Charles Sanders Peirce: Logic Charles Sanders Peirce was an accomplished scientist, philosopher, and mathematician, who considered himself primarily a logician. His contributions to the development of modern logic at the turn of the 20th century were colossal, original and influential. Formal, or deductive, logic was just one of the branches in which he exercized … Continue reading Peirce’s Logic →.

Recent crises in Europe and beyond have renewed a longstanding debate on the status and treatment of refugees. Hannah Arendt famously questioned the limits of universalistic human rights discourse based on the widespread phenomena of statelessness and displacement that emerged during and after World War II. In this paper, we analyze recent patterns of inclusion and exclusion of refugees in Italy through the lens of Arendtian narrative and theorizing. We consider three cases of interaction between families, schools, and other public (...) institutions in light of the shifting normative framework before and during the war in Ukraine. Two major insights emerge from this analysis. From a pedagogical point of view, the most promising educational practices with refugees are those centered on enabling their agency and corresponding experiences of "natality". From an ethical-political perspective, these practices highlight a latent tension between the universalistic scope of human rights enshrined in the human rights declarations and their structural dependence on the particular norms and procedures enacted by nation states. The understanding and teaching of human rights within our political communities is inseparable from the practices that engage with refugees. In this sense, our practices of inclusion and exclusion affect the understanding of national borders as a barrier or threshold with other political communities, but also the interpretation of our own ethical-political principles. (shrink)

A proposal for the biological grounding of intrinsic teleology and sense-making through the theory of autopoiesis is critically evaluated. Autopoiesis provides a systemic language for speaking about intrinsic teleology but its original formulation needs to be elaborated further in order to explain sense-making. This is done by introducing adaptivity, a many-layered property that allows organisms to regulate themselves with respect to their conditions of viability. Adaptivity leads to more articulated concepts of behaviour, agency, sense-construction, health, and temporality than those given (...) so far by autopoiesis and enaction. These and other implications for understanding the organismic generation of values are explored. (shrink)

A proposal for the biological grounding of intrinsic teleology and sense-making through the theory of autopoiesis is critically evaluated. Autopoiesis provides a systemic lan- guage for speaking about intrinsic teleology but its original formulation needs to be elaborated further in order to explain sense-making. This is done by introducing adaptivity, a many-layered property that allows organisms to regulate themselves with respect to their conditions of via- bility. Adaptivity leads to more articulated concepts of behaviour, agency, sense-construction, health, and temporality than (...) those given so far by autopoiesis and enaction. These and other implications for understanding the organismic generation of values are explored. (shrink)

In a recent article, I have explored the historical, mathematical, and philosophical issues related to the new theory of numerosities. The theory of numerosities provides a context in which to assign numerosities to infinite sets of natural numbers in such a way as to preserve the part-whole principle, namely if a set A is properly included in B then the numerosity of A is strictly less than the numerosity of B. Numerosities assignments differ from the standard assignment of size provided (...) by Cantor’s cardinality assignments. In this talk, I generalize some specific worries emerging from the theory of numerosities to a line of thought resulting in what I call a ‘good company’ objection to Hume’s Principle (HP). The talk has four main parts. The first takes a historical look at 19th-century attributions of equality of numbers in terms of one-one correlations and argues that there was no agreement as to how to extend such determinations to infinite sets of objects. This leads to the second part where I show that there are countably infinite many abstraction principles that are ‘good’, in the sense that they share the same virtues of HP and from which we can derive the axioms of second order arithmetic. The third part connects this material to a debate on Finite Hume Principle between Heck and MacBride and states the ‘good company’ objection. Finally, the last part gives a tentative taxonomy of possible neo-logicist responses to the ‘good company’ objection and makes a foray into the relevance of this material for the issue of cross-sortal identifications for abstractions. (shrink)

From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. (...) The articles have been translated for the first time from Dutch, French, and German, and the volume is divided into four sections devoted to Brouwer, Weyl, Bernays and Hilbert, and the emergence of intuitionistic logic. Each section opens with an introduction which provides the necessary historical and technical context for understanding the articles. Although most contemporary work in this field takes its start from the groundbreaking contributions of these major figures, a good, scholarly introduction to the area was not available until now. Unique and accessible, From Brouwer To Hilbert will serve as an ideal text for undergraduate and graduate courses in the philosophy of mathematics, and will also be an invaluable resource for philosophers, mathematicians, and interested non-specialists. (shrink)

