After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain (...) Frege’s and Schröder’s conceptions of the fulfilment of Leibniz’s scientific ideal. -/- In this paper I explain the reasons for Frege’s and Schröder’s mutual accusations of having created a mere calculus ratiocinator. On the one hand, Schröder’s construction of the algebra of relatives fits with a project for the reduction of any mathematical concept to the notion of relative. From this stance I argue that he deemed the formal system of Begriffsschrift incapable of such a reduction. On the other hand, first I argue that Frege took Boolean logic to be an abstract logical theory inadequate for the rendering of specific content; then I claim that the language of Begriffsschrift did not constitute a complete lingua characterica by itself, more being seen by Frege as a tool that could be applied to scientific disciplines. Accordingly, I argue that Frege’s project of constructing a lingua characterica was not tied to his later logicist programme. (shrink)

In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.

In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.

Recent historical studies have investigated the first proponents of methodological structuralism in late nineteenth-century mathematics. In this paper, I shall attempt to answer the question of whether Peano can be counted amongst the early structuralists. I shall focus on Peano’s understanding of the primitive notions and axioms of geometry and arithmetic. First, I shall argue that the undefinability of the primitive notions of geometry and arithmetic led Peano to the study of the relational features of the systems of objects that (...) compose these theories. Second, I shall claim that, in the context of independence arguments, Peano developed a schematic understanding of the axioms which, despite diverging in some respects from Dedekind’s construction of arithmetic, should be considered structuralist. From this stance I shall argue that this schematic understanding of the axioms anticipates the basic components of a formal language. (shrink)

It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken (...) as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text. (shrink)

In Begriffsschrift, Frege presented a formal system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. From a contemporary perspective, Begriffsschrift’s deductions are, in general, straightforward; it is assumed that all of them can be reproduced in a second-order formal system. Some deductions in this work present—according to this perspective—oddities that have led many scholars to consider it to be Frege’s inaccuracies which should be amended. (...) In this paper, we continue with the analysis of Begriffsschrift’s logic undertaken in an earlier work and argue that its deductive system must not be reconstructed as a second-order calculus. This leads us to argue that Begriffsschrift’s deductions do not need any correction but, on the contrary, can be explained in coherence with a global reading of this work and, in particular, with its fundamental distinction between function and argument. (shrink)

The global precedence effect, originally referring to processing hierarchical visual stimuli composed of letters, is characterised by both global advantage and global interference. We present herein a study of how this effect is modulated by the variables letter and sex. The Navon task, using the letters “H” and “S,” was administered to 78 males and 168 females. No interaction occurred between the letter and sex variables, but significant main effects arose from each of these. Reaction times revealed that the letter (...) “H” was identified more rapidly in the congruent condition both in the global and the local task, and the letter “S” in the incongruent condition for the local task. Also, although RTs showed a GPE in both males and females, males displayed shorter reaction times in both global and local tasks. Furthermore, luteal women showed higher d’ index in the congruent condition for the local task than both follicular women and hormonal contraceptive users, as well as longer exploration time of the irrelevant level during the global task than males. We conclude that, according to the linear periodicity law, the GPE is enhanced for compound letters with straight vs. curved strokes, whereas it is stronger in males than in females. Relevantly, luteal phase of the menstrual cycle seems to tilt women to rely on finer grained information, thus exhibiting an analytical processing style in global/local visual processing. (shrink)

Background: Frailty is a common syndrome among older adults and patients with several comorbidities. Grip strength is a representative parameter of frailty because it is a valid indicator of current and long-term physical conditions in the general population and patients with severe mental illnesses. Physical and cognitive capacities of people with SMIs are usually impaired; however, their relationship with frailty or social functioning have not been studied to date. The current study aimed to determine if GS is a valid predictor (...) of changes in cognitive performance and social functioning in patients with type-2 diabetes mellitus and SMIs. Methods: Assessments of social functioning, cognitive performance, and GS were conducted in 30 outpatients with type 2 diabetes mellitus, 35 with major depressive disorder, 42 with bipolar disorder, 30 with schizophrenia, and 28 healthy controls, twice during 1-year, follow-up period. Descriptive analyses were conducted using a one-way analysis of variance for continuous variables and the chi-squared test for categorical variables. Differences between groups for the motor, cognitive, and social variables at T1 and T2 were assessed using a one-way analysis of covariance, with sex and age as co-variates. To test the predictive capacity of GS at baseline to explain the variance in cognitive performance and social functioning at T2, a linear regression analysis was performed. Results: Predictive relationships were found among GS when implicated with clinical, cognitive, and social variables. These relationships explained changes in cognitive performance after one year of follow-up; the variability percentage was 67.7%, in patients with type-2 diabetes mellitus and 89.1% in patients with schizophrenia. Baseline GS along with other variables, also predicted changes in social functioning in major depressive disorder, bipolar disorder, and schizophrenia, with variability percentages of 67.3, 36, and 59%, respectively. Conclusion: GS combined with other variables significantly predicted changes in cognitive performance and social functioning in people with SMIs or type-2 diabetes mellitus. Interventions aimed to improve the overall physical conditions of patients who have poor GS could be a therapeutic option that confers positive effects on cognitive performance and social functioning. (shrink)

