Within a literary ontology, YHWH in the Hebrew Bible is technically also a fictional entity or object. In Hebrew Bible scholarship, a variety of philosophical issues surrounding fiction have received sustained and in-depth attention. However, the mainstream research on these matters tends to focus on the philosophical foundations of or backgrounds to a particular literary theory, rather than on metaphysical puzzles as encountered in the philosophy of fiction proper. To fill this gap, the present article seeks to provide a meta-theoretical (...) overview of the main contemporary philosophical perspectives on the metaphysics of fictional objects. Three views are discussed, namely possibilism, Meinongianism and creationism. Each view's theory is introduced and critically appropriated with reference to what is implied to be an answer to the question of what exactly the biblical character YHWH can meaningfully be said to be in the context of the metaphysics of fictional objects. In this way, the present study also goes beyond the traditional concern with the nature of God in Old Testament theology. (shrink)

In this paper, we compare two theories, modal Meinongianism and object theory, with respect to several issues that have been discussed recently in the literature. In particular, we raise some objections for MM, undermine some of the objections that its defenders raise for OT, and we point out some virtues of the latter with respect to the former.

In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's *Grundgesetze*. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (...) (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege's conception of numbers and logical objects. (shrink)

In this paper, I explore a line of argument against one form of realism about fictional characters : abstract artifact theory, the view according to which fictional characters like Harry Potter are part of our reality, but, they are abstract objects created by humans, akin to the institution of marriage and the game of soccer. I will defend artifactualism against an objection that Mark Sainsbury considers decisive against it: the category-mistake objection. The objection has it that artifactualism attributes to people (...) who produce and process sentences and thoughts about Harry Potter massive error, indeed, a category mistake about what kind of thing Harry Potter is; for an abstract object isn’t the sort of thing that can wear glasses, ride a double-decker bus, attend school. Given problems with this objection, artifactualism, I shall conclude, remains a tenable contender. (shrink)

In this entry I present one of the most hotly debated issues in contemporary analytic philosophy regarding the nature of fictional entities and the motivations that might be adduced for and against positing them into our ontology. The entry is divided in two parts. In the first part I offer an overview of the main accounts of the metaphysics of fictional entities according to three standard realist views, fictional Meinongianism, fictional possibilism and fictional creationism. In the second part I describe (...) two main kinds of arguments for or against positing fictional entities into our ontology. The first kind is traditionally inspired by the linguistic data coming from our talk about fictional characters. The second kind is more recent and it builds on genuine ontological considerations. (shrink)

Are there nonexistent objects, i.e., objects that do not exist? Some examples often cited are: Zeus, Pegasus, Sherlock Holmes, Vulcan (the hypothetical planet postulated by the 19th century astronomer Le Verrier), the perpetual motion machine, the golden mountain, the fountain of youth, the round square, etc. Some important philosophers have thought that the very concept of a nonexistent object is contradictory (Hume) or logically ill-formed (Kant, Frege), while others (Leibniz, Meinong, the Russell of Principles of Mathematics) have embraced it wholeheartedly. (...) This entry is an examination of the many questions which arise in connection with the view that there are nonexistent objects. The following are particularly salient: What reasons are there (if any) for thinking that there are nonexistent objects? If there are nonexistent objects, then what kind of objects are they? How can they be characterized? Is it possible to provide a consistent theory of nonexistent objects? What is the explanatory force of a consistent theory of nonexistent objects (if such a thing is possible)? (shrink)

Some recently-proposed counterexamples to the traditional definition of essential property do not require a separate logic of essence. Instead, the examples can be analysed in terms of the logic and theory of abstract objects. This theory distinguishes between abstract and ordinary objects, and provides a general analysis of the essential properties of both kinds of object. The claim ‘x has F necessarily’ becomes ambiguous in the case of abstract objects, and in the case of ordinary objects there are various ways (...) to make the definition of ‘F is essential to x’ more fine-grained. Consequently, the traditional definition of essential property for abstract objects in terms of modal notions is not correct, and for ordinary objects the relationship between essential properties and modality, once properly understood, addresses the counterexample. (shrink)

In this paper, the authors discuss Frege's theory of "logical objects" and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for (...) Logical Objects and banishes encoding formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: the theory of extensions, the theory of directions and shapes, and the theory of truth values. (shrink)

