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)

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)

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)

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)

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)

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)

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)

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)

What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a “critical” alternative to traditional plural logic.

Hume’s Principle states that the cardinal number of the concept F is identical with the cardinal number of G if and only if F and G can be put into one-to-one correspondence. The Schwartzkopff-Rosen Principle is a modification of HP in terms of metaphysical grounding: it states that if the number of F is identical with the number of G, then this identity is grounded by the fact that F and G can be paired one-to-one, 353–373, 2011, 362). HP is (...) central to the neo-logicist program in the philosophy of mathematics ; in this paper we submit that, even if the neo-logicists wish to venture into the metaphysics of grounding, they can avoid the SR Principle. In Section 1 we introduce neo-logicism. In Sections 2 and 3 we examine the SR Principle. We then formulate an account of arithmetical facts which does not rest on the SR Principle; we finally argue that the neo-logicists should avoid the SR Principle in favour of this alternative proposal. (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.

A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. (...) We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic. (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 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)

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)

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 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)

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)

In this article, we take into consideration two semantics of the future tense: linearism, according to which future-tense sentences are interpreted on a single history, and universalism, according to which they are evaluated by universally quantifying on the plurality of future histories that radiate from the present instant. Specifically, we focus on a objection advanced against universalism: if universalism were correct semantics of _will_, negated future-tense sentences of natural language should have two readings, depending on the scope of negation with (...) respect to the universal quantifier on histories. However, since natural language does not show this difference, one may conclude that there is no universal quantifier in the interpretation of these sentences. We show that this conclusion is premature. First, _will_ has clear scope interactions with indefinite nouns phrases, contrary to what linearism predicts. Second, it is possible to extend the treatment of vague predicates as partial predicates to _will_: Since partial predicates have no scope interactions with negation, this can account for the scopelessness of _will_. The partiality of truth conditions is not restricted to _will_ but also pertains to counterfactuals and generics and probably is part of a general tendency to maximize contraries. (shrink)

In addressing the problem of the (in)compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line ( $$\mathsf {TRL}$$ ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance (...) between Molinism and $$\mathsf {TRL}$$ models, Restall (Molinism and the thin red line. In: Perszyk K (ed) Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against $$\mathsf {TRL}$$ models. In particular, Restall believes that the implication $$p \rightarrow \mathbf {HF}p$$ is not true in $$\mathsf {TRL}$$ models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models (not just $$\mathsf {TRL}$$ ) the implication $$p \rightarrow \mathbf {HF}p$$ is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the $$\mathsf {TRL}$$ and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models (not just for Molinists) or can be accounted for by these models and so is not a problem for Molinists either. (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)

The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...) one which uses higher-order resources. (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 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.

This chapter contains sections titled: The Dialectic of Reason Observing Nature Observing the Nature of the Self References Further Reading.

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)

In Plato’s _Republic_ V, 449a-457b, Socrates argues that the guardian class of Kallipolis will comprise both men and women and that women with the appropriate nature ought to receive the same education and fulfill the same tasks as their male counterparts. In this article I argue, against competing interpretations of this claim as dependent either on the necessity of abolishing the oikos or on eugenic principles, that Socrates’ argument ought to be understood as a genuine argument about women’s natural capabilities (...) and ought to be interpreted in light of the Socratic debate about women’s virtues. Moreover, I show that the legal language mobilized, combined with polemical references to Aristophanes, serves the purpose of evoking Socrates’ trial, thus alerting the reader to the seriousness of the proposal in question. (shrink)

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)

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)

In this paper, we argue that Williamson’s arguments against luminosity and the KK principle do not work, at least in a scientific context. Both of these arguments are based on the presence of a so-called “buffer zone” between situations in which one is in a position to know p and situations in which one is in a position to know ¬p. In those positions belonging to the buffer zone ¬p holds, but one is not in a position to know ¬p. (...) The presence of this buffer zone triggers two types of sorites arguments. We show that this kind of argument does not hold in a scientific context, where the buffer zone is controlled by a quantitative measurement of the experimental error. (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.

