According to the traditional account Mendel's paper on pea hybrids reported a study of inheritance and its laws. Hence, Mendel came to be known as The Father of Genetics. This paper demonstrates that, in fact, Mendel's objective in his research was finding the empirical laws which describe the formation of hybrids and the development of their offspring over several generations. Having found these laws (and not the laws of inheritance that he is generally credited with) he proposed a theoretical scheme (...) involving the formation of germinal and pollen cells in hybrids and their combination in fertilization competent to explain why his laws took the form that they did. Mendel's research shows a pattern of development closely paralleling the stages of empirical investigation beginning at the level of qualitative description in common language rising through four levels of increasing abstraction and culminating in a fifth level, his simple mechanical theory. This mechanism met all the tests that a theory of this type must pass. In that respect Mendel was highly successful and this success might be the reason why he did not push his theory to a higher level, a sixth level involving the use of particulate determiners; despite this fact, Mendel was credited with having taken exactly that step. (shrink)

A survey of the emergence of early analytic philosophy as a subfield of the history of philosophy. The importance of recent literature on Frege, Russell, and Wittgenstein is stressed, as is the widening interest in understanding the nineteenth-century scientific and Kantian backgrounds. In contrast to recent histories of early analytic philosophy by P.M.S. Hacker and Scott Soames, the importance of historical and philosophical work on the significance of formalization is highlighted, as are the contributions made by those focusing on systematic (...) treatments of individual philosophers, traditions, and periods in relation to contemporary issues (rule-following, neo-Fregeanism, contextualism, theory of meaning). (shrink)

A survey of current evidence available concerning Wittgenstein's attitude toward, and knowledge of, Gödel's first incompleteness theorem, including his discussions with Turing, Watson and others in 1937–1939, and later testimony of Goodstein and Kreisel; 2) Discussion of the philosophical and historical importance of Wittgenstein's attitude toward Gödel's and other theorems in mathematical logic, contrasting this attitude with that of, e.g., Penrose; 3) Replies to an instructive criticism of my 1995 paper by Mark Steiner which assesses the importance of Tarski's semantical (...) work, both for our understanding of Wittgenstein's remarks on Gödel, and our understanding of Gödel's theorem itself. (shrink)

A survey of Wittgenstein's writings on logic and mathematics; an analytical bibliography of contemporary articles on rule-following, social constructivism, Wittgenstein, Godel, and constructivism is appended. Various historical accounts of the nature of mathematical knowledge glossed over the effects of linguistic expression on our understanding of its status and content. Initially Wittgenstein rejected Frege's and Russell's logicism, aiming to operationalize the notions of logical consequence, necessity and sense. Vienna positivists took this to place analysis of meaning at the heart of philosophy, (...) while Ramey took extensionalism to result. Wittgenstein's interest in rule-following emerged through his reactions to these attempted appropriations. (shrink)

Gilbert Meilaender argues that universities should eschew efforts to improve students’ moral character. I show that Meilaender’s arguments fail to offer any cogent reason for shunning university-based moral education. I then look to Thomas Aquinas in order to explain the connection between moral virtue and the practices common in university life. Using Aquinas as a guide, I argue that exemplary intellectual practice requires virtues that are subsidiary habits of the cardinal moral virtues themselves. The implication of this argument is as (...) follows: students require scrupulous moral training if they are to engage in exemplary intellectual practice. (shrink)

Turing was a philosopher of logic and mathematics, as well as a mathematician. His work throughout his life owed much to the Cambridge milieu in which he was educated and to which he returned throughout his life. A rich and distinctive tradition discussing how the notion of “common sense” relates to the foundations of logic was being developed during Turing’s undergraduate days, most intensively by Wittgenstein, whose exchanges with Russell, Ramsey, Sraffa, Hardy, Littlewood and others formed part of the backdrop (...) which shaped Turing’s work. Beginning with a Moral Sciences Club talk in 1933, Turing developed an “anthropological” approach to the foundations of logic, influenced by Wittgenstein, in which “common sense” plays a foundational role. This may be seen not only in “On Computable Numbers” and Turing’s dissertation ), but in his exchanges with Wittgenstein in 1939 and in two later papers, “The Reform of Mathematical Phraseology and Notation” and “Solvable and Unsolvable Problems”. (shrink)

