This paper gives two complete and elementary proofs that if the speed of light over closed paths has a universal value c, then it is possible to synchronize clocks in such a way that the one-way speed of light is c. The first proof is an elementary version of a recent proof. The second provides high precision experimental evidence that it is possible to synchronize clocks in such a way that the one-way speed of light has a universal value. We (...) also discuss an old incomplete proof by Weyl which is important from an historical perspective. (shrink)

This paper gives two complete and elementary proofs that if the speed of light over closed paths has a universal value c, then it is possible to synchronize clocks in such a way that the one-way speed of light is c. The first proof is an elementary version of a recent proof. The second provides high precision experimental evidence that it is possible to synchronize clocks in such a way that the one-way speed of light has a universal value. We (...) also discuss an old incomplete proof by Weyl which is important from an historical perspective. (shrink)

The strongly innovative theory of whole-parts relations outlined by Husserl in his Third logical Investigation—to which he attributed a basic value for his entire phenomenology—has recently attracted a renewed interest. Although many important issues have been clarified (especially by Kit Fine) the subject seems still worth being revisited. To this aim Husserlian universes are introduced. These are lower bounded distributive lattices endowed with a unary operation of defect and a binary relation of isogeneity. Husserl's contents are identified with nonzero elements (...) of a Husserlian universe and the dependence relations among contents are defined and studied starting from the idea that the defect of xis what x needs in order to ‘exist’ i.e., in order to be ‘closed’ with respect to the closure operation defined as the sup of x and its defect. It turns out that there are (at least) eight dependence relations which are worth to be considered. Many other questions concerning the world of contents (among them the proofs of the famous Husserl's Sätze) may now be discussed and clarified. Then the theory of species and genera is developed. Ultimate species (for short: species) are identified with equivalence classes of contents modulo isogeneity, and species in general (for short: genera) are identified with arbitrary unions of species. On the basis of the relation obtaining among two contents when they are isogeneous to two contents the first of which is a part of the second it becomes possible to develop a rather satisfying interpretation of Husserl's theory of the dependencies among species and genera and of the material a priori laws. By strengthening the notion of Husserlian universe into the notion of rigid Husserlian universe, the theory of species and genera obtains a stronger version. Three models of the theory are exhibited. The first one, suggested by combinatorial-topological considerations, identifies contents with finite non-empty sets of natural numbers; the second one identifies contents with non-empty sets of formulas of a formal language; the third one (not totally ‘rigid’) identifies contents with positive integers. (shrink)

At the beginning of his influential De Nominum Analogia, Thomas de Vio Cajetan mentions three mistaken positions on analogy. He does not attach names to these positions, but each one was held by distinguished Thomists of the fourteenth and fifteenth centuries. Furthermore, their proponents were responding to the same set of challenges from John Duns Scotus that set the agenda for the De Nominum Analogia. In this paper, I would like to do something that Cajetan did not do, and that (...) is, directly consider the merits of the first position in his list of mistaken accounts of analogy; namely, the position that analogy is constituted by disjunction. More specifically, this paper investigates the polemical use for which Hervaeus Natalis deployed analogy of disjunction; the reply of John Duns Scotus; and the implications of this back and forth for understanding the Thomist-Scotist dispute over the concept of being. (shrink)

The mental representation of one’s own body does not necessarily correspond to the physical body. For instance, a dissociation between perceived and actual reach-ability has been shown, that is, individuals perceive that they can reach objects that are out of grasp. We presented participants with 3D pictures of objects located at four different distances, namely near-reaching space, actual-reaching space, perceived-reaching space and non-reaching space. Immediately after they were presented with function, manipulation, observation or pointing verbs and were required to judge (...) if the verb was compatible with the object.Participants were faster with function and manipulation verbs than with observation and pointing verbs. Strikingly, with both function and manipulation verbs participants were faster when objects were presented in actual than the perceived reaching space. These findings suggest that our knowledge of the world is implicitly built online through behaviour, and is not necessarily reflected in explicit estimates or conscious representations. (shrink)