Ce recueil rassemble les textes des communications faites au deuxième séminaire de la « Escuela interlatina de altos Estudios en Lingüística aplicada », qui s’est tenu à San Millán de la Cogolla en septembre 2000 et dont le thème, en cette année mondiale des mathématiques, était précisément : Matemáticas y Tratamiento de Corpus. Après un prologue assez général de A. M. Municio, les vingt exposés sont répartis en quatre chapitres correspondant aux différentes sessions du séminaire : 1. Quanti..

Ce recueil rassemble les textes des communications faites au deuxième séminaire de la « Escuela interlatina de altos Estudios en Lingüística aplicada », qui s’est tenu à San Millán de la Cogolla en septembre 2000 et dont le thème, en cette année mondiale des mathématiques, était précisément : Matemáticas y Tratamiento de Corpus. Après un prologue assez général de A. M. Municio, les vingt exposés sont répartis en quatre chapitres correspondant aux différentes sessions du séminaire : 1. Quanti...

No presente artigo, interessa-nos apontar algumas possibilidades acerca da presença, no século X, da obra Formula Vitae Honestae, escrita por Martinho de Braga, que viveu na Galiza no século VI, na biblioteca de San Millán de la Cogolla, mosteiro localizado em La Rioja. De acordo com nossas conclusões, ainda parciais, vinculamos tal presença à identificação dos dois momentos históricos, o da Galiza no século VI e por La Rioja no X, marcados pela reorganização eclesiástica e monárquica.

Book reviewed in this article: Ethical Issues in Social Research. Edited by Tom L. Beauchamp, Ruth R. Faden, R. Jay Wallace, Jr., and LeRoy Walters. Baltimore: The Johns Hopkins University Press, 1982. xii + 436 pp. $25.00 (hardcover); $8.95 (paper). Ethics of Human Subject Research. Edited by Allan J. Kimmel, Jr. San Francisco: Jossey‐Bass, 1981. 106 pp. $6.95 (paper). Social Research Ethics. Edited by Martin Bulmer. New York: Holmes & Meier, 1982. xiv + 284 pp. $39.50 (hardcover); $14.50 (paper). The (...) Ethics of Social Research: Field‐work, Regulation and Publication. Edited by Joan E. Sieber. New York: Springer‐Verlag, 1982. x + 187 pp. $23.50 (hardcover). The Ethics of Social Research: Surveys and Experiments. Edited by Joan E. Sieber. New York: Springer‐Verlag, 1982. xii + 249 pp. $23.50 (hardcover). (shrink)

The Vida de Santa Oria is the most problematic of Gonzalo de Berceo's works. There is disagreement about its textual integrity, and important elements of its structure are imperfectly understood. The intent of this article is to demonstrate Berceo's use of literary and iconographic material prominent in the thirteenth-century monastic culture of San Millán de la Cogolla to construct a moral and eschatological definition of the contemplative life. The Vida de Santa Oria renders Christian eschatology through an elaborate symbolic (...) structure, circumscribed physically and spiritually by the cloister walls of San Millán, where Berceo, a secular priest, served as notary of one of the abbots. The economy of Berceo's communicative method is no small part of the excellence of his poem; his artistic self-cloistering mirrors the existential condition of his hagiographic subject. It derives from a conscious and complex choice, rather than from any limitation of his intellectual horizons. (shrink)

A psychoanalytic and philosophical exploration of sublimation as a key term in Jacques Lacan's theories of ethics and feminine sexuality.

