In lieu of an abstract, here is a brief excerpt of the content:Isaac Barrow on the Mathematization of Nature: Theological Voluntarism and the Rise of Geometrical OpticsAntoni MaletIntroductionIsaac Newton’s Mathematical Principles of Natural Philosophy embodies a strong program of mathematization that departs both from the mechanical philosophy of Cartesian inspiration and from Boyle’s experimental philosophy. The roots of Newton’s mathematization of nature, this paper aims to demonstrate, are to be found in Isaac Barrow’s (1630–77) philosophy of the mathematical sciences.Barrow’s attitude (...) towards natural philosophy evolved from his earnest interest in medicine of around 1650, when a young Cambridge graduate, to natural philosophy (apparently under Henry More’s influence); from his thesis on the insufficiency of the Cartesian hypothesis to geometrical optics and the strong program of mathematization of natural philosophy of the middle 1660s; from Lucasian professor of Mathematics to Chaplain of his Majesty and eminent Restoration divine. Contemporary accounts of Barrow’s life suggest that he grew ever more skeptical about the worth of natural philosophy and mathematics. 1 In his last years he became a prolific [End Page 265] author of sermons and theological works. Published shortly after his death by John Tillotson (1630–94), later archbishop of Canterbury, they occupy over two thousand folio pages. Overloaded with involved philosophical arguments, Barrow’s sermons were apparently not very popular, but they were highly regarded by scholars and the Anglican hierarchy. 2 It is on certain of his sermons, as well as on the philosophical discussions contained in the Mathematical Lectures that our account of Barrow’s philosophy of the mathematical sciences will rest. 3 Barrow’s understanding of the mathematical sciences will allow us to discuss together three issues often analyzed independently: the theological background to English natural philosophy, the changing notion of mixed mathematical sciences during the seventeenth century, and finally the philosophical foundations of modern geometrical optics.It has long been recognized that significant relationships exist between theological voluntarism or intellectualism and views on natural philosophy. In particular Robert Boyle’s theological voluntarism is seen as grounding his experimentalist approach to natural philosophy. It is not quite so clear, however, how well theological voluntarism may relate to a strong program of mathematization such as the one embodied in Newton’s Principia Mathematica. In fact it has been suggested that the relationship is a negative one. This is derived from the necessary character of mathematical laws, which would put unwanted restrictions on God’s absolute dominion over nature, and also from the notion that theological intellectualism is conducive to a deductive, a priori science—the paradigm of which is of course geometry. However, Barrow’s theological voluntarism lead him to heighten the role of mathematics within natural philosophy.During the seventeenth century the so-called mixed or subalternate mathematical sciences changed profoundly. In the Enlightenment mixed mathematics—meaning above all rational mechanics—became one of the most prestigious and influential disciplines. The mixed mathematics of the Enlightenment, however, was markedly different from the Aristotelian [End Page 266] mixed mathematical sciences. The differences are noticeable both in the subject matter and in the substitution of mathematical infinitesimal analysis for geometrical synthesis, but also in the way of grounding mathematical theory on empirical evidence. Barrow’s Mathematical Lectures (delivered at Cambridge from 1664 to 1666) offer a fresh insight into the metamorphosis of these sciences just when Newton’s “mathematical principles” were in the making. Not the least interesting feature of Barrow’s discussion is that God’s omnipotence allows an evaluation of the truth of mathematical theories that do not apply to this world. Therefore, Barrow is led to introduce the distinction between the internal consistency, or mathematical truth, of a mathematical theory and its physical truth. This, in turn, leads him to the notion that theories need testing.Barrow on Matter and GodRecent literature has established significant correlations between theological voluntarism and empiricism, as well as between theological intellectualism and rationalism. As E. B. Davis writes, “the Christian doctrine of creation is a dialogue between God’s unconstrained will, which utterly transcends the bounds of human comprehension, and God’s orderly intellect, which serves as the model for the human mind.” Intellectualist theology considers God’s omniscience His... (shrink)

In this paper I try to establish the relevance of Peirce's Semeiotics to the conceptual foundations of Cognitive Science. Given Cognitive Science's commitment to the Representational Theory of Mind, I try to clarify the nature of mental representation from the standpoint of Peirce's general theory of signs. As it turns out, mental representations, because of their special role as interpretants of non-mental signs, present especial problems for their interpretation, whose solution Peirce anticipated in a way very close to that developed (...) in Cognitive Science. (shrink)

