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)

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)

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.

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)

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

The purpose of this study was to determine the applicability of Buddhist practices in today’s workplaces. The findings were supported by interviews with Buddhist masters and Buddhist business practitioners, as well as literature review, through phenomenological analysis. As a means of presenting the main reasons why Buddhist practices should be considered in contemporary workplaces, a SWOT analysis is presented. In this analysis, a number of strengths for using Buddhist practices in workplaces are listed such as pro-scientific, greater personal responsibility, and (...) healthy detachment, while potential weaknesses such as non-harming, equanimity, and no competition are also reviewed. Both the strengths and the weaknesses could be listed in reverse if applied to a different extent. Among the opportunities were issues such as re-educating the world of business, enhancing personal ownership and a healthier society, while the threats comprised issues such as creating different imbalances, disinterest, and stationary development. (shrink)

This collection of John Mackie's papers on personal identity and topics in moral and political philosophy, some of which have not previously been published, deal with such issues as: multiple personality; the transcendental "I"; responsibility and language; aesthetic judgements; Sidgwick's pessimism; act-utiliarianism; right-based moral theories; cooperation, competition, and moral philosophy; universalization; rights, utility, and external costs; norms and dilemmas; Parfit's population paradox; and the combination of partially-ordered preferences.

Angelaki, Volume 17, Issue 2, Page 31-48, June 2012.

SUBJECTION AND SUB JECT1VATION ETIENNE BALIBAR will begin by sketching out a problematic, or research programme, on which have been working for some time ...

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)

This article analyses the forms of dividuation workers undergo when they are linked to technologies, such as algorithms or artificial intelligence. It examines functionalities and operations deployed by certain types of Talent Management software and apps—UKG, Tribepad, Afiniti, RetailNext and Textio. Specifically, it analyses how talented workers materialise in relation to the profiles and the statistical models generated by such artificial intelligence machines. It argues that these operate as a nooscope that allows the transindividual plane to be quantified through a (...) process known as dividuation. Finally, by way of conclusion, the notion of the dividual is presented as the logic that characterises the human–machine relationship in the case of artificial intelligence and as the horizon of what Felix Guattari called “machinic capitalism”. (shrink)

Este artículo presenta una explicación del sentido común moderno a partir de una reconstrucción de lecturas críticas de Marx y Schumpeter. Se defiende que nuestro sentido común está estrechamente relacionado con la tecnología y que esta comporta fetichismo y funcionalidad. El artículo tiene cuatro partes. Primeramente, expongo las consideraciones generales que requiere una aproximación filosófica al sentido común y concreto la filosofía de la historia en la que baso mi análisis. Segundo, argumento que el sentido común moderno es indisociable de (...) la moral y la política y ambas lo son de posibles conflictos de tipo radical en cuanto al ser humano y su historia. Tercero, comento por qué estos posibles conflictos tienen que ver con lo que Marx llama en El capital la maquinaria capitalista y desarrollo esta idea desde la teoría de los paradigmas tecnoeconómicos. Finalmente, sostengo que esta teoría neoschumpeteriana debe ser criticada desde la filosofía, así como adoptada para una teoría y práctica críticas del sentido común moderno, el cual tiene en las gestiones de la COVID-19 un punto culminante. (shrink)

This paper introduces an extension A of Kleene's axiomatization of Brouwer's intuitionistic analysis, in which the classical arithmetical and analytical hierarchies are faithfully represented as hierarchies of the domains of continuity. A domain of continuity is a relation R(α) on Baire space with the property that every constructive partial functional defined on {α : R(α)} is continuous there. The domains of continuity for A coincide with the stable relations (those equivalent in A to their double negations), while every relation R(α) (...) is equivalent in A to ∃αA(α, β) for some stable A(α, β) (which belongs to the classical analytical hierarchy). The logic of A is intuitionistic. The axioms of A include countable comprehension, bar induction, Troelstra's generalized continuous choice, primitive recursive Markov's Principle and a classical axiom of dependent choices proposed by Krauss. Constructive dependent choices, and constructive and classical countable choice, are theorems, A is maximal with respect to classical Kleene function realizability, which establishes its consistency. The usual disjunction and (recursive) existence properties ensure that A preserves the constructive sense of "or" and "there exists.". (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)