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)

In this paper I adopt Étienne Balibar’s distinction between three forms of universality—“universality as reality,” “fictive universality,” and “ideal universality”—in order to retrieve universalism for feminist politics. The paper articulates a proposal for the feminist adoption of a specific notion of universality, which I call political insurgent universality. This notion is not based on a definition of human essence or of women's nature. It is rather rooted in the “real universality” historically created by capitalism, that is, in the fact that (...) capitalism has generated a world in which people are interdependent and in which capitalist accumulation poses objective universal constraints on social reproduction. (shrink)

My aim in this essay is to lead the reader through the complexity of Hegel’s philosophical understanding of organic nature by highlighting its distinctive theoretical features and by examining these historically, both against the background of the approaches, achievements and trends of the empirical sciences of his time and in light of their scholarly reception.1 First, I focuss on Hegel’s definition of the ‘universal form’ of life, pointing to what the connection is, in his philosophy of nature, between the structure (...) of conceptual and living processes in the path to the individualization of matter. Second, since Hegel calls animal life “the truth of organics,” 2 I shall try to explain how in the philosophy of nature the Idea of life comes to differentiate itself into certain essential characteristics of immediate, finite and individual animals, passing through the stages of geological nature and vegetable organisms. (shrink)

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

Introduction to a special issue based on a summer school on set theory and high-order logic.

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.

What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show how (...) they diverge under more complex assumptions about the structure of meaningful predication, such as cumulative type theory. We conclude by arguing that maximally strong generality is the more theoretically valuable conception. (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)

According to some scholars, universalist semantics of the future are incompatible with classical ascriptions of probability. This alleged fact is used as an argument for the linearist semantics of the future. In this paper, we show that, on the contrary, universalist semantics of the future are in harmony with the theory of probability, while the advocates of linearist semantics have to pay high theoretical costs to maintain the coherence with the classical theory of probability.

This article addresses the notions of gender performativity and temporality in Butler’s early work on gender. The paper is articulated in four steps. First it gives an account of the role and nature of temporality in Butler’s theory of gender performativity. Second, it shows some similarities and connections between the role played by temporality in Butler’s theory of gender performativity and its role in Marx’s analysis of capital. Third, it raises some criticisms of Butler’s understanding of temporality and historicity, focusing (...) in particular on the lack of historicisation of her own categories in bothGender TroubleandBodies that Matter. This deficit is a consequence of the epistemological framework within which she is operating, in particular of her understanding of social practices and relations through the lens of linguistic concepts extrapolated from their theoretical context. The article concludes by referring to Floyd’s and Hennessy’s analyses of the formation of sexual identities as examples of the fruitful historicisation of gender performativity, which also sheds some light on the ‘the abstract character’ of the temporality of gender performativity. (shrink)

Les théories féministes de la reproduction ont été soumises à trois types d’objections : elles seraient soit fonctionnalistes, soit économicistes, ou biologisantes. Ces objections reposent sur un contresens concernant les notions marxistes de production et reproduction ainsi que sur une conception réifiée de la nature des sociétés capitalistes. De plus, ces objections ne sont pas capables de proposer une alternative convaincante et débouchent sur des impasses comme celles qui sont propres aux théories des systèmes double ou triple. Au contraire, le (...) concept de reproduction sociale permet de sortir de ces impasses en même temps qu’il rend possible une conception non-réductionniste du mode de production capitaliste dans laquelle le capital n’est pas conçu comme le sujet d’un processus strictement « économique ». (shrink)

The species concept is one of the central concepts in biological science. Although modern systematics speculates about the existence of a complex hierarchy of nested taxa, biological species are considered particularly important for the active role they play in evolution. However, neither theoretical biologists nor philosophers of biology have come to an agreement about what a species is. In this chapter, we address two questions pertaining to biological species: (1) are they individuals or universals? and (2) are they bona fide (...) or fiat entities? In section The Species-as-Individuals View, we illustrate the reasons that have led many scholars to support the view that species are individuals. In the next two sections, we show that the relational concepts of species – on which the species-as-individuals view is based – provide neither necessary nor sufficient conditions for species membership. This seriously undermines the species-as-individuals view. In the section A Conceptualist Model for the Metaphysics of Species, we advance the proposal that species are fiat concepts (and thus, universal entities partially dependent on the human mind) carved in a multi-dimensional space representing the properties that the biological organisms possess. The final section concludes. (shrink)

This chapter provides an overview of the philosophical and linguistic debate about the logic of plurals. We present the most prominent singularizing analyses of plurals as well as the main criticisms that such analyses have received. We then introduce an alternative approach to plurals known as plural logic, focusing on the question whether plural logic can count as pure logic.