We review the history of decipherment on the technologies used for numbers by the Inkas – khipus and yupanas. We offer a novel interpretation of the portable “checkerboard” yupana drawn in 1615, revealing a numerical algorithm. This analysis sheds new light on the Inka number system, questioning its inclusion of a concept of zero and its interpretation as a positional system. We conclude that Inka numbers and computational methods were likely non-positional, analogous to Mesopotamian, Egyptian, Greek, and Roman numbers. We (...) show the Inka multiplication method as similar to – but more efficient than – the Egyptian method in the Rhind Papyrus. This analysis shows the Inka number system to have ranked among the great mathematical traditions of the ancient world. (shrink)

Todd and Rabern (2021) have argued that if we assume that future contingents are untrue and if we accept the Retro-closure principle (???? → PF(????)), then the existence of a temporal omniscient entity becomes metaphysically impossible. Since the truth of a metaphysical and theological theory should not be dependent on questions of temporal semantics, Todd and Rabern conclude that, if one wishes to maintain that future contingents are untrue, one must abandon the Retro-closure principle. The aim of this paper is (...) to propose a temporal semantics system in which future contingents are untrue, the Retro-closure principle is valid, and the possibility of the existence of an omniscient and temporal being is guaranteed. (shrink)

Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.

In light of the close connection between the ontological hierarchy of set theory and the ideological hierarchy of type theory, Øystein Linnebo and Agustín Rayo have recently offered an argument in favour of the view that the set-theoretic universe is open-ended. In this paper, we argue that, since the connection between the two hierarchies is indeed tight, any philosophical conclusions cut both ways. One should either hold that both the ontological hierarchy and the ideological hierarchy are open-ended, or that neither (...) is. If there is reason to accept the view that the set-theoretic universe is open-ended, that will be because such a view is the most compelling one to adopt on the purely ontological front. (shrink)

Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main arguments for (...) and against the possibility of unrestricted quantification, highlighting some of the broader implications of the debate. (shrink)

This chapter contains sections titled: What Is ‘High’ and What Is ‘Low’ in the Significance of Reason The Standpoint of Reason: or When Certainty Is Not Yet Truth Philosophical Issues: Standard Views and Reappraisals References Further Reading.

The idea of omnipotence plays a crucial role within the framework of classical theism. God is typically considered omnipotent, that is, able to perform any action. Sometimes, it is said that for God there is no difference between will and action; everything he wishes happens. However, as one reflects on the concept of omnipotence, some rather complex questions arise; the range of God’s possible “actions” is not clear. What are the boundaries of the power of an omnipotent being, if these (...) boundaries exist at all? In this paper, we will examine an interesting question: is it possible that two omnipotent beings exist? Or, does the property of omnipotence necessarily imply the uniqueness of its instantiation? Intuitively, the existence of more than one omnipotent being seems to be contradictory. However, we will demonstrate that under some conditions the existence of two omnipotent beings is possible. (shrink)

A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn (1976), many solutions to the paradox have been offered. In this article, we (...) present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable. (shrink)

Background: Advances in biomedical sciences, technologies and care practices have resulted in an increase in ethical problems and a resulting growth of difficulties encountered by health workers in their professional activity. Objective: The main objective of this study was to analyse knowledge in the ethical field and experience with and the propensity for using ethics consultations by nurses and physicians. Methods: Between March and June 2014, a cross-sectional observational study was conducted on a sample of 351 nurses and 128 physicians (...) in four central Italian hospitals. For data collection, a semi-structured questionnaire was used, consisting of 21 items divided into four sections exploring (1) demographic and occupational characteristics, (2) knowledge in the ethics field, (3) experience with ethical issues and (4) the propensity to use ethics consultation. Ethical considerations: Research ethics approval was obtained from the Italian Nurses Professional Board. Results: The results show that both nurses and physicians are faced with ethically sensitive situations. Nurses were found to have better judgement concerning their own knowledge than physicians, but more physicians were found to have a deeper level of specific training in ethics issues. The propensity to ask for ethics consultations to address ethical issues was found to be significantly associated with the degree to which ethical issues have deepened (and the level of experience acquired in this field). Conclusion: The presence of a consulting service that can lead to shared choices may represent, together with basic and continuing education, a valid support for professional growth in the ethical field for both physicians and nurses. (shrink)