Abstractionist programs in the philosophy of mathematics have focused on abstraction principles, taken as implicit definitions of the objects in the range of their operators. In second-order logic (SOL) with predicative comprehension, such principles are consistent but also (individually) mathematically weak. This paper, inspired by the work of Boolos (Proceedings of the Aristotelian Society 87 , 137–151, 1986) and Zalta (Abstract Objects, vol. 160 of Synthese Library, 1983), examines explicit definitions of abstract objects. These axioms state that there is a (...) unique abstract encoding all concepts satisfying a given formula φ(F), with F a concept variable. Such a system is inconsistent in full SOL. It can be made consistent with several intricate tweaks, as Zalta has shown. Our approach in this article is simpler: we use a novel method to establish consistency in a restrictive version of predicative SOL. The resulting system, RPEAO, interprets first-order PA in extensional contexts, and has a natural extension delivering a peculiar interpretation of PA2. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

The general topic of this paper is the ontological commitment to so-called "fictitious objects", that is, things and characters of fictional stories, like Sherlock Holmes and Pegasus. Discourse about fiction seems to entail an ontological commitment to fictitious entities, a commitment that is often deemed inconsistent with empirical facts. For instance, "Pegasus is a flying horse" seems to entail "There are flying horses" as well as "Pegasus exists" (according to some widely accepted logical principles). I discuss two solutions that have (...) been proposed in the literature. The first one amounts to rejecting sentences like "Pegasus is a flying horse" as false, at least if they are taken at face value. This solution is called the "story operator strategy". It consists in paraphrasing sentences like "Pegasus is a flying horse" by means of the expression "according to a story" such that they are interpreted as an elliptic formulation of, e.g., "According to a story, Pegasus is a flying horse". I spell out the difficulties of the story operator strategy and opt for a realist ontology of fiction. A novel interpretation of the story operator "according to a story" is given, which is not only consistent with but even sheds new light on such a realist ontology. In particular, it is shown how the story operator can be used as a tool to introduce the so-called "modes of predication distinction" (which is an essential ingredient of many realist ontologies of fiction) in a commonsensical way. (shrink)

Ludwig Wittgenstein has often been called a quietist. His work has inspired a rich and varied array of theories in moral philosophy. Some prominent meta-ethicists have also been called quietists, or ‘relaxed’ as opposed to ‘robust’ realists, sometimes with explicit reference to Wittgenstein in attempts to clarify their views. In this chapter, I compare and contrast these groups of theories and draw out their importance for contemporary meta-ethical debate. They represent countercultures to contemporary meta-ethics. That is, they reject in different (...) ways one or more of the common assumptions that, whilst not universally shared, shape how to understand and engage in contemporary meta-ethical debate. Despite striking similarities, I argue that the ‘quietist’ label has obscured the views it is used to describe, the crucial differences between them, and the challenge that they offer to the predominant culture of meta-ethical enquiry. That challenge is this: there are plausible different ways of understanding and doing meta-ethics to those of the meta-ethical orthodoxy. We ignore such heterodoxy at our own peril. (shrink)

[Draft substantially revised, September 2021] David Lewis acclimated us to talk of “nonactual concreta that exist,” regarding talking donkeys and the like. I shall argue that this was not for the best, and try to normalize a way of describing them as “actual concreta that do not exist.” The basis of this is a defense of the Meinongian thesis “there are objects of which it is true that there are no such objects,” re: fictitious and illusory objects. I first formulate (...) the problem of negative existentials in a novel way, and discuss why this new version is more forceful against anti-Meinongians. Additional data is also pressed against anti-Meinongians--e.g., the truth of ‘Pegasus is imaginary’, and a reading of ‘There actually are illusory objects’ where it comes out true. The Meinongian, in contrast, easily and uniformly explains the same data, by allowing the existence Pegasus, pink elephants, and the like. But contra Meinong, these cases suggest that the nonexistent objects are mind-dependent objects, and I clarify and defend this suggestion from several objections. The resulting Meinongianism is thus “conservative” in that it merely acknowledges the sense in which there are mind-dependent objects, imaginary and illusory objects being prime examples. Of special note, the “ideology” is conservative as well in that the typical Meinongian jargon of “nuclear” or “encoded” properties is paraphrased away. New suggestions about the ontology of abstracta, mere possibilia, and impossibilia are sketched in light of this. Comparisons are also made with Thomasson, Crane, and McGinn, among others. (shrink)

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the (...) term ‘platonism’ is spelled with a lower-case ‘p’. (See entry on Plato.) The most important figure in the development of modern platonism is Gottlob Frege (1884, 1892, 1893-1903, 1919). The view has also been endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948, 1951). (shrink)

In this paper, the author shows how one can independently prove, within the theory of abstract objects, some of the most significant claims, hypotheses, and background assumptions found in Kripke's logical and philosophical work. Moreover, many of the semantic features of theory of abstract objects are consistent with Kripke's views — the successful representation, in the system, of the truth conditions and entailments of philosophically puzzling sentences of natural language validates certain Kripkean semantic claims about natural language.

