Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...) constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular. (shrink)

This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council, Grant Number 681404.

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

Research indicates that religious values and ethical behavior are closely associated, yet, at a firm level, the processes by which this association occurs are poorly understood. Family firms are known to exhibit values-based behavior, which in turn can lead to specific firm-level outcomes. It is also known that one’s family is an important incubator, enabler, and perpetuator of religious values across successive generations. Our study examines the experiences of a single, multigenerational business family that successfully enacted their religious values in (...) their business. Drawing upon intergenerational solidarity and values-based leadership theory, and by way of an interpretive, qualitative analysis, we find that the family’s religious values enhanced their cohesion and were manifested in their leadership style, which, in turn, led to outcomes for the business. Our findings highlight the processes that underlie the relationship between religious values and organizational outcomes in family firms and offer insights into the role of solidarity in values-based leadership. (shrink)

Towards biodeconstruction -- Between life and death: différance -- The absolute programme -- The text and the living -- Between life and death: the bond -- Beyond life death: autoimmunity -- Living on: the arche-performative.

Modal Meinongianism is the most recent neo-Meinongian theory. Its main innovation consists in a Comprehension Principle which, unlike other neo-Meinongian approaches, seemingly avoids limitations on the properties that can characterize objects. However, in a recent paper A. Sauchelli has raised an objection against modal Meinongianism, to the effect that properties and relations involving reference to worlds at which they are instantiated, and specifically to the actual world or parts thereof, force a limitation of its Comprehension Principle. The theory, thus, is (...) no better off than other neo-Meinongian views in this respect. This article shows that the notion part of actuality in Sauchelli’s paper is ambiguous from the modal Meinongian viewpoint. Accordingly, his objection splits into two, depending on its disambiguation. It is then explained how neither interpretation forces modal Meinongianism to limit its Comprehension Principle. A third problem connected to Sauchelli’s objection is addressed: how to account for our felicitously referring to nonexistent objects via descriptions that embed reference to properties not actually instantiated by the objects. Overall, the replies to these difficulties provide good insights into the workings of the new Meinongian theory. (shrink)

This paper argues that Umberto Eco had a sophisticated theory of abductive reasoning and that this theory is fundamentally akin to Peirce’s both in the analysis and in the justification of this kind of reasoning. The first section expounds the essentials of Peirce’s theory of abduction, and explains how Peirce moved from seeing abduction as a kind of reasoning to seeing it as a stage of the larger process of inquiry. The second section deals with one of Eco’s paradigmatic examples (...) of abduction, i.e., William of Baskerville’s abduction concerning the horse Brunellus in the overture of The Name of the Rose, and shows that, just like in Peirce’s three-stages model of inquiry, William’s abductions are verified by means of deduction and induction. The third section examines the problem of the justification of abductive reasoning, and argues that both Peirce and Eco solved this problem through the idea that the justification of abduction is itself abductive (meta-abduction in Eco, ur-abduction in Peirce). (shrink)

In Soph. 237b7–239a11 Plato lays out a sequence of arguments that are generally considered homogenous. An analysis of each argument can shed light on the need to differentiate their respective nature. Firstly, it will be shown that the arguments do not work only at the linguistic level, contrary to the way these passages are interpreted by most of commentators. The meta–linguistic nature of the third argument will be particularly emphasised. Secondly, it will be argued that the three arguments follow each (...) other according to a crescendo. The implications of this argumentative structure will be specifically appreciated. Both these results of the analysis induce to attribute a crucial importance to the notion of medamos on: the arguments do not aim to definitively exclude the possibility of a Parmenidean non–being; they play a positive role within the inquiry of the Stranger of Elea, inasmuch the thematisation of Parmenidean non–being is seriously taken into account and embraced at this stage of the dialogue. In fact it is only through this dialectical step that the Stranger gains the chance to proceed in the direction of a relational ontology and a new concept of non–being. The positive role played by the medamos on presupposes that this expression and the equivalent ones are not mere absurdities and can find place in the Platonic use of language; this implies that the notion of medamos on must have a justification in the framework of Platonic relational ontology and conception of language. The consideration of this aspect eventually gives the opportunity to return to the three arguments and present an explanation of their positioning in that stage of the dialogue. (shrink)

Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds (...) of such multiple readings. While readings of the first kind do not capture any essential difference among notations but only among vocabularies, corresponding to readings of the second and the third kind two general parameters according to which notations may differ are defined: linearity vs. non-linearity, and tabularity vs. non-tabularity. This answers the question of how there can be substantially different but expressively equivalent logical notations. (shrink)

This paper intends to verify the extent and effectiveness of the transforming appropriation of the Derridean concept of ‘differance’ by Stiegler with respect to the problems that, according to Stiegler, make this creative critical operation necessary; in particular with respect to the most recent question concerning the possibility of thinking about and putting into practice a ‘neganthropological différance’ capable of facing the ecological crisis that today seems to threaten the very existence of life on earth. The paper goes back to (...) Technics and Time 1. to analyze the distinction between ‘vital difference’ and ‘noetic difference’ that constitutes the condition of possibility of the ‘neganthropological différance.’ In this perspective, the distinction proposed by Stiegler seems to re-propose the hierarchically oriented oppositional structure that characterizes metaphysical thought and in particular the opposition between man and animal, attributing to the human being the ability to free himself from the constraints of his biological-natural condition. Finally, the paper attempts to account for the repercussions of this approach on the very possibility of an effective response to the ecological crisis, concluding with a provocation regarding the role that theory can and must play with regard to such an urgent and far-reaching problem. (shrink)

This article intends to read the profound dynamics that characterise the current war in the light of certain classical philosophical categories such as the relationship established by Hegel between substance and subject, the difference between the concept of substance and the concept of function as it was discussed by Cassirer, and finally the binomial power over life and right of death reread by Foucault in a biopolitical key. In the light of these polarities, it is in fact possible to identify (...) two opposing worldviews – on which depend two completely different ways of understanding the function of the state, the weight to be ascribed to rights, and even two different ways of conceiving and conducting war – that do not necessarily coincide with the two opposing sides in the field. (shrink)

La fundamental idea orteguiana de que «mi vida» es «razón», difiere radicalmente de la concepción fenomenológica de la razón que alumbra Husserl en Ideen, esencialmente fundada en el ser. La razón vital es teoría del hombre, que es su proyecto circunstancial; su estímulo argumental procede de una reflexión estética sobre todo orientada a la comprensión del realismo y del idealismo artísticos, y cuyas consecuencias filosóficas serán decisivas.

By addressing social issues, rather than maximizing profits, social enterprises are said to contribute to the well-being of societies. In this paper, we test whether social enterprises fulfil this expectation. The paper applies regression analysis to a unique dataset obtained by merging survey data from the Global Entrepreneurship Monitor with official statistics on social enterprises in Luxembourg. Results suggest that social enterprises contribute to subjective well-being, which is an encompassing measure of people’s satisfaction with their own life. We find that (...) when the share of social enterprises in a city increases, the ill-being of poor and unemployed people declines. Therefore, policy makers who seek to increase the well-being of economically disadvantaged people could adopt policies to promote the creation of social enterprises. (shrink)

1. Da Leibniz a Kant.--2. L'algebra della logica.

Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 80, Chap. 7], we show that there is a tight connection between the depth of a classifiable shallow theory [Formula: see text] and the Borel rank of the isomorphism relation [Formula: see text] on its models of size [Formula: see text], for [Formula: see text] any cardinal satisfying [Formula: see text]. This is achieved by (...) establishing a link between said rank and the [Formula: see text]-Scott height of the [Formula: see text]-sized models of [Formula: see text], and yields to the following descriptive set-theoretical analog of Shelah’s Main Gap Theorem: Given a countable complete first-order theory [Formula: see text], either [Formula: see text] is Borel with a countable Borel rank, or it is not Borel at all. The dividing line between the two situations is the same as in Shelah’s theorem, namely that of classifiable shallow theories. We also provide a Borel reducibility version of the above theorem, discuss some limitations to the possible complexities of [Formula: see text], and provide a characterization of categoricity of [Formula: see text] in terms of the descriptive set-theoretical complexity of [Formula: see text]. (shrink)

In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in (...) Frege's logical system. In this paper, we challenge Dummett's view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege's connectives in some sense “contain” the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense‐compositional. Finally, we consider the semantic and pragmatic aspects of Frege's horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege's logic. (shrink)