On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

Suppose that you're certain that a certain sentence, e.g. "Frida is tall", lacks a determinate truth value. What cognitive attitude should you take towards it—reject it, suspend judgment, or what else? We show that, by adopting a seemingly plausible principle connecting credence in A and Determinately A, we can prove a very implausible answer to this question: i.e., all indeterminate claims should be assigned credence zero. The result is striking similar to so-called triviality results in the literature on modals and (...) conditionals. (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)

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)

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)

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)

According to the orthodox account developed by Kaplan, indexicals like I, you, and now invariably refer to elements of the context of speech. This essay argues that the orthodoxy is wrong. I, you, and the like are shifted by certain modal operators and hence can fail to refer to elements of the context, for example, I can fail to refer to the speaker. More precisely, indexicals are syntactically akin to logical variables. They can be free, in which case they work, (...) roughly, on the Kaplan model. But they can also be bound: this happens, in a systematic fashion, when they are in the scope of epistemic modals or attitude verbs. The new view has two interesting philosophical consequences. First, it vindicates a broadly Fregean perspective on referential expressions, essentially refuting the idea that indexicals are rigid designators. Second, it suggests a new picture of the interaction between context and linguistic meaning: compositional semantics does not need to look at the context and hence has no need for a context parameter. (shrink)

On a popular view dating back to Russell, descriptions, both definite and indefinite alike, work syntactically and semantically like quantifiers. I have an argument against Russell's view. The argument supports a different picture: descriptions can behave syntactically and semantically like variables. This basic idea can be implemented in very different systematic analyses, but, whichever way one goes, there will be a significant departure from Russell. The claim that descriptions are variables is not new: what I offer is a new way (...) of defending it. The argument centers on attitude reports. I argue that we should recognize a new reading of descriptions under attitude reports, which I call ‘singular opaque’. The existence of this reading cannot be explained on the traditional Russellian view, and demands a switch to the variable view. Along the way, some interesting new facts about attitude reports come to light. (shrink)

Know-how and expressivism are usually regarded as disjoint topics, belonging to distant areas of philosophy. This paper argues that, despite obvious differences, the two debates have important similarities. In particular, semantic and conceptual tools developed by expressivists can be exported to the know-how debate. On the one hand, some of the expressivists' semantic resources can be used to deflect Stanley and Williamson's influential argument for factualism about know-how: the claim that knowing how to do something consists in knowing a fact. (...) On the other, expressivism provides the resources to formulate a nonfactualist account of know-how. On this account, know-how has a kind of nonpropositional content and plays the role of guiding performance of action, rather than recording information from the environment. (shrink)

Statements about the future are central in everyday conversation and reasoning. How should we understand their meaning? The received view among philosophers treats will as a tense: in ‘Cynthia will pass her exam’, will shifts the reference time forward. Linguists, however, have produced substantial evidence for the view that will is a modal, on a par with must and would. The different accounts are designed to satisfy different theoretical constraints, apparently pulling in opposite directions. We show that these constraints are (...) jointly satisfied by a novel modal account of will. On this account, will is a modal but doesn't work as a quantifier over worlds. Rather, the meaning of will involves a selection function similar to the one used by Stalnaker in his semantics for conditionals. The resulting theory yields a plausible semantics and logic for will and vindicates our intuitive views about the attitudes that rational agents should have towards future-directed contents. (shrink)

Suppose you’re certain that a claim—say, ‘Frida is tall’—does not have a determinate truth value. What attitude should you take towards it? This is the question of the cognitive role of indeterminacy. This paper presents a puzzle for theories of cognitive role. Many of these theories vindicate a seemingly plausible principle: if you are fully certain that A, you are rationally required to be fully certain that A is determinate. Call this principle ‘Certainty’. We show that Certainty, in combination with (...) some minimal side premises, entails a very implausible claim: whenever you’re certain that it’s indeterminate whether A, it is rationally required that you reject A. This is a surprising result, which requires abandoning at least some intuitive views about indeterminacy and cognitive role. (shrink)