How to model meaning processes (semiosis) in artificial semiotic systems? Once all computer simulation becomes tantamount to theoretical simulation, involving epistemological metaphors of world versions, the selection and choice of models will dramatically compromise the nature of all work involving simulation. According to the pragmatic Peircean based approach, semiosis is an interpreter-dependent process that cannot be dissociated from the notion of a situated (and actively distributed) communicational agent. Our approach centers on the consideration of relevant properties and aspects of Peirce’s (...) pragmatic concept of semiotics. Upon developing this approach, we have no pretensions of our being able to present an exhaustive analysis of the differences between Peirce and other theoretical positions. Nevertheless, our contribution will serve to demonstrate how theorists contribute toward revealing certain fundamental ‘semiotic constraints’ that will be of interest and importance. (shrink)

Paul Signac and Color in Neo-Impressionism is a groundbreaking examination of the artistic technique of "divisionism" in terms of modern scientific theory of color. Truly interdisciplinary in his approach, Floyd Ratliff treats the evolution of both color theory and artistic practice in an integrated way. Signac was the principal advocate for the new movement launched by Georges Seurat in the 1880s. The book is handsomely illustrated with both Neo-Impressionist paintings and scientific drawings and diagrams. Ratliff's five-part essay provides an (...) extended introduction to a translation of Signac's monograph, From Eugene Delacroix to Neo-Impressionism, widely regarded as the basic document of the movement, but never before available in English. This will be an invaluable reference for scholars in art and design, as well as students of the psychology and neurophysiology of color vision and those interested in the relation between the arts and the sciences. Its clarity of style also makes it accessible to the general reader interested in art history, painting, or the perception of color, particularly with its glossary of technical and art terms, index, and bibliography. (shrink)

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the trajectories of the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function’s trajectory. The quantum effective (...) mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality. (shrink)

A look at Wittgenstein's comments on the incompleteness theorem with an inter-pretation that is consistent with what Gödel proved.

This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his later (...) remarks on _Lebensformen_ is offered which factors in his reading of Alan Turing’s “On computable numbers, with an application to the _Entscheidungsproblem_“, as well as his discussions with Turing 1937-1939. An interpretation of the five occurrences of _Lebensform_ in the PI is then given in terms of a logical “regression” to _Lebensform_ as a fundamental notion. This regression characterizes Wittgenstein’s mature answer to the question, “What is the nature of the logical?”. (shrink)

C.S. Peirce, the founder of pragmatism, was an American philosopher and mathematician whose influence has been enormous on the field of semiotics. Merrell uses Pierce's theories to reply to the all-important question: "What and where is meaning?".

Contemporary philosophers often construe mercy as a supererogatory notion or a matter of punitive leniency. Yet it is false that no merciful actions are obligatory. Further, it is questionable whether mercy is really about punitive leniency, either exclusively or primarily. As an alternative to these accounts, I consider the view offered by St. Thomas Aquinas. He rejects the claim that we are never obligated to be merciful. Also, his view of mercy is not restricted to legal contexts. For him, mercy's (...) scope is considerably broader, as it concerns a wide range of needs and hardships to which human beings are vulnerable. Such a view, I submit, affords a kind of normative depth lacking in many contemporary accounts. Unlike those views that construe mercy as either a supererogatory or legal concept, Aquinas's account illuminates mercy's obligatory nature and encourages us to make mercy a more salient fixture of our moral lives. (shrink)

This paper brings Lotman's semiotic space to bear on Peirce's categories of the universe's processes. Particular manifestations of cultural semiotic space within the semiosphere are qualified as inconsistent and/or incomplete, depending upon the cultural context. Inconsistency and incompleteness are of the nature of vagueness and generality respectively, that are themselves qualified in terms of overdetermination and underdetermination, the first being of the nature of the category of Firstness and the second of the nature Thirdness. The role of Secondness is unfolded (...) by acts of distinguishing the possibilities of Firstness into this and that, here and there, there and then, and all the distinctions that follow. Secondness, then, with respect to cultural semiotic space, gives rise to hegemony, to dominance and subervience, superordination and subordination. Commensurate with this interpretation of Secondness, the realms of overdetermination and underdetermination are labeled homogeny and heterogeny respectively. These theoretical assumptions will then be used as a modeling device providing an interpretation for various key aspects of Latin American cultures. (shrink)

Three premises set the stage for a Peirce based notion of resemblance, which, as Firstness, cannot be more than vaguely distinguished from Secondnessand Thirdness. Inclusion of Firstness with, and within, Secondness and Thirdness, calls for a nonbivalent, nonlinear, context dependent mode of thinkingcharacteristic of semiosis — that is, the process by which everything is always becoming something other than what it was becoming — and at the same time itincludes linear, bivalent classical logic as a subset. Certain aspects of the (...) Dao, Buddhist philosophy, and Donald Davidson’s ‘radical interpretation’ affordadditional, and perhaps unexpected, support for the initial set of three premises. (shrink)