The specific type of torture to which Abu Ghraib prisoners were submitted was predicated on the assumption that hejab, or the islamic system of modest, makes Muslims especially vulnerable to shame. This paper investigates this supposed link between hejab and the affect of shame through an analysis of the philosophical and psychoanalytic literature on shame and the films of the iranian filmmaker, Abbas Kiarostami. Beginning with a discussion of the massive impact of hejab regulations on Iranian cinema, the author shows (...) how Kiarostami’s critique of these regulations becomes a powerful argument for shame as against the modesty system. (shrink)

A survey conducted among 50 members of the Los Angeles Workforce, all within the age range of 20-50 years, and with a minimum of 2 years of work experience and a minimum of 2 years of college education, delivered results that may be of interest to managers in their efforts to enhance workers' satisfaction and successfully transcend the challenges of these times. The focus of this study was on values that mattered most in challenging times to members of the workforces. (...) The hypothesis that inner-and inter-human aspects would be considered more important than money and status in such times was highly supported, with values such as love and relationships, and positive motivation, in an overwhelming lead. While financial worries were undoubtedly considered, it was underscored that in times of trouble, employees reach inwardly and outwardly to inner-human and inter-human connectedness. (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)

Civic engagement in the form of social and moral awareness projects has grown in popularity among higher education practitioners in the past decades, and even more among business schools as a response to the many embarrassingly self-centered business CEO acts in recent years. Research thus far shows a wide variety of advantages tied to social and moral awareness projects, varying from greater understanding of students about the needs in society, and improved connections between the sponsoring institution and the community, to (...) more focus in students’ selection of future careers, and greater personal and professional emotional intelligence levels among these students. This article reviews the achievements of 156 undergraduate and graduate business students in regards to their social and moral responsibility projects, and the preferences they displayed in selecting the topics of these projects. (shrink)

In The Myth of Matriarchal Prehistory, Cynthia Eller describes a dangerous, ‘ennobling lie’ that must be overturned in order for women to have a viable future. The so-called matriarchal myth which she attempts to debunk is the idea that human societies have not always supported male domination in social structure and religious practice and that societies have existed in which women and the entire natural world were honored. This article examines Eller’s stated assumption that such ideas are utopian inventions and (...) that male dominance is the most reasonable, scientifically sound approach to an interpretation of prehistory. (shrink)

In this paper, we offer an argument in favor of the modular character of mind, based on a more detailed proof of the modular character of the linguistic capacity: in comparing the properties of different components of grammar in a specific area we will draw general consequences about the properties of the cognitive system. More specifically, we analyze and compare the properties, in logical form (LF)and in phonology, of “empty eIements” - eIements that are “visible” or “full” at some level (...) of representation, but not at another level.Our analysis shows that empty eIements are governed at LF by principIes on variables. binding conditions, and thematic principles, that relate eIements at a distance. In phonology, on the other hand, empty elements, i.e., empty segments and empty properties, can be obtaines by deletion and are governed by very different principles (underspecification, principles relating to recoverability of deletion effects), andthese principles relates eIements under strict adjacency. In addition, when a principle seems to be operating in a similar fashion in both components, as in the case of the Projection Principle, it involves lexical properties, which are properties affecting all components. We conclude, hence, that grammar is a modular system, with different components following different principles but related of course, among other things, by the properties of lexical structure.It follows from this analysis that a theory that views language as part of a homogeneous cognitive capacity cannot be mantained: cognition cannot be nonmodular in a strict sense, since a subpart of it, the linguistic capacity is modular itself. We conclude also that the linguistic capacity being modular, we ean only expect that, when studied in more detail, other cognitive capacities will be shown to differ intheir structure still more from the language system. (shrink)