On a traditional view, the semantics of natural language makes essential use of a context parameter, i.e. a set of coordinates that represents the situation of speech. In classical semantic frameworks, this parameter plays two key roles: first, context contributes to determining the content of utterance; second, it is crucial for defining logical consequence. I point out that recent empirical proposals about context shift in natural language (in particular, context-shifting semantics in the style of Anand and Nevins 2004) are incompatible (...) with the traditional view of context. At the same time, there is increasing cross-linguistic support for this brand of context shift. Hence I suggest that context has no place in semantic theory proper. We should revert back to so-called multiple-indexing frameworks that were developed by Montague and others, and relegate context to the postsemantic stage. (shrink)

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)

This paper develops an information-sensitive theory of the semantics and probability of conditionals and statements involving epistemic modals. The theory validates a number of principles linking probability and modality, including the principle that the probability of a conditional If A, then C equals the probability of C, updated with A. The theory avoids so-called triviality results, which are standardly taken to show that principles of this sort cannot be validated. To achieve this, we deny that rational agents update their credences (...) via conditionalization. We offer a new rule of update, Hyperconditionalization, which agrees with Conditionalization whenever nonmodal statements are at stake but differs for modal and conditional sentences. (shrink)

A long-standing tension in semantic theory concerns the reconciliation of positive gradable adjective (GA) ascriptions and comparative GA ascriptions. Vagueness-based ap- proaches derive the comparative from the positive, and face non-trivial challenges with incommensurability and non-GA comparatives. Classic degree-based approaches effectively derive the positive from the comparative, out of sync with the direction of evidence from morphology, and create some difficulties in accounting for GA scale-mates with differing thresholds (e.g., cold ∼ warm ∼ hot). We propose a new reconciliation that (...) capitalizes on recent proposals analyzing GAs as predicates of states. On our account, GAs lexically involve both a threshold property and a background state structure. Positive occurrences of GAs make use of the threshold property, while comparative occurrences make use of degrees representing elements of the background structure. Our approach preserves the virtues of classic degree-based approaches while offering a natural account of scale-mates, and without appeal to covert morphemes like POS or related devices. As we show, it is possible to inject our solution back into the classic degree-based approach, but we find reasons to prefer our states-based account. (shrink)

How can expressivists make sense of the practice of communication? If communication is not a joint enterprise aimed at sharing information about the world, why do we engage in communication the way we do? Call this *the problem of communication*. Starting from basic assumptions about the rationality of speakers and the nature of assertion, we argue that speakers engaging in conversation about normative matters must presuppose that there is a unique normative standard on which the attitudes of conversational participants ought (...) to converge. This gives the beginning of a solution to the problem of communication on behalf of expressivists. (shrink)

We advocate and develop a states-based semantics for both nominal and adjectival confidence reports, as in "Ann is confident/has confidence that it's raining", and their comparatives "Ann is more confident/has more confidence that it's raining than that it's snowing". Other examples of adjectives that can report confidence include "sure" and "certain". Our account adapts Wellwood's account of adjectival comparatives in which the adjectives denote properties of states, and measure functions are introduced compositionally. We further explore the prospects of applying these (...) tools to the semantics of probability operators. We emphasize three desirable and novel features of our semantics: (i) probability claims only exploit qualitative resources unless there is explicit compositional pressure for quantitative resources; (ii) the semantics applies to both probabilistic adjectives (e.g., "likely") and probabilistic nouns (e.g., "probability"); (iii) the semantics can be combined with an account of belief reports that allows thinkers to have incoherent probabilistic beliefs (e.g. thinking that A & B is more likely than A) even while validating the relevant purely probabilistic claims (e.g. validating the claim that A & B is never more likely than A). Finally, we explore the interaction between confidence-reporting discourse (e.g., "I am confident that...") and belief-reports about probabilistic discourse (e.g.,"I think it's likely that.."). (shrink)