In this article, I draw upon the ‘post-Kantian’ reading of Hegel to examine the consequences Hegel’s idea of God has on his metaphysics. In particular, I apply Hegel’s ‘recognition-theoretic’ approach to his theology. Within the context of this analysis, I focus especially on the incarnation and sacrifice of Christ. First, I argue that Hegel’s philosophy of religion employs a distinctive notion of sacrifice (kenotic sacrifice). Here, sacrifice is conceived as a giving up something of oneself to ‘make room’ for the (...) other. Second, I argue that the idea of kenotic sacrifice plays a fundamental role in Hegel’s account of Christ. Third, I conclude by sketching some of the consequences of Hegel’s idea of a God who renounces his own divinity for an idealistically conceived metaphysics. My main thesis is that the notion of incarnation is conceived by Hegel as the expression of a spirit that advances only insofar as it is willing to withdraw and make room for the other. A kenotic reading of the Hegelian notion of the incarnation is also useful in terms of a clarification of the dispute between ‘left Hegelians’ and ‘right Hegelians’ concerning the status of the idea of God in Hegel’s philosophy. (shrink)

_Peirce’s Speculative Grammar: Logic as Semiotics _offers a comprehensive, philologically accurate, and exegetically ambitious developmental account of Peirce’s theory of speculative grammar. The book traces the evolution of Peirce’s grammatical writings from his early research on the classification of arguments in the 1860s up to the complex semiotic taxonomies elaborated in the first decade of the twentieth century. It will be of interest to academic specialists working on Peirce, the history of American philosophy and pragmatism, the philosophy of language, the (...) history of logic, and semiotics. (shrink)

In his third essay on earthquakes, Kant refers to “Pater Bina’s” electric interpretation of seismic phenomena. Although not a distinguished scholar, and maybe for that reason frequently confused with a certain “Father Isidore Binet”, Bina was nevertheless a noteworthy author. A Cassinese benedictine, Andrea Bina was a philosopher interested in sciences just like Kant; he studied Newton, translated Wolff, invented a seismoscope and was appreciated by his contemporaries at home and beyond the Alps. Kant’s laconic quotation, followed by a value (...) judgement regarding only Bina’s “audacity”, raises some questions, including, in primis those about the meaning of his hasty judgment. A plausible well-grounded answer should be looked for in the bio-bibliographical outline of the neglected author and in the perusal of his writings. The analysis of Bina’s Ragionamento sopra le cagioni de’ terremoti (1751) contributes to our knowledge of the eighteenth-century cultural background and helps us understand the degree of knowledge of the seismic phenomena acquired by men who – amidst many difficulties and hindered by the limits of their science – could only rely on secondhand data often imbued with misconceptions. Comparing Bina’s work – although indirectly – with Kant’s Fortgesetzte Betrachtung der seit einiger Zeit wahrgenommenen Erderschütterungen (1756) may help bring to light some convergences, as well as differences, which might be of use in clarifying some peculiarities of the Prussian Naturforscher. (shrink)

We examine Charles S. Peirce's mature views on the logic of science, especially as contained in his later and still mostly unpublished writings. We focus on two main issues. The first concerns Peirce's late conception of retroduction. Peirce conceived inquiry as performed in three stages, which correspond to three classes of inferences: abduction or retroduction, deduction, and induction. The question of the logical form of retroduction, of its logical justification, and of its methodology stands out as the three major threads (...) in his later writings. The other issue concerns the second stage of scientific inquiry, deduction. According to Peirce's later formulation, deduction is divided not only into two kinds but also into two sub-stages: logical analysis and mathematical reasoning, where the latter is either corollarial or theorematic. Save for the inductive stage, which we do not address here, these points cover the essentials of Peirce's latest thinking on the l.. (shrink)

A novel theoretical framework for an embodied, non-representational approach to language that extends and deepens enactive theory, bridging the gap between sensorimotor skills and language. -/- Linguistic Bodies offers a fully embodied and fully social treatment of human language without positing mental representations. The authors present the first coherent, overarching theory that connects dynamical explanations of action and perception with language. Arguing from the assumption of a deep continuity between life and mind, they show that this continuity extends to language. (...) Expanding and deepening enactive theory, they offer a constitutive account of language and the co-emergent phenomena of personhood, reflexivity, social normativity, and ideality. Language, they argue, is not something we add to a range of existing cognitive capacities but a new way of being embodied. Each of us is a linguistic body in a community of other linguistic bodies. The book describes three distinct yet entangled kinds of human embodiment, organic, sensorimotor, and intersubjective; it traces the emergence of linguistic sensitivities and introduces the novel concept of linguistic bodies; and it explores the implications of living as linguistic bodies in perpetual becoming, applying the concept of linguistic bodies to questions of language acquisition, parenting, autism, grammar, symbol, narrative, and gesture, and to such ethical concerns as microaggression, institutional speech, and pedagogy. (shrink)