Three premises set the stage for a Peirce based notion of resemblance, which, as Firstness, cannot be more than vaguely distinguished from Secondness and Thirdness. Inclusion of Firstness with, and within, Secondness and Thirdness, calls for a nonbivalent, nonlinear, context dependent mode of thinking characteristic of semiosis — that is, the process by which everything is always becoming something other than what it was becoming — and at the same time it includes linear, bivalent classical logic as a subset. Certain (...) aspects of the Dao, Buddhist philosophy, and Donald Davidson’s ‘radical interpretation’ afford additional, and perhaps unexpected, support for the initial set of three premises. (shrink)

In 1969 Stanley Cavell's Must We Mean What We Say? revolutionized philosophy of ordinary language, aesthetics, ethics, tragedy, literature, music, art criticism, and modernism. This volume of new essays offers a multi-faceted exploration of Cavell's first and most important book, fifty years after its publication. The key subjects which animate Cavell's book are explored in detail: ordinary language, aesthetics, modernism, skepticism, forms of life, philosophy and literature, tragedy and the self, the questions of voice and audience, jazz and sound, Wittgenstein, (...) Austin, Beckett, Kierkegaard, Shakespeare. The essays make Cavell's complex style and sometimes difficult thought accessible to a new generation of students and scholars. They offer a way into Cavell's unique philosophical voice, conveying its seminal importance as an intellectual intervention in American thought and culture, and showing how its philosophical radicality remains of lasting significance for contemporary philosophy, American philosophy, literary studies, and cultural studies. (shrink)

Bevir?s view that theories are prior to theorists, just in so far as they are prior to any observations which one might make and, by extension, any facts which one might invoke in support of any particular interpretative conclusions, is problematic when applied to intellectual history, for although it is in one sense true that all facts are ineluctably constituted by some or other underlying theory, it is also true that, in a vast number of important situations, all human beings (...) share the same basic theory. The most important implication of this shared stock of concepts, observations and facts, is that we shall often be able to see numerous aspects of a long?dead author?s world in much the same way as he or she saw it. (shrink)

Peirce’s occasional allusion to what he calls ‘nothingness’ motivates this dialogue. The dialogue consists of two interlocutors deliberating over the notion, implicit in recent mathematics, science, logic, and philosophy, and patterned in literature and the arts, of life, and the physical universe as a whole, as a process of self-reflexive, interdependent, interrelated, interactive self-organization, from ‘nothingness’ to what is construed as what is.

O presente artigo procede, em primeiro lugar, a um exame das evidências disponíveis referentes à atitude de Wittgenstein em relação ao, bem como conhecimento do, primeiro teorema da incompletude de Gödel, incluindo as suas discussões com Turing, Watson e outros em 1937-1939, e o testemunho posterior de Goodstein e Kreisel Em segundo lugar, o artigo discute a importância filosófica e histórica da atitude de Wittgenstein em relação ao teorema de Gödel e outros teoremas da lógica matemática, contrastando esta atitude com (...) a de, por exemplo, Penrose. Finalmente, a autora responde também a criticas instrutivas feitas por Mark Steiner a um artigo seu publicado em 1995, as quais estabelecem a importância do trabalho semântico de Tarski, quer para o nosso entendimento das observacoes de Wittgenstein. /// This paper presents, first, a survey of current evidence available concerning Wittgenstein's attitude toward, and knowledge of, Gödel's first incompleteness theorem, including his discussions with Turing, Watson and others in 1937-1939, and later testimony of Goodstein and Kreisel Secondly, the article discusses the philosophical and historical importance of Wittgenstein's attitude toward Gödal's and other theorems in mathematical logic, contrasting this attitude with that of, e. g., Penrose. Finally, the author also replies to an instructive criticism of her 1995 paper by Mark Steiner which assesses the importance ofTarskih semantical work, both for our understanding of Wittgenstein's remarks on Godel, and our understanding ofGodeVs theorem itself. (shrink)

In 1991 Nancy Floyd bought her first handgun. Soon she was participating in Ladies Day at her local shooting range and reading Women & Guns magazine. In 1993 she began interviewing and photographing women who were fellow gun owners. In 1997 she started researching "gun women" from the past to see how they were represented in the popular imagination. Now she has brought her work together in a book, filled with remarkable photographs and candid first-person stories, accompanied by an (...) eye-opening illustrated history of female gun ownership in America. Sympathetic but unsentimental, Floyd presents gun-toting women young and old, including an eleven-year-old girl competing in her first gun competition, a woman whose grandmother was killed by an intruder, and a war veteran who experienced firefights while stationed in Iraq. Whatever you might think about gun-toting women before you open this book, your preconceptions are sure to be shattered by the end.--From publisher description. (shrink)

