ b 1 - and Σ b 2 -definable in the theories S 1 2 and T 1 2 . (2) New characterizations of (multi)functions that are (...) Σ b 2 - and Σ b 3 -definable in the theory T 2 2 . (3) A new non-conservation result: the theory T 2 2 (α) is not ∀Σ b 1 (α)-conservative over the theory S 2 2 (α). To prove that the theory T 2 2 (α) is not ∀Σ b 1 (α)-conservative over the theory S 2 2 (α), we present two examples of a Σ b 1 (α)-principle separating the two theories: (a) the weak pigeonhole principle WPHP (a 2 , f, g) formalizing that no function f is a bijection between a 2 and a with the inverse g, (b) the iteration principle Iter (a, R, f) formalizing that no function f defined on a strict partial order ( $\{0,\dots,a\}$ , R) can have increasing iterates. (shrink)

This collection of essays, written on four continents by scientists, philosophers and humanists, was initially presented to Karl R. Popper on his sixtieth birthday as a token of critical admiration and in recognition of his work. But the volume also stands on its own as a remarkable series of statements utilizing Popper's critical vision in the study of philosophy proper, logic, mathematics, science as method and theory, and finally to the study of society and history. What is remarkable is that (...) Popper worked in all of these areas, not in a cursory or discursive way, but with the utmost clarity and rigor.. The core position of this volume and its contributors is that the progress of knowledge is not a linear accumulation of definitive acquisitions but a zigzagging process in which counterexamples and unfavorable evidence ruin generalizations and prompt the invention of more comprehensive and sometimes deeper generalizations, to be criticized in their turn. A critical approach to problems, procedures, and results in every field of inquiry is therefore a necessary condition for the continuance of progress. The title of this volume then is, in a sense, an homage to Popper's critical rationalism and critical empiricism. The essays are a tribute to his unceasing and uncompromising quest, not for final certainty, but for closer truth and increased clarity. Among the contributors are outstanding figures in philosophy and the exact sciences in their own right, including Herbert Feigl, R. M. Hare, J.O. Wisdom, Nicholas Rescher, David Bohm, Paul K. Feyerabend, F. A. Hayek, and Adolf Grunbaum. Social science contributions include Hans Albert on social science and moral philosophy, W. B. Gallie, on the critical philosophy of history, Pieter Geyl on The Open Society and its Enemies, and George H. Nadel on the philosophy of History. (shrink)

Designed to fill a large gap in American philosophy scholarship, this bibliography covers the first four decades of the pragmatic movement. It references most of the philosophical works by the twelve major figures of pragmatism: Charles S. Peirce, William James, John Dewey, George H. Mead, F.C.S. Schiller, Giovanni Papini, Giovanni Vailati, Guiseppe Prezzolini, Mario Calderoni, A.W. Moore, John E. Boodin, and C.I. Lewis. It also includes writings of dozens of minor pragmatic writers, along with those by commentators and critics (...) of pragmatism. It encompasses literature not only concerning pragmatism as an alliance of philosophical theories of meaning, inquiry, belief, knowledge, logic, truth, ontology, value, and morality, but also as an intellectual and cultural force impacting art, literature, education, the social and natural sciences, religion, and politics. This bibliography contains 2,794 main entries and more than 2,000 additional references, organized by year of publication. 2,101 of the references include annotation. Its international scope is focused on writings in English, French, German, and Italian, though many other languages are also represented. Peter H. Hare contributed the Guest Preface. The introduction contains an historical orientation to pragmatism and guides to recent studies of pragmatic figures. This work is extensively cross-referenced, and it has exhaustive and lengthy author and subject indexes. (shrink)

R F Dearden; Play and Pleasure, Journal of Philosophy of Education, Volume 5, Issue 1, 30 May 2006, Pages 37–41, https://doi.org/10.1111/j.1467-9752.1971.tb0044.

R F Dearden; Theory and Practice in Education, Journal of Philosophy of Education, Volume 14, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-.