Universalistic claims about the nature of justice are presumed to require larger commitments from a global perspective than partialist claims. This essay departs from standard partialist accounts by anchoring partialist claims in a different account of the nature of responsibility. In contrast to substantive responsibility, which is akin to an obligation and derived from principles, relational responsibilities grow out of relationships and their complex intertwining. While such accounts of responsibility are less clear cut, they will prove in the long run (...) to be more valuable in thinking about global ethics. I illustrate this point by considering the moral issue surrounding abandoned relationships. The approach offered here—partiality that rests upon relational responsibilities—makes the responsibilities owed by those in higher income countries towards lower income countries much richer and more complex than is usually presumed. (shrink)

Contributors to this volume demonstrate how the ethics of care factors into a variety of social policies and institutions, and can indeed be useful in thinking about a number of different social problems. Divided into two sections, the first looks at care as a model for an evaluative framework that rethinks social institutions, liberal society, and citizenship at a basic conceptual level. The second explores care values in the context of specific social practices or settings, as a framework that should (...) guide thinking. (shrink)

In 1991, Jones developed an issue-contingent model of ethical decision making in which moral intensity is posited to affect the four stages of Rest's 1986 model. Jones claimed that moral intensity, which is "the extent of issue-related moral imperative in a situation", consists of six characteristics: magnitude of consequences, social consensus, probability of effect, temporal immediacy, proximity, and concentration of effect. This article reports the findings of two studies that analyzed the factor structure of moral intensity, operationalized by a 12-item (...) Perceived Moral Intensity Scale adapted from the work of Sing-hapakdi et al. [1996, Journal of Business Research, 36, 245-255] and Frey [2000, Journal of Business Ethics, 26, 181-195]. The two items that were purported to measure CE were dropped due to their inability to effectively tap into the characteristic proposed by Jones. Factor analyses of the remaining 10 items supported a 3-factor structure, with the MC, PE, and TI items loading on the first factor, the PX items loading on the second factor, and the SC items loading on the third factor. These factors were labeled: Probable Magnitude of Consequences, Proximity, and Social Consensus. The authors conclude that moral intensity consists of three characteristics, rather than the six posited by Jones. (shrink)

Are social movements responsible for their unfinished agendas? Feminist successes in opening the professions to women paved the way for the emergence of the upper middle-class two-career household. These households sometimes hire domestic servants to accomplish their child care work. If, as I shall argue, this practice is unjust and furthers social inequality, then it poses a moral problem for any feminist commitment to social justice.

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)

Resumen: Este artículo postula que el mejor modo de leer la Relectio de Indis de Francisco de Vitoria es considerar que no solo se trata de un texto que pertenece al género de análisis político. Para fundar esta hipótesis de lectura la investigación discurre en tres niveles: analiza el contexto de producción del texto; fija las características de los textos de análisis político y propone un autor y lector modelos de la Relectio. La conclusión de la investigación distingue entre interpretación (...) y uso del texto, y sostiene que la interpretación de la Relectio exige que el lector empírico conozca los tres niveles de análisis, mientras que el uso del texto exige considerar que él trata un conjunto de soluciones a problemas perennes en las sociedades: los dilemas interculturales.: This article postulates that the best way of reading Francisco Victoria’s Relectio of Indis is having in mind that it not only is about a text which belongs to the political analysis genre. To support this reading hypothesis, the investigation proceeds in three levels: First, it analyzes the context of production of the text; second, it sets the features of the texts of political analysis and; third, it proposes an author and model reader of the Relectio. The conclusion of the investigation distinguishes between interpretation and the use of text as well as it holds that the interpretation of the Relectio demands the empiric reader to know the three levels of analysis, whereas the use of the text demands him to deal with a set of solutions to perennial problems in societies: intercultural dilemmas. (shrink)

This article studies the differences between traditional financial intermediaries (commercial banks, savings banks and cooperative banks) and ethical banks based on property rights, in which the owner decides the ideology, principles, standards and objectives of the organisation. In ethical banking, affinity centres on positive social and ethical values. The article consequendy focuses on an index proposed both to differentiate ethical banks from other types of banks, and also to pinpoint the differences between the various ethical banks themselves.This is the Radical (...) Affinity Index (RAI), which groups banks together in terms of their stance on ethical commitment, concentrating on ethical ideology and principles (information transparency, placement of assets, guarantees and participation) and using a sample of 114 European banks. The evidence shows that transparency of information and placement of assets are factors that differentiate ethical banks from other financial intermediaries.Guarantees and participation are characteristics specific to ethical banks; these variables, however, do not offer clear evidence to our analysis. (shrink)