In the semantic debate about plurals, pluralism is the view that a plural term denotes some things in the domain of quantification and a plural predicate denotes a plural property, i.e. a property that can be instantiated by many things jointly. According to a particular version of this view, untyped pluralism, there is no type distinction between objects and properties. In this article, I argue against untyped pluralism by showing that it is subject to a variant of a Russell-style argument (...) put forth by Timothy Williamson and that it clashes with a plural version of Cantor’s theorem. I conclude that pluralists should postulate a type distinction between objects and properties. (shrink)

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...) that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)

In this paper, we will defend a particular version of the timeless solution to the problem of divine foreknowledge and human freedom. Our strategy is grounded on a particular temporal framework, which models the flow of time and a libertarian understanding of freedom. The propositions describing a certain act by an agent have an indeterminate truth value until the agent makes her choice; therefore, they become true or false when a decision is made. In order to account for this change (...) of truth value, a multiple frame structure is introduced in which every frame presents a privileged time, with its past and the possible alternative futures, which are still open. God atemporally knows all the frames and the truth values of propositions with respect to each one. Since divine knowledge of what an agent decides in a certain temporal frame depends on the agent’s act itself, divine knowledge does not conflict with the agent’s free will. (shrink)

This chapter contains sections titled: General Characteristics of the Concept of Natural Life The Path to the Individualization of Matter Chemistry and Individuality: The Appearance and Disappearance of Life Contradiction in Chemicals The Necessary Limits of the Inorganic The Path to the Free Individuality of Life Conclusion References Abbreviations Works Cited.

Published in honor of Sergio Galvan, this collection concentrates on the application of logical and mathematical methods for the study of central issues in formal philosophy. The volume is subdivided into four sections, dedicated to logic and philosophy of logic, philosophy of mathematics, philosophy of science, metaphysics and philosophy of religion. The contributions adress, from a logical point of view, some of the main topics in these areas. The first two sections include formal treatments of: truth and paradoxes; definitions by (...) abstraction; the status of abstract objects, such as mathematical objects and universal concepts; and the structure of explicit knowledge. The last two sections include papers on classical problems in philosophy of science, such as the status of subjective probability, the notion of verisimilitude, the notion of approximation, and the theory of mind and mental causation, and specific issues in metaphysics and philosophy of religion, such as the ontology of species, actions, and intelligible worlds, and the logic of religious belonging. (shrink)

Analytic philosophy of religion has witnessed a significant increase in interest in the ontological presuppositions of the various theological doctrines. This special issue collects new essays on various divine attributes.

La pensée est un patrimoine discret et secret au point qu'elle n'est pas habituellement considérée comme un patrimoine au sens propre. Pourtant elle est à l'origine de tous les autres. Probablement sans l'exercice de cette faculté qui leur est propre, les êtres humains n'auraient jamais conçu leurs monuments extraordinaires ni leurs constructions admirables. Du plus petit phénomène jusqu'à la loi générale qui en coordonnerait les enchaînements, la recherche cultivée à l'intérieur de jardins divers et multiples tout le long de l'histoire (...) révèle un désir caché d'absolu. Comme si le jardinier dans l'aspiration d'élargir son horizon avait été amené à un certain moment à pousser les murs et à se retrouver chez le voisin, dans le monde et hors du monde par étapes successives. Un jeu de l'observation, de la mémoire et de l'imagination. En 2003, dans le cadre idéal de la Chartreuse de Valbonne, quelques représentants de disciplines diverses allaient reprendre ce jeu autour d'un thème aussi libre que contraignant tel que l'Espace Spirituel peut l'être. Quelques architectes, mathématiciens, musicologues, musiciens, et philosophes évoquent l'expression : Espace Spirituel chacun selon son angle de vue. L'idée d'Espace dans une cathédrale, dans le désert ou dans un chou fleur... Le Spirituel traverse les cultures du christianisme au judaïsme à l'indouisme. Le regard a l'écoulement du temps et les vignobles de la Chartreuse de Valbonne comme perspective. (shrink)