Large Language Models (LLMs) are generative AI systems capable of producing original texts based on inputs about topic and style provided in the form of prompts or questions. The introduction of the outputs of these systems into human discursive practices poses unprecedented moral and political questions. The article articulates an analysis of the moral status of these systems and their interactions with human interlocutors based on the Habermasian theory of communicative action. The analysis explores, among other things, Habermas's inquiries into (...) the analogy between human minds and computers, and into the status of atypical participants in the linguistic community such as genetically modified subjects and animals. Major conclusions are the LLMs seem to qualify as authors that originally participate in discursive practices but do display only a structurally derivative form of communicative competence and fail to meet the status of communicative agents. In this sense, while the contribution of AI writing systems in public discourse and deliberation can support the process of mutual understanding within the community of speakers, the human actors involved in the development, use, and diffusion of these systems share a collective responsibility for the disclosure of AI authorship and verification and adjudication of validity claims. (shrink)

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 paper investigates the link between informational consequence and credence. I first suggest a natural constraint, namely that informational consequence should preserve certainty: on any rational credence distribution, when the premises of an informational inferences have credence 1, the conclusion also has credence 1. Then I show that the certainty‐preserving constraint leads to triviality. In particular, the following three claims are incompatible: (i) informational consequence is extensionally distinct from classical consequence; (ii) informational inferences preserve certainty; (iii) credences obey (a subset (...) of) classical Bayesian constraints. The proof is straightforward, but the theoretical implications are substantial. Informational theorists need to either give up the idea that credence applies to epistemic discourse, or develop a nonclassical theory of credence and credal update. Moreover, the result also suggests that there is a connection between informational consequence and triviality results, including classical triviality results like Lewis's. (shrink)

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

This article begins by examining the status of “difference” in representations of perspectivist cosmologies, which are themselves often represented as radically different to Euro-American cosmologi...

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)

In his later years, Peirce devoted much energy to the project of a book on logic, whose intended title was “Logic, considered as Semeiotic.” That the science of logic is better considered as semeiotic is indeed one of the most fundamental tenets of Peirce’s mature philosophy of logic. But what is the primary motivation for considering logic as semeiotic and what advantages did Peirce see in doing so? If logic is to be considered as semeiotic, this can only mean that (...) its objects and their functioning are to be described in purely semeiotical terms. But did Peirce succeed in providing such a description? This paper focuses on the semeiotical functioning of the fundamental triad of logic: terms (rhemes), propositions (dici-signs), and arguments; it also discusses the idea of an extension of the science of logic and offers examples of the kind of extension that Peirce had in mind. (shrink)

That words express a conceptual content is uncontroversial. This does not entail that their content should break down neatly into a grammatical part, relevant for language and to be analyzed in linguistic terms, and a conceptual part, relevant for cognition and to be analyzed in psychological terms. Various types of empirical evidence are reviewed, showing that the conceptual content of words cannot be isolated from their linguistic properties, because it is affected and shaped by them. The view of words as (...) labels or containers for a non-linguistic conceptual content stems from a naive disregard of the complex and structured nature of lexical knowledge. On the contrary, knowledge of language is shown not just to organize and categorize conceptual content in a way not reducible to non-linguistic cognition, but also to affect its scope, as the range of verbalized concepts is both limited by abstract templates and expanded by productive word formation. This suggests that lexical knowledge is a distinctively linguistic dimension of conceptualization, and that words do not so much label or package concepts, as provide an inner form for conceptual knowledge. (shrink)

Natural language conditionals seem to be subject to three logical requirements: they invalidate Antecedent Strengthening, they validate so-called Simplification of Disjunctive Antecedents, and they allow for the replacement of logically equivalent clauses in antecedent position. Unfortunately, these requirements are jointly inconsistent. Conservative solutions to the puzzle drop Simplification, treating it as a pragmatic inference. I show that pragmatic accounts of Simplification fail, and develop a truthmaker semantics for conditionals that captures all the relevant data. Differently from existing truthmaker semantics, my (...) semantics extends, rather than replaces, standard possible worlds semantics. The main innovation is the notion of a truthmaker in play: this notion is cognitive, rather than metaphysical, and can be defined in a purely syntactic way. (shrink)

Christ as symbol in Kant¿s religion -- Hegel's conception of God -- The reality of religion in Hegel's idealist metaphysics -- Hegel's version of the ontological argument for the existence of God -- The trinity and the I -- The death of God and recognition of the self -- Beyond subjectivism -- The relevance of Hegel's philosophy of religion today.