In this monograph R. W. Beardsmore presents a lucid and readable presentation of what he takes moral reasoning to be and what he expects moral reasoning to accomplish. It is another in the long list of works which attempt to apply later-Wittgensteinian insights to the problems of ethics. The common moves run this way: Wittgenstein insists that to say that something is justified, or to say there are justifiable reasons for some position implies some fundamental agreement in our language game. (...) Moral argumentation can only take place within the context of a shared ethical language game. This moral viewpoint invests, what appear to be facts with value. According to Beardsmore the importance of shared moral viewpoints is missed by R. M. Hare with his dichotomizing of fact and value and his insistence on a decision of principle. Beardsmore also attacks the position of Phillipa Foot whom he sees on the opposite side of the issue from Hare. He sees Foot as insisting on the necessary dependence of values upon facts, which leads to her inability to account for changing moral viewpoints. Beardsmore tries to show that these views of Foot and Hare agree at least on one point, that there must be one specific way to give reasons for moral positions and hence solve moral disputes. Beardsmore has made a significant contribution by offering an illuminating application of Wittgenstein's insights to the problems of ethical theory. If they did nothing more, these insight's would be important in so far as they help to unlock the hold that the fact-value dichotomy has imposed on ethical theory for so long.--R. F. D. (shrink)

This spirited work is better Milton than ontology, cosmology and physics. Milton drew on many sources for the cosmic imagery of Paradise Lost, but he did not unite the traditions thoroughly. Curry is rather too kind to Milton, calling him syncretic when he is merely eclectic.--R.F.T.

In this group of well-written essays Randall discusses explicitly the group of ideas which have been implicit in his earlier works in intellectual history. The first section, which deals with the philosophy of history, argues that particular things have particular histories, and that these histories belong to them on the basis of what they are taken to be and expected to become. The metaphysics of the second section is a pluralistic analysis of actual experience and its symbolic representation.--R. F. T.

The first volume of this French textbook series to appear in English. Gardeil's exposition is usually in the form of a paraphrase of Thomas' conclusions on questions raised by Aristotle's De Anima, but he also treats the more peculiarly thomistic problems of knowledge of individuals, the soul, and God. The Value of this work as an introduction to Thomas' psychology is enhanced by the inclusion of almost sixty pages of texts in an appendix.--R. F. T.

Exercises in symbolization and problem-solving are provided in a format which allows space for completing the exercises and removing pages for easy correction.--R. F. T.

In this loosely organized study Hyma undertakes to correct almost every misstatement made about Luther in recent years. Although some of the individual items will be of interest to Luther specialists, the work as a whole makes no clear impression.--R. F. T.

In preparing this second edition of his commentary, Weldon has left the historical sections materially unaltered but has almost tripled the critical treatment. This leads to a far more valuable book, particularly since he has replaced long summary passages with systematic treatment of the issues Kant raises.--R. F. T.

Why Christianity, with its conception of agapé was successful in winning the allegiance of the late Romans is the question which leads Ferguson to his examination of the Homeric virtues and the Stoic morality. He finds the classical virtues are incapable of "providing that basis for an universal morality for which people were seeking" because they were each linked to a vanished society or failed to reach to the heart of men's moral strivings. His analysis of the pagan virtues is (...) less than sympathetic, though thoughtful and based on considerable learning.--R. F. T. (shrink)

This balanced and thorough study of the loyalty programs reviews the history of prosecutions and the dismissals under them, and makes detailed proposals for their revision.--R. F. T.

Moritz collects a number of rather elaborate bits of empirical evidence to refute Berkeley's subjectivism.--R. F. T.

A popular philosophy based on popularized science. Viscount Samuel puts forward a common-sense realism, but defends it with little more than the assertion that scientists cannot decide among themselves precisely what they want to put in its place. --R. F. T.