Idiots burn books for the same reason philosophers write them – they matter. But why exactly do political philosophy books matter, not to mention the hundreds of articles published every year? In part because they are interesting, but also because they are influential. They are mind-altering and, in turn, world-altering. Political philosophers write their books for the same reason political revolutionaries read them – they change the world. In this short and original book, Jonathan Floyd explains three things: what (...) political philosophy is, how you can do it, and why you might want to. Accessibly written for those coming to the subject for the first time, it is also a must-read for scholars whose research takes in the nature, methods, and purposes of their field. It is also a must-burn for anyone who dreams of a dumber, thicker, less enlightened world. (shrink)

Throughout his philosophy of mathematics, Steiner’s views bear affinities and contrasts with those of Wittgenstein. From his early insistence on an intelligible notion of mathematical “explanation”, to his remarks on the necessity of certain extensions of mathematical concepts, to his analysis of the ideas of logicism, “surveyability” and “applicability” in mathematics and his reading of Kripke on rule-following, Steiner probed fundamental issues in contemporary philosophy of mathematics. This essay responds to Steiner’s interpretations of Wittgenstein, focusing especially on his Humean reading (...) of rules as “hardened” regularities. (shrink)

For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics grew from his Early and Middle philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.

The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action, trajectories and loci of transit times are developed in the region near the two point sources. The trajectory through any point in Euclidean 3-space also passes simultaneously through both point sources.

While postmodernists have claimed that the failure of the Enlightenment was a failure of philosophical courage, this plenary address explores how its greatest shortcoming actually was its hubris. Paying attention to how Western scholars have centered pride in their elitist purview was their ultimate worldview, this article examines ‘pride’ as the doctrinal dimension of the good life in contemporary Western society and culture. Furthermore, it implores postmodern Christian social ethicists to reform their stewardship to the telos of the field's highest (...) ideals and role, in order to confront the shortcomings of the Enlightenment and help realize its greater capacity for social transformation. Borrowing the Gandhian critique of ‘knowledge without character’, the author surveys how the existential crisis of higher education, the political manipulation of journalism, and the policy practices of politicians, public intellectuals, and pundits operate in addressing post-imperial/postmodern legacies have legitimated implicit biases and dehumanizing projects that pass off stereotypes as scholarship and hate as hermeneutics. (shrink)

Wittgenstein's treatment of number words and arithmetic in the Tractatus reflects central features of his early conception of philosophy. In rejecting Frege's and Russell's analyses of number, Wittgenstein rejects their respective conceptions of function, object, logical form, generality, sentence, and thought. He, thereby, surrenders their shared ideal of the clarity a Begriffsschrift could bring to philosophy. The development of early analytic philosophy thus evinces far less continuity than some readers of Wittgenstein, from Russell and the Vienna positivists to many contemporary (...) readers of the Tractatus, have supposed. (shrink)

Three premises set the stage for a Peirce based notion of resemblance, which, as Firstness, cannot be more than vaguely distinguished from Secondnessand Thirdness. Inclusion of Firstness with, and within, Secondness and Thirdness, calls for a nonbivalent, nonlinear, context dependent mode of thinkingcharacteristic of semiosis — that is, the process by which everything is always becoming something other than what it was becoming — and at the same time itincludes linear, bivalent classical logic as a subset. Certain aspects of the (...) Dao, Buddhist philosophy, and Donald Davidson’s ‘radical interpretation’ affordadditional, and perhaps unexpected, support for the initial set of three premises. (shrink)

When is it permissible to move an issue out of normal politics and treat it as a security issue? How should the security measures be conducted? When and how should the securitization be reversed? Floyd offers answers to these questions by combining security studies' influential securitization theory with philosophy's long-standing just war tradition, creating a major new approach to the ethics of security: 'Just Securitization Theory'. Of interest to anyone concerned with ethics and security, Floyd's innovative approach enables (...) scholars to normatively evaluate past and present securitizations, equips practitioners to make informed judgements on what they ought to do in relevant situations, and empowers the public to hold relevant actors accountable for how they view security. (shrink)