Disjunctions in the scope of possibility modals give rise to a conjunctive inference, generally referred to as ‘free choice.’ For example, Emma can take Spanish or Calculus suggests that Emma can take Spanish and can take Calculus. This inference is not valid on standard semantics for modals in combination with a Boolean semantics for disjunction. Hence free choice has sparked a whole industry of theories in philosophy of language and semantics. This paper investigates free choice in sentences involving a non-monotonic (...) modified numeral, under which we embed a possibility modal scoping over disjunction. One example is Exactly one student can take Spanish or Calculus. As we point out, the presence of certain readings of these sentences is a key test for a prominent approach, which analyzes free choice as a kind of scalar implicature. We report on two experiments investigating the readings of such sentences, using an inferential task. Our results are challenging for the implicature approach. We sketch two possible solutions within this approach, either adopting a different recent implicature algorithm, or exploring a different meaning for modified numerals with exactly. Both of them suffer from a variety of problems. We then discuss a third solution, which exploits a recent account of free choice based on homogeneity. This approach can account for our results, in combination with plausible assumptions about homogeneity projection, though it too has open issues with related cases. Regardless of which solution is chosen, non-monotonic contexts turn out to be an important test case for theories of free choice, implicature, and modified numerals. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (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 (1) Brouwer, (2) Weyl, (3) Bernays and Hilbert, and (4) 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)

This paper deals with a case of Virgilian ambiguity, namely the famous hemistich at Aen. 4.298 omnia tuta timens. By highlighting a plausible reading with a causal force (‘fearing everything too calm’, ‘because of the excessive calmness’), it seeks to demonstrate that this hemistich is an ambiguous passage. This view is confirmed through the imitation by Valerius Flaccus, who, in alluding to the Virgilian passage (Argonautica 8.408–12), highlights its ambiguity by including both of the most plausible readings.

Can taxation and the redistribution of wealth through the welfare state be conceived as a modern system of circulation of the gift? But once such a gift is institutionalized, regulated and sanctioned through legal mechanisms, does it not risk being perverted or corrupted, and/or not leaving room for genuinely altruistic motives? What is more: if the market’s utilitarian logic can corrupt or ‘crowd out’ altruistic feelings or motivations, what makes us think that the welfare state cannot also be a source (...) of corruption? To explain the standard answers to the abovementioned questions as well as their implications I will first re-examine two opposing positions assumed here as paradigmatic examples of other similar positions: on the one hand, Titmuss’s work and the never-ending debate about it; on the other, Godbout’s position, in-so-far as it shows how Titmuss’s arguments can easily be turned upside down. I will then introduce and reinterpret Einaudi’s “critical point” theory as a more complex and richer anthropological explanation of the problems and answers considered herein. Through the analysis of these paradigmatic positions I will develop two interrelated arguments. 1) The way these problems are posed as well as the standard answers to them are: a) subject to fallacies: the dichotomy fallacy and the fallacy of composition; b) too reductive and simplistic: we should at least try to clarify what kind of ‘gift’ or ‘corruption’ we are thinking about, and who or what the ‘giver’, the ‘corrupter’, the ‘receiver’ and/or the ‘corrupted’ party are. 2) The answers to these problems cannot be found by merely following a theoretical approach, nor can they be merely based on empirical evidence; instead, they need to take into account the forever troublesome, ambiguous and unpredictable matter of human freedom. (shrink)

A significant body of research concludes that stable beliefs of perceived consumer effectiveness lead to sustainable consumption choices. Consumers who believe that their decisions can significantly affect environmental and social issues are more likely to behave sustainably. Little is known, however, about how perceived consumer effectiveness can be increased. We find that feelings of guilt and pride, activated by a single consumption episode, can regulate sustainable consumption by affecting consumers’ general perception of effectiveness. This paper demonstrates the impact that guilt (...) and pride have on perceived consumer effectiveness and shows how this effect rests on the ability of these emotions to influence perceptions of agency. After experiencing guilt or pride, consumers see themselves as the cause of relevant sustainability outcomes. The process of causal attribution associated with these emotions influences consumers’ use of neutralization techniques. Through the reduction in consumers’ ability to neutralize their sense of personal responsibility, guilt and pride positively influence perceived consumer effectiveness. The inability to rationalize-away their personal responsibility, persuades consumers that they affect sustainability outcomes through their decisions. The research advances our understanding of sustainable consumption and identifies a new avenue for the regulation of individual consumer behavior that has significant implications for the development of sustainable marketing initiatives. (shrink)

The study of evil and the different forms in which it manifests itself has long been the interest of a significant number of scholars, mainly philosophers and theologians. Yet, following the libera...