In, the author proposes a survey of Zalta’s Object Theory and, more specifically, of the Modal Axiom of Encoding. MAE claims that if something x possibly encodes a property F, then x necessarily encodes F. According to Bourgeois-Gironde, MAE fails to account for intentional phenomena which occur in conceivability-contexts. His solution is based on the notion of quasi-encoding: x quasi-encodes F iff x possibly encodes F. In this paper, I show that Bourgeois-Gironde’s concern is misguided and that Zalta’s framework captures (...) the conceivability-phenomena at issue by modeling Husserl’s notion of Noemata. I then argue that his solution is superior to Bourgeois-Gironde’s. The philosophical significance of such a discussion nonetheless goes well beyond the debate between these two authors. Indeed, Zalta’s theory of Noemata is only sketched and needs to be further explored to see, on the one hand, whether and how Object Theory successfully describes the behavior of objects in conceivability-contexts, and, on the other hand, to test the efficacy of its primitive notions that are – as the contemporary debate on Neomeinongianism largely shows – anything but uncontroversial. (shrink)

For many recent readers of Hegel, Wilfrid Sellars’s 1956 London lectures on the “Myth of the Given” have signaled an important rapprochement between Hegelian and analytic traditions in philosophy. Here I want to explore the ideas of another philosopher, also active in London in the 1950s, who consciously pursued such a goal: John N. Findlay. The ideas that Findlay brought to Hegel—sometimes converging with, sometimes diverging from those of Sellars—had been informed by his earlier study of the Austrian philosopher Alexius (...) Meinong, and transformations of Meinong’s ideas by his student, the logician Ernst Mally. These ideas that Findlay found Hegel-friendly are ones that have had a particular bearing on more recent analytic modal metaphysics, especially via the work of Findlay’s own former student, Arthur Prior. Given this, we might not be surprised at the similarities between the type of actualist interpretation of modal logic that Prior offered in opposition to David Lewis’s variant on Leibnizian possibilism, and Hegel’s approach to the category of “Actuality” [Wirklichkeit] at the end of the Objective Logic of The Science of Logic. But the similarities, I suggest, do not end there, as elements of Hegel treatment of predication in the Subjective Logic parallel similar elements found in the work of Mally and, more recently, “modal actualists” such as Prior and Stalnaker. In this paper I explore some puzzling features of Hegel’s treatment of predication in the Subjective Logic from the point of view of the need for a logic for thought about the modally complex actual world, as Hegel conceived it. (shrink)

This paper serves as a kind of field guide to certain passages in the literature which bear upon the foundational theory of abstract objects. The foundational theory assimilates ideas from key philosophers in both the analytical and phenomenological traditions. I explain how my foundational theory of objects serves as a common ground where analytic and phenomenological concerns meet. I try to establish how the theory offers a logic that systematizes a well-known phenomenological kind of entity, and I try to show (...) the various ways the theory systematizes the ideas of many analytic philosophers. The ideas of Plato, Leibniz, Frege, Russell, Goedel and even Kripke become connected through those of Brentano, Meinong, Husserl, and Mally. -/- The field guide will not only document the passages in which the distinction between two kinds of predication originates, but also document the other surprising, and often unrelated, contexts where the distinction reappears in the work of others. It will also document ways in which the theory can be used to represent precisely the ideas of the philosophers mentioned above. The resulting guide will bring together the works of many different authors, including some clearly within the analytic tradition, some clearly within the phenomenological tradition, and some who straddle the divide. (shrink)

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...) In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (shrink)

Intentionality is the power of minds to be about, to represent, or to stand for, things, properties and states of affairs. The puzzles of intentionality lie at the interface between the philosophy of mind and the philosophy of language. The word itself, which is of medieval Scholastic origin, was rehabilitated by the philosopher Franz Brentano towards the end of the nineteenth century. ‘Intentionality’ is a philosopher's word. It derives from the Latin word intentio, which in turn derives from the verb (...) intendere, which means being directed towards some goal or thing. The entry falls into eleven sections. (shrink)

Presented here are translations of two essays of the Austrian logician, philosopher and experimental psychologist Ernst Mally, originally delivered at the Third International Congress of Philosophy in Heidelberg, Germany. Both essays conclude with discussion between Mally and Kurt Grelling. Mally was a student of Alexius Meinong and a contributor to logical investigations in the field of object theory (Gegenstandstheorie). In these essays, Mally introduces a vital distinction between formal and extra-formal ?determinations? (Bestimmungen), and he argues that formal determinations are not (...) part of the identity conditions for intended objects, but provide the basis for a theory of pure logical and mathematical relations. Mally then proceeds to develop a formal logic of formal and extra-formal determinations, whose interrelations of ontic and modal predications provide an analysis of fundamental object theory concepts. (shrink)