Se trata de una consideraeión de la ultima propuesta teórica de Víctor Sánchez de Zavala para la Pragmatica, desde la perspectiva de sus fundamentos conceptuales, de la filosofia de la mente subyacente. Se repasan sus argumentos para sentirse insatisfecho con el enfoque intencionalista estándar de la Pragmática y se intenta reconstruir su coneepeión alternativa a este respecto, implícita en su nuevo marco teórieo. Lo que aparece, al final es una concepeión dinámica de las relaciones reciprocas entre pensamiento y lenguaje.The aim (...) is to offer an overview of Víctor Sánchez de Zavala’s last theoretical proposal for Pragmatics, from the standpoint of its conceptual foundations, of the underlying philosophy of mind. His criticisms of the standard, intentionalist, approach are revised, and a reconstruction of his alternative view, implicit in his proposal, is advanced. The outcome is a dynamic view of the mutual links between thought and language. (shrink)

We show that externalization is a feature not only of moral judgment, but also of value judgment in general. It follows that the evolution of externalization was not specific to moral judgment. Second, we argue that value judgments cannot be decoupled from the level of motivations and preferences, which, in the moral case, rely on intersubjective bonds and claims.

L’article passe en revue le développement de l’histoire des femmes au Moyen Âge en Espagne depuis ses origines, la fin des années 1970, et discute l’influence que les thèses de Georges Duby ont exercée sur elle. Il relève que les regards venus de l’étranger ont contribué à discréditer et faire abandonner les préoccupations nationalistes qui avaient longtemps obsédé l’historiographie autochtone jusque dans la façon d’envisager et représenter les femmes. Le long et fécond parcours de l’histoire des femmes dans les vingt (...) dernières années est alors examiné, depuis l’orientation fondamentalement juridique et positiviste qui a marqué ses débuts jusqu’aux recherches récentes sur l’identité et la subjectivité féminines ou aux polémiques sur le pouvoir des femmes et leur participaton à la vie politique. La portée des thèses de G. Duby dans cette évolution ainsi que les critiques qu’elles se sont attirées sont finalement considérées. (shrink)

Building on the discussion between Stephen Darwall and Michael Tomassello, we propose an alternative evolutionary account of moral motivation in its two-pronged dimension. We argue that an evolutionary account of moral motivation must account for the two forms of moral motivation that we distinguish: motivation to be partial, which is triggered by the affective relationships we develop with others; and motivation to be impartial, which is triggered by those norms to which we give impartial validity. To that aim, we present (...) the second-person standpoint of morality, first as Darwall conceives of it, and then as we reinterpret it from a naturalistic approach. Then we synthesize Tomasello’s evolutionary account of morality, and Darwall’s objections to it. To reply to those objections, building on Tomasello’s proposal, we argue that the motivation to be impartial, and the feeling of obligation to comply with normative requirements, appeared when humans anticipated and, critically, internalized others’ sanctions to the violation of social norms. Consequently, we posit that social norms and sanctions appeared first at the community level, and only after that were they internalized in the form of self-directed reactive attitudes. Finally, we derive some corollaries that follow from our proposal. (shrink)

We give a presentation of Post algebras of ordern+1 (n1) asn+1 bounded Wajsberg algebras with an additional constant, and we show that a Wajsberg algebra admits a P-algebra reduct if and only if it isn+1 bounded.

In this paper, we take Darwall’s analytical project of the second-person standpoint as the starting point for a naturalistic project about our moral psychology. In his project, Darwall contends that our moral notions constitutively imply the perspective of second-personal interaction, i.e. the interaction of two mutually recognized agents who make and acknowledge claims on one another. This allows him to explain the distinctive purported authority of morality. Yet a naturalized interpretation of it has potential as an account of our moral (...) psychology. We propose a naturalistic interpretation of Darwall’s work to address some of the main issues about our moral psychology. First, we explain why moral norms motivate us; namely, because of these second-personal relations. We provide a naturalized version of this solution. Second, we articulate how intersubjective interactions take place effectively; grounding duties to particular other subjects, and being related to distinctive moral emotions. Third, we address the question of the limits of the moral community, proposing that it comprises all agents capable of second-personal interactions. Finally, we explain the emergence of community norms through intersubjective interaction. Since all group members can adopt alternatively the second-personal stance to each other, demands are sanctioned and recognized in a triangulation process which explains the emergence of group norms. (shrink)

A cross-cultural analysis of trust and cooperation networks in Northern Ghana (NGHA) and Oaxaca (OAX) was carried out by means of ego networks and interviews. These regions were chosen because both are inhabited by several ethnic groups, thus providing a good opportunity to test the cultural group selection hypothesis. Against the predictions of this approach, we found that in both regions cooperation is grounded in personal trust groups, and that social cohesion depends on these emotional bonds. Moreover, in agreement with (...) Fiske's notion of “evolved proclivities”, we also found two distinct kinds of trust networks, one for each region, which vary in terms of the degree of ethnic interrelation. This pattern suggests that social cohesion increases when environmental resources are scarce. (shrink)