The acquisition by the Bodleian Library in 1948 of the Lovelace papers has made possible a number of historically oriented papers on Locke and his philosophy, e.g., J. Yolton's John Locke and the Way of Ideas, J. W. Gough's, Locke's Political Philosophy, and W. v.Leyden's publication of the Essays on the Law of Nature. Cranston's biography is a distinguished addition to this list: it makes full use of the source material and is as thorough as one could ask in revealing (...) the concerns--especially political concerns --of Locke's life. It is rather less satisfactory in its treatment of his epistemological development. --R. F. T. (shrink)

Molesworth's elementary text covers a good deal that would usually be called epistemology, treating logicians as varied as Socrates, Locke, and Russell. It tends to be conservative and sympathetic to the "classical" logic of the eighteenth and nineteenth centuries.--R. F. T.

Taking Locke's epistemology as a starting-point, Maine de Biran elaborated the notions of expectation of resistance and kinaesthetic response into a theory which attempted to account for the origin of our ideas of personal identity and causation. In this clear and intelligent study, Hallie compares Maine de Biran to the British empiricists, finding him most in sympathy with Berkeley; he also assesses the importance and limitations of this internal critique of empiricism for both empiricism and later French philosophy.--R. F. T.

ALTHOUGH THE IDEA OF A VIOLATION OF NATURAL LAW IS NOT NECESSARILY INVOLVED IN THE IDEA OF THE MIRACULOUS, THERE IS "ONE KIND" OF MIRACLE WHICH SEEMS TO INVOLVE IT. HUME’S DISCUSSION OF THE EVIDENCE FOR MIRACLES RELATES TO THIS KIND AND IS INTERPRETABLE AS AN ARGUMENT AGAINST ITS POSSIBILITY. ALSO THERE IS AN ARGUMENT THAT THE EXPRESSION "VIOLATION OF NATURAL LAW" SIGNIFIES A CONFUSION IN WHICH THE IDEAS OF NATURAL LAW AND LEGAL LAW COLLAPSE INTO EACH OTHER. NEITHER OF (...) THESE ARGUMENTS IS EFFICACIOUS. FURTHERMORE, THE CONTENTION THAT THERE CAN BE NO SUCH THING AS ESTABLISHING THE "ABSENCE" OF A NATURAL CAUSE IS OPEN TO OBJECTION. HOWEVER, TO BE CONCEIVED AS A VIOLATION OF NATURAL LAW, A MIRACLE MUST BE THOUGHT OF AS AN OCCURRENCE WHICH IS BOTH EMPIRICALLY CERTAIN AND CONCEPTUALLY IMPOSSIBLE--WHICH OUGHT TO MAKE THE NOTION RIDICULOUS. AND YET IT NEED NOT. (shrink)

This pioneer work in comparative political analysis manifests once more the growing influence of behavioral approaches on the study of politics. In this case the general topic is the voting pattern of justices on the highest courts of several Pacific nations and India. Various heuristic and explanatory models are employed to determine the influence of such variables as age, culture, and political orientation on the adjudicative behavior of these men over a determinate period. Although the articles by twelve different authors (...) are not all of the same analytic caliber as those contributed by the editors themselves, they collectively offer an insight into the possibilities as well as into the pitfalls of behavioral studies of the judiciary. As the editors note, such a work is necessarily hypothetical and exploratory, raising more questions than it answers. Philosophers will be interested mainly in the methodological problems of concept formation and explanation which this book raises and seeks to resolve. The article by Edward J. Weissman, "Mathematical Theory and Dynamic Models," is particularly valuable from that point of view. Moreover, by classifying and comparing the other contributions to this volume, Weissman's article furnishes a certain unity which the book as a whole sorely lacks. Geared primarily for those who are familiar with such techniques as smallest-space analysis and the use of recursive causal models, this work nevertheless can be read with profit by social philosophers, philosophers of law and those interested in general questions of methodology.--T. R. F. (shrink)