A growing body of literature documents the important role played by moral outrage or moral anger in stakeholders’ reactions to cases of corporate social irresponsibility. Existing research focuses more on the consequences of moral outrage than a systematic analysis of how appraisals of irresponsible corporate behavior can lead to this emotional experience. In this paper, we develop and test, in two field studies, an extended model of moral outrage that identifies the cognitions that lead to, and are associated with, this (...) emotional experience. This research contributes to the existing literature on reactions to corporate social irresponsibility by explaining how observers’ evaluation of irresponsible corporate behavior leads to reactions of moral anger. The paper also helps clarify the difference between moral outrage and other types of anger and offers useful insights for managers who have to confront public outrage following cases of irresponsible corporate behavior. Finally, the analysis of the causes of stakeholders’ anger at irresponsible corporations opens important avenues for future research that are presented in the paper. (shrink)

The publication of Guido Calabresi’s book “The Future of Law and Economics” has drawn a substantial amount of attention among law and economics scholars. We thought that the best way to devote special attention to this book was to devote a Special issue to it. This article situates Calabresi’s book among other reflections on the future of the discipline, introduces and explains the reasons behind this Special issue and discuss the organization and content of it. -/- We emphasize how Calabresi’s (...) historical-conceptual standpoint allows him to isolate the stakes of different future developments around the question of how could further appreciation of legal institutions that defy the standard economic assumptions help the field develop theoretically. Overall, the contributors all shared Calabresi’s attempt to restore the balance between Law and Economics and the need to better account for the “whole unanalysed experience of human race”, often neglected by the Economic Analysis of Law approach. Most disagreements are about the ‘how’. In any case, the search for the Law and Economics ‘not (yet) taken’ or for other “Law and … ” approaches is always open to the Future. (shrink)

This introduction explains the reasons behind this Special issue and discuss the organization and content of it. The difficulty of a genuine dialogue and understanding between economics, law and humanities, seems to be due not only to the fragmentation of reflections on man, but to a real ‘conflict of anthropologies’. What kind of conceptions of man and human values are presupposed by and / or privileged by economics, law, economic approaches to law and social sciences? How and when do these (...) conceptions come into conflict within and between disciplines? How do these conceptions of man and his values influence the conceptions of economics, law and institutions, and vice versa, how do these last conceptions influence the former? What are the normative, regulatory and practical implications of assuming an anthropological and / or axiological perspective instead of another? This Special issue aims at exploring the possibility of finding a common ground for discussion between economics, law and humanities, through the analysis and comparison of both the conceptions of man, human action and values assumed by economics, law and humanities, and their normative implications. The contributions to this Special issue and its organization are outlined at the end of this introduction. (shrink)

The paper aims to address the following two questions: what kind of discourse is that which attempt to found or defend the autonomy or the boundaries of a discipline? Why do such discourses tend to turn into normative, dogmatic-excommunicating discourses between disciplines, schools or scholars? I will argue that an adequate answer may be found if we conceive disciplines as dogmatics, where such discourses often take the form of a discourse on the foundation of a discipline, a foundation in the (...) name of which the scholar speaks and with which he/she entertains an identity relationship. To this purpose I will re-examine the methodological discourses of (and debates between) Pareto, Croce and Einaudi on the demarcation issue between philosophy, economics and value-judgments as highly instructive to understand such issues. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 937-947, December 2021.

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)

Il libro ricostruisce la vita e il pensiero di Jean Guitton (1901-1999), il grande amico di Paolo VI, a quasi ventʼanni dalla sua morte. La vicenda umana di questo scrittore e filosofo cristiano ha attraversato quasi integralmente il XX secolo quale testimone diretto di eventi epocali: i primi tentativi ecumenici, le due guerre mondiali, le radicalizzazioni ideologiche del secondo dopoguerra, lʼera atomica e il Concilio Vaticano II. Il primo capitolo del volume è dedicato alla ricostruzione della vita di Guitton (...) e alle sue prime sintesi accademiche; ed esso fanno seguito altri due capitoli che trattano della sua antropologia (il tempo, il pudore, l'amore umano) e della sua cristologia filosofica (le condizioni di possibilità della rivelazione, la filosofia della risurrezione, la sua innovativa mariologia). Ne viene il ritratto di un pensiero di impronta umanista, ben radicato nella tradizione francese e che forse, come già lamentava Yves Congar nel 1963, non ha avuto, fino ad oggi, quellʼattenzione e quellʼaccoglienza che sembra meritare. (shrink)