Empirical studies such as Goyal et al. (J Polit Econ 114(2):403–412, 2006) or Newman (Proc Natl Acad Sci USA 101(Suppl. 1):5200–5205, 2004) show that scientific collaboration networks present a highly unequal and hierarchical distribution of links. This implies that some researchers can be much more active and productive than others and, consequently, they can enjoy a much better scientific reputation. One may think that big intrinsical differences among researchers can constitute the main driving force behind these inequalities. Nevertheless, this model (...) shows that, under specific circumstances, very similar individuals may self-organize themselves forming unequal and hierarchical structures. (shrink)

La meva intenció en les pàgines següents és analitzar la teoria del llenguatge que es troba en el Cràtil de Plató. D'una banda, s'analitza la concepció del significat de les paraules quePlató sembla defensar en aquest diàleg; de l'altra, s'ocupa del problema dels orígens delllenguatge. Aquestes qüestions s'estudien en relació amb la perspectiva ontològica i epistemològicade Plató: essencialisme, teoria de la reminiscència i les tesis dels sofistes sobre laimpossibilitat de parlar amb falsedat. La conclusió és que en el Cràtil podem (...) trobar ja la preparació de la teoria del llenguatge que Plató necessitarà per a la seva ulterior teoria de les idees. (shrink)

Este artículo se ocupa del problema de cuál pueda ser la naturaleza de la creencia y cuál la mejor explicación de su normatividad. Se analizan diversas teorías que desarrollan el modelo ¿estado más contenido¿, y se presenta como alternativa una concepción de filiación wittgensteiniana que entiende la creencia como acción simbólica y expresiva. This paper is devoted to the question of the nature of belief, and what the best explanation of its normativity is. Several theories based on the model "state (...) plus content" are analysed, and is presented a wittgensteinianan conception which understands belief as symbolic and expressive action. (shrink)

In this paper a non-paradoxical interpretation of Hobbes’s defence of scientific realism of materialistic type is proposed. It attempts to explain how this author was able to defend the truth of materialism and at the same time to deny that it could be demonstrated in a metaphysical way. The key to his position depends on the metaphorical use of the concept of ‘imitation’ and the treatment of the infinite and irresistible power as the philosophically relevant attribute of God. So Hobbes’s (...) intention would consist of saying that the explanation, but not the demonstration, of the truth of materialism depends on the ontological parity and continuity between the world and the human being, in the way in which they are explained by empirical science. In this sense Hobbes’s project, very different to Descartes’s one, would be an attempt to naturalise the epistemology that yet is conscious of the metaphysical limits affecting the naturalistic proposals of philosophy. (shrink)

The present article commences analyzing the origins and influences of the religious discourse on the configuration of the modern constitutional discourse and the contributions of the jus-positivism in the consolidation of this sacred-civil language. The second issue is the definition of the U.S. Constitution as a mixed and not as a democratic constitution, with regard to the influences of Plato, Aristotle, Cicero and Polybius to the Drafters of the first modern constitutional text; stability and equilibrium took preference over democracy in (...) a wide sense. I also analyze how the Drafter’s decision has conditioned the modern constitutional system up to the present. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples (...) to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

The classical Glivenko theorem asserts that a propositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK-logic with negation by a family of connectives implicitly defined by equations and compatible with BCK-congruences. Many of the logics in the current literature are natural expansions of BCK-logic with negation. The validity of (...) the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one-variable formula in the language of BCK-logic with negation. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples (...) to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

Using the theory of BL-algebras, it is shown that a propositional formula ϕ is derivable in Łukasiewicz infinite valued Logic if and only if its double negation ˜˜ϕ is derivable in Hájek Basic Fuzzy logic. If SBL is the extension of Basic Logic by the axiom (φ & (φ→˜φ)) → ψ, then ϕ is derivable in in classical logic if and only if ˜˜ ϕ is derivable in SBL. Axiomatic extensions of Basic Logic are in correspondence with subvarieties of the (...) variety of BL-algebras. It is shown that the MV-algebra of regular elements of a free algebra in a subvariety of BL-algebras is free in the corresponding subvariety of MV-algebras, with the same number of free generators. Similar results are obtained for the generalized BL-algebras of dense elements of free BL-algebras. (shrink)

In this paper we discuss Prinz’s Kantian arguments in “Is Empathy Necessary for Morality?”. They purport to show that empathy is not necessary for morality because it is not part of the capacities required for moral competence and it can bias moral judgment. First, we show that even conceding Prinz his notions of empathy and moral competence, empathy still plays a role in moral competence. Second, we argue that moral competence is not limited to moral judgment. Third, we reject Prinz’s (...) notion of empathy because it is too restrictive, in requiring emotional matching. We conclude that once morality and empathy are properly understood, empathy’s role in morality is vindicated. Morality is not reduced to a form of rational judgment, but it necessarily presupposes pro-social preferences and motivation and sensitivity to inter-subjective demands. (shrink)