This is one of the best written and most comprehensive studies of the development of Sartre’s thought yet to appear in English, which is not to say that it covers every facet of his variegated career. Written by the former editor of Yale French Studies and current chairman of the Department of Romance Languages at Wesleyan University, Connecticut, it emphasizes Sartre’s literary works and thus belongs most properly in the category of literary criticism or the history of ideas. Still, McMahon (...) does not ignore Sartre’s philosophical writings. Indeed, he gives particular attention to The Critique of Dialectical Reason, a volume often avoided by authors who approach Sartre from a literary tradition. But the philosophic sources are usually consulted to explain or illustrate the literary, which provide the object of the author’s prime concern. McMahon underscores three concepts which measure Sartre’s intellectual growth, viz., freedom, love, and history. Regarding freedom, Sartre has "completed" the unfinished analyses of Being and Nothingness with their excessive individualism by his growing awareness that freedom is more than the ability to say "No" to the Other; it has a positive content and requires collective action to be maintained. Likewise, love is now conceived as a bond of promises which envisages the achievement of common projects. McMahon labels this rather cold-blooded concept "pragmatic love." Finally, history, which emerges as Sartre’s absolute, is now understood as a force conditioning men and limiting the availability of their choices. Sartre has come under the sway of Engels’ dictum: "Men make their history themselves, but they make it within a given milieu which conditions them." Sartre relies heavily upon the power of dialectic to keep individual choice afloat in a sea of historical forces. Whether or not he succeeds is a current question. McMahon believes that he does not. Because what he calls the "shift of emphasis" in Sartre’s thought from the individual to the social involves a growing interest in the sciences humaines, McMahon’s failure to consider Sartre’s political writings at any length is the chief disappointment of this excellent study. And then there is that stepchild of Sartriana, Existentialism is a Humanism. Following Cumming and others, McMahon chooses to ignore this essay, probably because Sartre himself has repudiated it. But if anyone is to portray Sartre "warts and all," and McMahon does not hesitate to expose the blemishes, then the reckless and inconsistent statements of this short lecture are most revealing. They indicate the freewheeling motions of a "shift" underway. Each chapter is followed by a short but helpful discussion of related themes and works. To capture the world of Jean-Paul Sartre is a most ambitious project. McMahon has met this challenge with insight and style.—T. R. F. (shrink)

Reading the Republic without reference to the less familiar Laws can lead to a distorted view of Plato's political theory. In the Republic the philosopher describes his ideal city; in his last and longest work he deals with the more detailed considerations involved in setting up a second-best 'practical utopia.' The relative neglect of the Laws has stemmed largely from the obscurity of its style and the apparent chaos of its organization so that, although good translations now exist, students of (...) philosophy and political science still find the text inaccessible. This first full-length philosophical introduction to the Laws will therefore prove invaluable. The opening chapters describe the general character of the dialogue and set it in the context of Plato's political philosophy as a whole. Each of the remaining chapters deals with a single topic, ranging over material scattered through the text and so drawing together the threads of the argument in a stimulating and readily comprehensible way. Those topics include education, punishment, responsibility, religion, virtue and pleasure as well as political matters and law itself. Throughout, the author encourages the reader to think critically about Plato's ideas and to see their relevance to present-day philosophical debate. No knowledge of Greek is required and only a limited background in philosophy. Although aimed primarily at students, the book will also be of interest to more advanced readers since it provides for the first time a philosophical, as opposed to linguistic or historical, commentary on the Laws in English. (shrink)

This Companion provides a fresh and comprehensive account of this outstanding work, which remains among the most frequently read works of Greek philosophy, indeed of Classical antiquity in general. The sixteen essays, by authors who represent various academic disciplines, bring a spectrum of interpretive approaches to bear in order to aid the understanding of a wide-ranging audience, from first-time readers of the Republic who require guidance, to more experienced readers who wish to explore contemporary currents in the work’s interpretation. The (...) three initial chapters address aspects of the work as a whole. They are followed by essays that match closely the sequence in which topics are presented in the ten books of the Republic. Since the Republic returns frequently to the same topics by different routes, so do the authors of this volume, who provide the readers with divergent yet complementary perspectives by which to appreciate the Republic’s principal concerns. (shrink)