In the author's Relative lawlessness in intuitionistic analysis [this JOURNAL. vol. 52 (1987). pp. 68-88] and An intuitionistic theory of lawlike, choice and lawless sequences [Logic Colloquium '90. Springer-Verlag. Berlin. 1993. pp. 191-209] a notion of lawless ness relative to a countable information base was developed for classical and intuitionistic analysis. Here we simplify the predictability property characterizing relatively lawless sequences and derive it from the new axiom of closed data (classically equivalent to open data) together with a natural principle (...) of invariance under finite translation. We characterize relative lawlessness in terms of a notion of forcing. Finally, we study relative lawlessness on an arbitrary fan and show that the collection of lawless binary sequences (which is comeager in the sense of Baire) has probability measure zero. The reasoning is predominantly constructive. (shrink)

Are social movements responsible for their unfinished agendas? Feminist successes in opening the professions to women paved the way for the emergence of the upper middle-class two-career household. These households sometimes hire domestic servants to accomplish their child care work. If, as I shall argue, this practice is unjust and furthers social inequality, then it poses a moral problem for any feminist commitment to social justice.

RESUMEN:Este trabajo tiene por objeto analizar la articulación entre la afirmación del carácter racional de la fe, esto es, su dimensión latitudinaria, el escepticismo epistemológico, y su derivación práctica en un concepto de tolerancia restringido al interior del protestantismo. Se subrayará, en este sentido, el carácter estratégico de la articulación entre racionalidad de la fe y escepticismo, en cuanto permite apelar a la ignorancia con vistas a la tolerancia, sin por ello dejar de sostener la interpretación protestante del cristianismo, en (...) detrimento de la interpretación católica.PALABRAS CLAVE:LOCKE - LATITUDINARISMO - ESCEPTICISMO - TOLERANCIA - PROTESTANTISMOABSTRACT:This paper aims to analyze the articulation between faith rationality assertion, i.e. its latitudinarian aspect, its epistemological skepticism, and its practical implication in a restricted concept of tolerance within Protestantism. In this regard, we will emphasize the strategic feature of the link between faith rationality and skepticism, as it allows appealing to ignorance towards tolerance, without dropping the Protestant interpretation of Christianity, to the detriment of Catholic interpretation.KEYWORDS:LOCKE - LATITUDINARIANISM - SKEPTICISM - TOLERATION - PROTESTANTISM. (shrink)

The Question of the Self Perhaps the clearest access to the question of the self in Dogen lies in the fascicle of Shobogenzo entitled "Genjo-koan. ...

This paper develops a simple, conceptual, mathematical model for the evolution of holobionts. Its purpose is to clarify how holobiont selection may cause evolutionary change in the traits of holobionts.

En este artículo analizo la idea de que se puede hacer filosofía a través de la poesía y trato de darle sentido a la expresión “poesía filosófica”. Sostengo que hay básicamente dos modos de entender esta expresión: 1) como ejemplificación, es decir, la poesía puede servir como ejemplo filosófico de distintas maneras; y 2) como articulación de una teoría filosófica. Aquí analizo la idea de que se puede obtener un tipo de conocimiento sui generis a través de la poesía, así (...) como la de que la poesía puede justificar supuestas verdades filosóficas. Rechazo estas dos ideas y, con ellas, la tesis de que se puede articular una teoría filosófica a través de la poesía. Sin embargo, acepto que no hay nada intrínseco a la poesía que le impida hacerlo, aunque, en general, esto no sucede. (shrink)

Kripke recently suggested viewing the intuitionistic continuum as an expansion in time of a definite classical continuum. We prove the classical consistency of a three-sorted intuitionistic formal system IC, simultaneously extending Kleene’s intuitionistic analysis I and a negative copy C° of the classically correct part of I, with an “end of time” axiom ET asserting that no choice sequence can be guaranteed not to be pointwise equal to a definite sequence. “Not every sequence is pointwise equal to a definite sequence” (...) is independent of IC. The proofs are by Crealizability interpretations based on classical ω-models ${\cal M}$ = $\left$ of C°. (shrink)

The management of covid-19 and the so-called "new normality" have brought with a timely debate of ideas about the future of sovereignty. Leaving aside hegemonic and neoliberal technophilia, this debate has generated two mutually exclusive approaches based on controversial statements by the philosopher Giorgio Agamben, namely: one that foresees an undemocratic horizon subject to new technologies and another that emphasizes the transversal character and contradictory of these. In this work, by appealing to the theory of techno-economic paradigms, I critically set (...) out the main reasonings of the debate and I reflect on the future of democracy. (shrink)