In this paper we characterize, classify and axiomatize all axiomatic extensions of the IMT3 logic. This logic is the axiomatic extension of the involutive monoidal t-norm logic given by ¬φ3 ∨ φ. For our purpose we study the lattice of all subvarieties of the class IMT3, which is the variety of IMTL-algebras given by the equation ¬(x 3) ∨ x ≈ ⊤, and it is the algebraic counterpart of IMT3 logic. Since every subvariety of IMT3 is generated by their totally (...) ordered members, we study the structure of all IMT3-chains in order to determine the lattice of all subvarieties of IMT3. Given a family of IMT3-chains the number of elements of the largest odd finite subalgebra in the family and the number of elements of the largest even finite subalgebra in the family turns out to be a complete classifier of the variety generated. We obtain a canonical set of generators and a finite equational axiomatization for each subvariety and, for each corresponding logic, a finite set of characteristic matrices and a finite set of axioms. (shrink)

Business Ethics: A European Review, EarlyView.

In this paper we prove that the equational class generated by bounded BCK-algebras is the variety generated by the class of finite simple bounded BCK-algebras. To obtain these results we prove that every simple algebra in the equational class generated by bounded BCK-algebras is also a relatively simple bounded BCK-algebra. Moreover, we show that every simple bounded BCK-algebra can be embedded into a simple integral commutative bounded residuated lattice. We extend our main results to some richer subreducts of the class (...) of integral commutative bounded residuated lattices and to the involutive case. (shrink)

We discuss the discovery of technologies involving knotted netting, such as textiles, basketry, and cordage, in the Upper Paleolithic. This evidence, in our view, suggests a new way of connecting toolmaking and syntactic structure in human evolution, because these technologies already exhibit an which we take to constitute the key transition to human cognition.

Let ${\mathbb{BRL}}$ denote the variety of commutative integral bounded residuated lattices (bounded residuated lattices for short). A Boolean retraction term for a subvariety ${\mathbb{V}}$ of ${\mathbb{BRL}}$ is a unary term t in the language of bounded residuated lattices such that for every ${{\bf A} \in \mathbb{V}, t^{A}}$ , the interpretation of the term on A, defines a retraction from A onto its Boolean skeleton B(A). It is shown that Boolean retraction terms are equationally definable, in the sense that there is (...) a variety ${\mathbb{V}_{t} \subsetneq \mathbb{BRL}}$ such that a variety ${\mathbb{V} \subsetneq \mathbb{BRL}}$ admits the unary term t as a Boolean retraction term if and only if ${\mathbb{V} \subseteq \mathbb{V}_{t}}$ . Moreover, the equation s(x) = t(x) holds in ${\mathbb{V}_{s} \cap \mathbb{V}_{t}}$ . The radical of ${{\bf A} \in \mathbb{BRL}}$ , with the structure of an unbounded residuated lattice with the operations inherited from A expanded with a unary operation corresponding to double negation and a a binary operation defined in terms of the monoid product and the negation, is called the radical algebra of A. To each involutive variety ${\mathbb{V} \subseteq \mathbb{V}_{t}}$ is associated a variety ${\mathbb{V}^{r}}$ formed by the isomorphic copies of the radical algebras of the directly indecomposable algebras in ${\mathbb{V}}$ . Each free algebra in such ${\mathbb{V}}$ is representable as a weak Boolean product of directly indecomposable algebras over the Stone space of the free Boolean algebra with the same number of free generators, and the radical algebra of each directly indecomposable factor is a free algebra in the associated variety ${\mathbb{V}^{r}}$ , also with the same number of free generators.A hierarchy of subvarieties of ${\mathbb{BRL}}$ admitting Boolean retraction terms is exhibited. (shrink)

Lattice BCK logic is the expansion of the well known Meredith implicational logic BCK expanded with lattice conjunction and disjunction. Although its natural axiomatization has three rules named modus ponens, ∨‐rule and ∧‐rule, we show that we can give an equivalent presentation with just modus ponens and ∧‐rule, however it is impossible to obtain an equivalent presentation with modus ponens as unique rule. In this paper we study and characterize all axiomatic extensions of lattice BCK logic with modus ponens as (...) unique rule. We obtain an infinite chain of proper axiomatic extensions with this property. Moreover, we prove that there is no weakest axiomatic extension of Lattice BCK‐logic admitting modus ponens as unique rule. (shrink)