This volume presents an historical and philosophical revisiting of the foundational character of Turing's conceptual contributions and assesses the impact of the work of Alan Turing on the history and philosophy of science. Written by experts from a variety of disciplines, the book draws out the continuing significance of Turing's work. The centennial of Turing's birth in 2012 led to the highly celebrated "Alan Turing Year", which stimulated a world-wide cooperative, interdisciplinary revisiting of his life and work. Turing is widely (...) regarded as one of the most important scientists of the twentieth century: He is the father of artificial intelligence, resolver of Hilbert's famous Entscheidungsproblem, and a code breaker who helped solve the Enigma code. His work revolutionized the very architecture of science by way of the results he obtained in logic, probability and recursion theory, morphogenesis, the foundations of cognitive psychology, mathematics, and cryptography. Many of Turing's breakthroughs were stimulated by his deep reflections on fundamental philosophical issues. Hence it is fitting that there be a volume dedicated to the philosophical impact of his work. One important strand of Turing's work is his analysis of the concept of computability, which has unquestionably come to play a central conceptual role in nearly every branch of knowledge and engineering. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Inventing Philosophy’s Other: Phenomenology in America by Jonathan StrassfeldGregory FloydSTRASSFELD, Jonathan. Inventing Philosophy’s Other: Phenomenology in America. Chicago: The University of Chicago Press, 2022. 363 pp. Cloth, $95.00; paper, $30.00Recent years have witnessed an increase in scholarly attention paid to the intellectual history and development of socalled Continental philosophy. That attention has turned to not only key figures and philosophical schools but also to the historical factors, social (...) conditions, and institutions that have aided, hindered, and otherwise directed its itinerary across the European continent and eventual migration to the “new world.” Edward Baring’s Converts to the Real: Catholicism and the Making of Continental Philosophy (Harvard University Press, 2019) is a well-researched and intricate account of the European development of phenomenology’s growth from “a provincial philosophy of southwest Germany into a movement that spanned Europe.” Baring argues convincingly that European networks of Catholic scholars and institutions were essential to the dissemination of the ideas and works of early phenomenologists, and his work offers a salutary reappraisal of neoscholasticism as a vibrant, internally diverse, and philosophically sophisticated movement attentive to and engaged in the dominant questions of its day. The various contributors to the 2020 volume, The Catholic Reception of Continental Philosophy in North America (University of Toronto Press) take up the story as it begins again amid American and Canadian Catholic institutions of higher learning. They offer an extended account of the historical, institutional, and conceptual relationships between Catholicism and Continental philosophy on North American soil up to the present day.To these, Jonathan Strassfeld’s Inventing Philosophy’s Other: Phenomenology in America offers a necessary complement. Strassfeld tells another and essential side of the story focused on eleven “elite” universities—Harvard in particular—and the way in which American scholars in the first half of the century and European émigrés in the second half set the conditions for an at times fruitful at times fraught engagement with Continental thought in America. Key to that analysis is the contention that in the first half of the twentieth century, Harvard and other leading institutions that would later become bastions of analytic philosophy were the first to take interest in phenomenology sending scholars to study with its founders and engaging a tradition that they [End Page 366] “encountered as a work in progress” and as possessing natural points of contact with various strands of American philosophy such as new realism, critical realism, pragmatism, and the philosophy of language.Strassfeld then documents the reversal of that early philosophical pluralism and the foreclosure of the possibility of philosophical integration due to the rapid ascendancy of analytic philosophy between 1950 and 1969, showing that foreclosure to be neither a necessary outcome nor the triumph of a superior philosophical approach: “[B]oth the intra-university mandates of new interdisciplinary formations and changing inter-university dynamics of hiring and promotion after World War II transformed the ecosystem of philosophical reproduction catalyzing the rise of analysis and decline of humanistic pluralism in American philosophy.”The consequence of the decrease in faculty specializing in phenomenological and Continental areas from elite institutions was twofold. First, Continental philosophy increasingly “relied on a network of departments and organizations that were defined by the resistance to the practice and influence of mainstream American philosophy.” Second, it became of increasing interest to nonphilosophical disciplines such as sociology, psychology, geography, architecture, and anthropology, which sought to transcend culturally ascendant forms of scientific reductivism. In both ways, Strassfeld argues, Continental thought became “an unassimilated other” within the American academy.In telling this story, Inventing Philosophy’s Other uses a distinctive alphanumeric structure. One set of numbered chapters introduces the essential doctrines and early figures of phenomenology and chronicles its varied transpositions on American soil. These numbered chapters are punctuated by a set of shorter alphabetic chapters that present portraits of American-born or expatriated phenomenologists. The dual structure of the work tells the story of phenomenology in America along two axes: an intellectual history of ideas, institutions, and social practices as well as an interpenetrating history of constitutive figures.A major strength of Strassfeld’s work is that he brings a historian’s care... (shrink)