Current research has documented how cases of irresponsible corporate behavior generate negative reactions from consumers and other stakeholders. Existing research, however, has not examined empirically whether the characteristics of the victims of corporate malfeasance contribute to shaping individual reactions. This study examines, through four experimental surveys, the role played by the national identity of the people affected on consumers’ intentions to spread negative word of mouth. It is shown that national identity influences individual reactions indirectly; mediated by perceived similarity and (...) sympathy. Consumers perceive foreign victims as different from the self and this reduces the sympathy experienced towards them. Sympathy is an emotion that shapes consumer reactions and regulates WOM. The study identifies two moderating processes of this effect. Individuals who score high on collective narcissism are most likely to be strongly biased against foreign victims. In-group bias is also moderated by the perceived severity of the crisis. When a case is perceived as very serious, perceived similarity plays a less important role in generating sympathy because consumers focus on the perceived suffering of the victims. Hence, in-group bias is stronger in cases perceived as having minor consequences. The paper contributes to the literature on corporate social irresponsibility and offers implications for both scholars and managers. (shrink)

Meaningful places -- Fictional objects -- Migrant objects -- Multicultural and transcultural objects -- Objects as props -- Conclusion.

I argue that classical counterfactual semantics in the style of Stalnaker, Lewis, and Kratzer validates an inference pattern that is disconfirmed in natural language. The solution is to alter the algorithm we use to handle inconsistency in premise sets: rather than checking all maximally consistent fragments of a premise sets, as in Krazter’s semantics, we selectively remove some of the premises. The proposed implementation starts from standard premise semantics and involves a new ‘filtering’ operation that achieves just this removal. The (...) resulting semantics is interestingly related to the semantics for counterfactuals emerging from Judea Pearl’s causal models framework in computer science: in particular, filtering is a possible worlds semantics counterpart of Pearl’s interventions. (shrink)

An algebraization of the notion of topology has been proposed more than 70 years ago in a classical paper by McKinsey and Tarski, leading to an area of research still active today, with connections to algebra, geometry, logic and many applications, in particular, to modal logics. In McKinsey and Tarski’s setting the model theoretical notion of homomorphism does not correspond to the notion of continuity. We notice that the two notions correspond if instead we consider a preorder relation \( \sqsubseteq (...) \) defined by \(a \sqsubseteq b\) if _a_ is contained in the topological closure of _b_, for _a_, _b_ subsets of some topological space. A _specialization poset_ is a partially ordered set endowed with a further coarser preorder relation \( \sqsubseteq \). We show that every specialization poset can be embedded in the specialization poset naturally associated to some topological space, where the order relation corresponds to set-theoretical inclusion. Specialization semilattices are defined in an analogous way and the corresponding embedding theorem is proved. Specialization semilattices have the amalgamation property. Some basic topological facts and notions are recovered in this apparently very weak setting. The interest of these structures arises from the fact that they also occur in many rather disparate contexts, even far removed from topology. (shrink)

Il presente volume raccoglie il corso di Filosofia tenuto dall'autore nell'Istituto di Cultura Superiore Religiosa per laici, destinato a studenti e professionisti desiderosi di una prima iniziazione alla conoscenza dei vari orientamenti del pensiero filosofico moderno e alla riflessione sui principali problemi della filosofia, riguardanti specialmente il mondo e Dio, la vita e l'uomo, che prima o poi si presentano spontaneamente a chiunque pensa e riflette, e la cui soluzione vuole esercitare un notevole influsso sulla vita di ciascuno. Paolo (...) Dezza per molti anni professore di Metafisica Generale nella Pontificia Universita Gregoriana e per 10 anni Rettore nella stessa Universita, e stato Cardinale della Santa Romana Chiesa. (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...

The aim of this article is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to developments in the study of early modern mathematics and the rediscovery of Bruno's first mathematical writings (four dialogues on Fabrizio's Mordente proportional compass), we are in a position to better understand Bruno's mathematics. In particular, this article aims to reopen (...) the question of whether Bruno anticipated the concept of infinitesimal quantity. It does so by providing an analysis of the dialogues on Mordente's compass and of the historical circumstances under which those dialogues were written. (shrink)