This article considers the attempt by a prominent fifteenth-century follower of Thomas Aquinas, Dominic of Flanders, to address John Duns Scotus’ most famous argument for the univocity of being. According to Scotus, the intellect must have a concept of being that is univocal to substantial and accidental being, and to finite and infinite being, on the grounds that an intellect cannot be both certain and doubtful through the same concept, but an intellect can be certain that something is a being (...) while doubting whether it is a substance or accident, finite or infinite. The article shows how Flandrensis’ reply in defence of analogy of being hinges on a more fundamental disagreement with Scotus over the division of the logically one. It also shows how Flandrensis’ answer to this question commits him to a position on the unity of the concept of being that lies between the positions of Scotus and of Flandrensis’ earlier Thomistic sources. (shrink)

This book is focused on the first three parts of Bolzano's Theory of Science and introduces a more systematic reconsideration of Bolzano's logical thought. In undertaking this task, the book is intended as an exploration, not so much of the more specifically discursive aspects of Bolzano's logical thought - already amply studied - as much as on identifying the singularly coherent and systematic nature of the logic presented in Bolzano's work.

Logic was understood by the Stoics in a broad sense, as the doctrine that included analysis of the forms of argumentation, rhetoric, theory of concepts and propositions, epistemology, and philosophy of language. The distinguishing characteristic of Stoic logic is the fact that it is fundamentally a logic of propositions, unlike the logic of terms belonging to the Aristotelian tradition. This study offers a new treatment of Stoic logic, in which the various topics are retraced and critically assessed.

By analysing the policies and ideas of German social democracy, the British Labour Party and the Italian Communist Party, this article explores their attitude towards science and their imagination of the future in the 1950s. Deeply different, social democrats and communists shared a positivist attitude in favour of scientific progress and high modernity. This painted their attitude towards the space race, peaceful nuclear power and automation. Science was conceived as a neutral power to be supported, but it required political guidance (...) to harness it and turned it into social progress. Thus, their disagreement was over the political implications for capitalist societies experiencing growing prosperity. Science was also a powerful rhetorical argument to castigate the conservatives for failing the nation and allowing it to decline and fall behind its competitors. The article combines comparison and transnational history, innovating the latter by introducing the concepts of horizontal, vertical and antagonistic transnationalism. (shrink)

Fifty-plus years ago, Ralph McInerny’s The Logic of Analogy characterized Francis Silvestri of Ferrara’s doctrine of analogy as a confusing hybrid of the thought of Thomas Aquinas and of Thomas Cajetan. Since then, scholarship on fifteenth-century Thomism has flourished, thanks especially to the efforts of Ashworth, Bonino, Hochschild, Riva, and Tavuzzi. In light of these decades of scholarship, in this article I reconsider Francis Silvestri’s doctrine of analogy. I attempt to show the merits of his contribution to the Thomist tradition’s (...) ongoing reflection on analogy, especially the dispute among Thomists and with Scotists over abstracting an analogous concept, the unity of the concept used analogously, and the use of analogy in demonstration. I argue that Francis’s hybrid succeeds in finding a place for analogy of attribution in names said analogously of God and creatures while still meeting Cajetan’s standards for answering Scotist objections to demonstration through analogous terms. (shrink)

Thomas de Vio Cajetan produced a highly influential Thomistic treatise on analogy entitled De nominum analogia. The merits of this work have been contested since the sixteenth century. Notable twentieth-century Thomists who adopted many of the teachings of De nominum analogia include Jacques Maritain and Yves Simon. Joshua Hochschild’s The Semantics of Analogy highlighted the significance of chapter ten, where Cajetan applies his theory to resolve the problem of demonstrations that use analogous terms, with the explicit purpose of addressing a (...) serious challenge from Scotists regarding the use of analogy in metaphysics. This paper examines the criticism of Cajetan’s way of using analogous terms in demonstrations by the seventeenth-century Franciscan Scotist Bartolomeo Mastri. It shows how the Thomist differs from the Scotist and analyzes these rival positions. (shrink)