This paper has a twofold aim. The first is to offer a precise definition of soft fact. Without such definition it is impossible to assess the Ockhamist solution to the problem of divine foreknowledge and human freedom in an accurate way. The second purpose is to identify the costs of such a solution, distinguishing them from some of the other costs usually ascribed to Ockhamism, which Ockhamism does not actually need to pay. In particular, it is argued that Ockhamism is (...) committed to the view that a true future exists and to a form of backward causation. (shrink)

This paper provides an overview of semiotic studies about advertising, beginning with the early work done in the 1960s. Advertising communication plays a particular role in semiotic studies in the second half of the twentieth century. Pioneering studies of advertising messages, in particular those of Roland Barthes and Umberto Eco, date to the 1960s and were carried out for the most part using the tools of classical rhetoric. Following a period in which semiotics displayed a relative lack of interest in (...) advertisements, in the 1980s advertising texts were used as examples in applied narratological analysis by Jean-Marie Floch and others. This occurred at the same time as the so-called “passion turn of semiotics,” which stressed that the passions and emotions present in texts are crucial issues in textual semiotics, and it also seemed to offer fresh perspectives for the analysis of advertising communication. The passion turn took account of the evolution of advertising itself, since modern advertising is more and more interested in conveying passions and emotions. The effectiveness of an advert tends to be closely bound up with the presentation of sensations associated with a given product or brand. Recently, semioticians have begun to study more general features of advertising and marketing discourse. (shrink)

The timeless solution to the problem of divine foreknowledge and human freedom has many advantages. Still, the relationship between a timeless God and temporal beings is problematic in a number of ways. In this paper, we focus on the specific problems the timeless view has to deal with when certain assumptions on the metaphysics of time are taken on board. It is shown that on static conception of time God’s omniscience is easily accounted for, but human freedom is threatened, while (...) a dynamic conception has no problems with human freedom, but, on this view, some truths seem not to be knowable by a timeless God. We propose Fragmentalism as a metaphysics of time in which the divine timeless knowledge of temporal events and human freedom can be reconciled. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 109 Heft: 1 Seiten: 9-46.

The paradox that appears under Burali-Forti’s name in many textbooks of set theory is a clever piece of reasoning leading to an unproblematic theorem. The theorem asserts that the ordinals do not form a set. For such a set would be—absurdly—an ordinal greater than any ordinal in the set of all ordinals. In this article, we argue that the paradox of Burali-Forti is first and foremost a problem about concept formation by abstraction, not about sets. We contend, furthermore, that some (...) hundred years after its discovery the paradox is still without any fully satisfactory resolution. A survey of the current literature reveals one key assumption of the paradox that has gone unquestioned, namely the assumption that ordinals are objects. Taking the lead from Russell’s no class theory, we interpret talk of ordinals as an efficient way of conveying higher-order logical truths. The resulting theory of ordinals is formally adequate to standard intuitions about ordinals, expresses a conception of ordinal number capable of resolving Burali-Forti’s paradox, and offers a novel contribution to the longstanding program of reducing mathematics to higher-order logic. (shrink)

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of (...) predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory. (shrink)

This book deals with an old conundrum: if God knows what we will choose tomorrow, how can we be free to choose otherwise? If all our choices are already written, is our freedom simply an illusion? This book provides a precise analysis of this dilemma using the tools of modern ontology and the logic of time. With a focus on three intertwined concepts - God's nature, the formal structure of time, and the metaphysics of time, including the relationship between temporal (...) entities and a timeless God - the chapters analyse various solutions to the problem of foreknowledge and freedom, revealing the advantages and drawbacks of each. Building on this analysis, the authors advance constructive solutions, showing under what conditions an entity can be omniscient in the presence of free agents, and whether an eternal entity can know the tensed futures of the world. The metaphysics of time, its topology and the semantics of future tensed sentences are shown to be invaluable topics in dealing with this issue. Combining investigations into the metaphysics of time with the discipline of temporal Logic this monograph brings about important advancements in the philosophical understanding of an ancient and fascinating problem. The answer, if any, is hidden in the folds of time, in the elusive nature of this feature of reality and in the infinite branching of our lives. (shrink)

Edited by Cinzia Arruzza and Dmitri Nikulin, _Philosophy and Political Power in Antiquity_ is a collection of essays examining reflections by ancient philosophers on the implicit tension between political activity and the philosophical life from a variety of critical perspectives.