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on (...) the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

This paper investigates what happens when we merge two different lines of theorizing about counterfactuals. One is the comparative closeness view, which was developed by Stalnaker and Lewis in the framework of possible worlds semantics. The second is the interventionist view, which is part of the causal models framework developed in statistics and computer science. Common lore and existing literature have it that the two views can be easily fit together, aside from a few details. I argue that, on the (...) contrary, transplanting causal-models-inspired ideas in a possible worlds framework yields a new semantics. The difference is grounded in different algorithms for handling inconsistent information, hence it touches on issues that are at the very heart of a semantics for contrary-to-fact conditionals. Roughly, Stalnaker/Lewis semantics requires us to evaluate the consequent of a counterfactual at all closest antecedent-verifying possibilities. Causal-models-based semantics also does this, but in addition uses the information contained in the antecedent, together with background causal information, to shift what worlds count as closest. This makes systematically different predictions and generates a new logic. The upshot is that we have a new semantics to study, and a substantial theoretical choice to make. (shrink)

The adoption and reporting of CSR policies have important ethical and managerial implications that need scrutiny. This study answers the call of CSR scholars for further studies in controversial sectors by focusing on the voluntary reporting practices of companies that market products or services that generate addiction among consumers. It contributes to the debate on organizational legitimacy and corporate reporting by empirically analyzing whether and how corporations in the tobacco, alcohol and gambling industries disclose their CSR actions and what reactions (...) such disclosures generate in stakeholders. Drawing on legitimacy theory and organizational façades, we apply a consequent mixed-methods design (initiation approach) built on (i) a content analysis of reports prepared by a large set of companies listed on the European, British, US, Canadian, Australian and New Zealand stock exchanges and (ii) an experiment on how different actions taken by the companies (preventive vs. remedial) elicit different perceptions of company hypocrisy and action effectiveness. While previous analyses have focused on “sin” or “harm” industries, this is one of the first to assess how companies account for “addiction”, which is more difficult for them to report and legitimate due to long-term negative consequences. This study contributes to the literature on the instrumental use of CSR reporting by empirically investigating how addiction companies shape their organizational façades and manage organizational legitimacy through disclosure. Moreover, the experimental evidence advances the knowledge of how cognitive mechanisms influence stakeholders in terms of legitimacy assessment and the perceived hypocrisy/effectiveness of CSR disclosure. (shrink)

In the Posterior Analytics Aristotle contrasts demonstrations with syllogisms through signs. In the Prior Analytics he defines a sign as a demonstrative premise. One is thus led to ask: is a sign a demonstration? This book reconstructs the history of the notion of "demonstration through signs" from roughly the third through to the thirteenth century. It examines the work of Aristotle's Greek, Arabic, and Latin commentators, both within and outside the tradition of the Posterior Analytics.

Some philosophers find the following thesis attractive: for every logical constant C there is a set of logical rules of inference R such that a subject knows the meaning of C if and only if she accepts the rules in R. I point out some obvious but, apparently, easily forgotten difficulties concerning this thesis.

It is well-known that by 1882, Peirce, influenced by Cayley’s, Clifford’s and Sylvester’s works on algebraic invariants and by the chemical analogy, had already achieved something like a diagrammatic treatment of quantificational logic of relatives. The details of that discovery and its implications to some wider issues in logical theory merit further investigation, however. This paper provides a reconstruction of the genesis of Peirce’s logical graphs from the early 1880s until 1896, covering the period of time during which he already (...) was acquainted with the works of his Johns Hopkins colleagues on the mathematical theory of graphs and was reaching the very first forms of his theory and method of... (shrink)

Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs, which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be (...) derived from AGs, and argue that AGs analyse and represent assertions and illocutionary content in a way which is motivated both by its logical properties and its historical connection with the ideas that led to the development of the graphical method. (shrink)