The paper examines the all too often neglected role of the Czech philosopher and mathematician Bernard Bolzano for Husserl’s work, from ca. 1893–1894 onwards. Husserl himself finds it important to stress in an appendix to chapter 10 of the Prolegomena to Pure Logic that his investigations are not “in any sense mere commentaries upon, or critically improved expositions of, Bolzano’s thought patterns”, but that they “have been crucially stimulated by Bolzano …”. The paper examines early Bolzano’s ideas on the ground-consequence (...) relation, Bolzano’s logical universe as presented in his masterpiece, the monumental Wissenschaftslehre, the role of Hermann Lotze in making Husserl receptive for Bolzano and, finally, a lecture course on logic held by Husserl at the University of Halle in 1896, working out just what Husserl is taking, and not taking, from Bolzano. (shrink)

Catholic Philosophy has long acknowledged the primary place of Metaphysics, and a primary question of metaphysicians is “what is Metaphysics about?” This paper engages this primary metaphysical question through the lens of Scholastic dispute over the adequate subject matter of Metaphysics. Chrysostom Iavelli defended the position that the subject of Metaphysics is real being common to God and creatures against the position of his predecessor Dominic Flandrensis who had argued that it is categorical being to the exclusion of uncreated being. (...) I find Flandrensis’s position represented in the writings of notable contemporary Thomists, but not Iavelli’s. This paper, offers a sixteenth-century Thomist’s position on the subject matter of Metaphysics as a challenge to current Thomist consensus. It attempts to prompt a re-investigation of the reasons behind the current consensus both as a philosophical position and as an interpretation of St. Thomas Aquinas. (shrink)

Since the first decade of the 14th Century, Thomas Aquinas’s disciples have struggled to explain and defend his doctrine of analogy. Analogy after Aquinas: Logical Problems, Thomistic Answers relates a history of prominent Medieval and Renaissance Thomists’ efforts to solve three distinct but interrelated problems arising from their reading both of Aquinas’s own texts on analogy, and from John Duns Scotus’s arguments against analogy and in favor of univocity in Metaphysics and Natural Theology. The first of these three problems concerns (...) Aquinas’s at least apparently disparate statements on whether a name is said by analogy through a single concept or through diverse concepts. The second problem concerns the model of analogy suited for predicating names analogously across the categories of being or about God and creatures. Is “being” said analogously about God and creatures, or substance and accidents, on the model of how “healthy” is said of medicine and an animal, or on the model of how “principle” is said of a point and a line? The third problem comes from outside challenges to Aquinas’s thought, in particular Scotus’ claims that univocal names alone can mediate valid demonstrations, and any demonstration that failed to use its mediating terms univocally would fail by the fallacy of equivocation. Analogy after Aquinas makes a unique contribution to the study of philosophical theology in the tradition of Thomas Aquinas by showing the historical and philosophical connection between these three problems, as well as the variety of solutions proposed by leading representatives of this tradition. Thomists considered in the book include: Hervaeus Natalis (1250-1323), Thomas Sutton (1250-1315), John Capreolus (1380-1444), Dominic of Flanders (1425-1479), Paul Soncinas (d. 1494), Thomas dio vio Cajetan (1469-1534), Francis Silvestri of Ferrara (1474-1528), and Chrysostom Javelli (1470-1538). (shrink)

This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought. Ettore Carruccio covers the evolution of mathematics from (...) the most ancient times to our own day. In simple and non-technical language, he observes the changes that have taken place in the conception of rational theory, until we reach the lively, delicate and often disconcerting problems of modern logical analysis. The book contains an unusual wealth of detail (including specimen demonstrations) on such subjects as the critique of Euclid's fifth postulate, the rise of non-Euclidean geometry, the introduction of theories of infinite sets, the construction of abstract geometry, and-in a notably intelligible discussion-the development of modern symbolic logic and meta-mathematics. Scientific problems in general and mathematical problems in particular show their full meaning only when they are considered in the light of their own history. This book accordingly takes the reader to the heart of mathematical questions, in a way that teacher, student and layman alike will find absorbing and illuminating. The history of mathematics is a field that continues to fascinate people interested in the course of creativity, and logical inference quite part and in addition to those with direct mathematical interests. Ettore Carruccio, who until his retirement was professor of philosophy at the University of Turin. He has made many contributions to mathematical and logical theory as well as to the history of the science. Isabel Quigly was the literary editor of The Tablet for many years. (shrink)