In constructional ontology, entities emerge by construction, that is, from the application of constructors to objects. We explore this approach to ontology, focusing on three modules: the constructors, the inputs to the constructors, and the constructional process. Our aim is to identify and assess some key theoretical choices arising in an ontology of this kind.

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...) main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

Russian-speaking homecare workers deploy two divergent discursive practices—professionalism and sainthood—in understanding carework. These two meaning-making systems have consequences for how this work is performed and experienced by workers. Surprisingly, the division is not based on gender. Instead, immigration laws filter Jewish and Orthodox Christian immigrants from the former Soviet Union into two separate sets of resettlement institutions. The characteristics of these separate institutional settings shape the discursive tools available to these two groups, leading Jewish refugees to deploy professionalism while Orthodox (...) Christian immigrants deploy sainthood. These discursive practices affect gendered identities, allowing workers in some cases to renegotiate hegemonic notions of masculinity and create new models of “feminine” caregiving. (shrink)

According to the singular conception of reality, there are objects and there are singular properties, i.e. properties that are instantiated by objects separately. It has been argued that semantic considerations about plurals give us reasons to embrace a plural conception of reality. This is the view that, in addition to singular properties, there are plural properties, i.e. properties that are instantiated jointly by many objects. In this article, I propose and defend a novel semantic account of plurals which dispenses with (...) plural properties and thus undermines the semantic argument in favor of the plural conception of reality. (shrink)

In this paper we will give a critical account of Plantinga’s well-known argument to the effect that the existence of an omnipotent and morally perfect God is consistent with the actual presence of evil. After presenting Plantinga’s view, we critically discuss both the idea of divine knowledge of conditionals of freedom and the concept of transworld depravity. Then, we will sketch our own version of the Free-Will Defence, which maintains that moral evil depends on the misuse of human freedom. However, (...) our argument does not hinge on problematic metaphysical assumptions, but depends only on a certain definition of a free act and a particular interpretation of divine omniscience. (shrink)

Non-bivalent semantics of the future tense assert that propositions regarding future contingents are neither true nor false. One of the most relevant non-bivalent semantics is supervaluationism :264–281, 1970; Thomason, in: Gabbay, Guenthner Handbook of philosophical logic, Springer, Berlin, 1984), which preserves important logical principles. Recently, non-bivalent semantics are under attack from some pragmatics arguments: these semantics would be incompatible with our practices of asserting future contingents and with the probability we ascribe to such assertions :251–271, 2014; Cariani and Santorio in (...) Mind 127:129–165, 2018). The aim of this paper is to defend supervaluationism against this kind of criticism. We argue that, if probability is interpreted as the subjective belief in a proposition and if a semantic contextualism is adopted, supervaluationism makes correct predictions concerning the norms that govern our practices of asserting future contingents. Obviously, other arguments can be proposed against supervaluationism, but they must be of a different kind, such as metaphysical arguments. (shrink)

Sentences that exhibit sensitivity to order (e.g. 'John and Mary arrived at school in that order' and 'Mary and John arrived at school in that order') present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference (Hewitt 2012) and articulated reference (Ben-Yami 2013). The aim of this article is to show that sensitivity to order should be accounted for (...) without altering the standard formulation of plural logic. In particular, sensitivity to order does not call for a fine-grained notion of plural reference. We point out that the phenomenon in question is quite broad and that current proposals are not equipped to deal with the full range of cases in which order plays a role. Then we develop an alternative and unified account, which locates the phenomenon not in the way in which plural terms can refer, but in the meaning of special expressions such as 'in that order' and 'respectively'. (shrink)

The significance of the notions of actuality and potentiality in Plotinus' thought can hardly be overstated. Throughout the Enneads, they are crucial to understanding the specific causality of intelligible realities and the relation of participation between intelligible and sensible realms. In Ennead II.5, Plotinus for the first time provides a systematic clarification of his peculiar use of these terms, through a sustained revision of Aristotle's own elaboration of the topic and of his terminology. The treatise discusses the different meanings of (...) potentiality and actuality as well as the way each of them applies or does not apply to the sensible realm, to the intelligible realm, and to matter. (shrink)