This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform (...) program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals. (shrink)

I discuss three ways of responding to the logical omniscience problems faced by traditional ‘possible worlds’ epistemic logics. Two of these responses were put forward by Hintikka and the third by Cresswell; all three have been influential in the literature on epistemic logic. I show that both of Hintikka's responses fail and present some problems for Cresswell’s. Although Cresswell's approach can be amended to avoid certain unpalatable consequences, the resulting formal framework collapses to a sentential model of knowledge, which defenders (...) of the ‘possible worlds’ approach are frequently critical of. (shrink)

In this article, I explore the problems of ficta ‘generation’ and ‘properties’ in light of the philosophies of Alexius Meinong and Roman Ingarden. Comparing Ingarden and the historical Meinong is not a novel idea. By contrast, comparing Ingarden and a phenomenological Meinong has not, to my knowledge, yet been explored. Here, I rely on Alberto Voltolini’s ‘phenomenological conception of außerseiende entities’. I devise Ingarden’s phenomenological ontology to account for the problems of ascription and generation that cripple Meinong’s account. In short, (...) I argue that Ingarden’s account is better suited to accommodate ficta’s generation and properties in a way that does not complicate our approach to fiction. (shrink)

Ultralogic as Universal? is a seminal text in non-classcial logic. Richard Routley presents a hugely ambitious program: to use an 'ultramodal' logic as a universal key, which opens, if rightly operated, all locks. It provides a canon for reasoning in every situation, including illogical, inconsistent and paradoxical ones, realized or not, possible or not. A universal logic, Routley argues, enables us to go where no other logic—especially not classical logic—can. Routley provides an expansive and singular vision of how a universal (...) logic might one day solve major problems in set theory, arithmetic, linguistics, physics, and more. It circulated in typescript in the late 1970s before appearing as the Appendix to Exploring Meinong's Jungle and Beyond. With engaging, forceful prose, unsparing criticism of entrenched institutions, and many tantalizing proof sketches, Ultralogic? has had a major influence on the development of paraconsistent and relevant logic. This new edition makes this work available for a modern audience, newly typeset and corrected, along with extensive notes, and new commentary essays. (shrink)

Similar to Meinong, Abū Hāšim al-Ğubbāī held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study is mostly done through three topics: the characterization principle, objecthood, and the ontological status of existence. Moreover, Abū Hāšim’s theory of nonexistent objects is based on his theory of states, according to which some things, namely states, which among other things include existence, are neither existent (...) nor nonexistent. In this paper, we have also discussed two arguments on behalf of this claim and then we have examined them from a Meinongian perspective. (shrink)

Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal philosophies of mathematics are each based upon an insight or truth about the nature of mathematics that can be validated. (1) includes the multiverse approach to set theory. (2) helps us to understand (...) the significance of the distinguished non‐logical individual and relation terms of even inconsistent theories. (3) is a metaphilosophical form of mathematical pluralism and hasn't been discussed in the literature. In what follows, I show how the analysis of theoretical mathematics in object theory exhibits all three forms of mathematical pluralism. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for (...) producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

This paper describes a modal conception of sets, according to which sets are 'potential' with respect to their members. A modal theory is developed, which invokes a naive comprehension axiom schema, modified by adding `forward looking' and `backward looking' modal operators. We show that this `bi-modal' naive set theory can prove modalized interpretations of several ZFC axioms, including the axiom of infinity. We also show that the theory is consistent by providing an S5 Kripke model. The paper concludes with some (...) discussion of the nature of the modalities involved, drawing comparisons with noneism, the view that there are some non-existent objects. (shrink)

This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead (...) to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis. (shrink)

This paper develops a (nontrivial) theory of cardinal numbers from a naive set comprehension principle, in a suitable paraconsistent logic. To underwrite cardinal arithmetic, the axiom of choice is proved. A new proof of Cantor’s theorem is provided, as well as a method for demonstrating the existence of large cardinals by way of a reflection theorem.

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...) is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason. (shrink)

In a recent article, Emil Badici contends that the inclosure schema substantially fails as an analysis of the paradoxes of self-reference because it is question-begging. The main purpose of this note is to show that Badici's critique highlights a necessity condition for the success of dialectic about paradoxes. The inclosure argument respects this condition and remains solvent.

Once one draws a distinction between loyal non-existent items, which do not exist in a non-universal sense of the first-order existence predicate, and non-items, which fail to exist in a universal sense of that predicate, one may allow for the former but not for the latter in the overall ontological domain, so as to adopt a form of soft Parmenideanism. There are both theoretical and empirical reasons for this distinction.

In this paper I want to claim, first, that despite close similarities, noneism and Crane’s psychological reductionism are different ontological doctrines. For unlike the latter, the former is ontologically committed to objects that are nonentities. Once one splits ontological from existential commitment, this claim, I guess, is rather uncontroversial. Second, however, I want to claim something more controversial; namely, that this ontological interpretation of noneism naturally makes noneism be nonstandardly read as a form of allism, to be however appropriately distinguished (...) from Quinean allism in terms of the different scope of the overall ontological domain on which the only particular/existential quantifier that there is ranges. This may orient a noneist towards a syncretistic view of existence, according to which, appearances notwithstanding, existence as a whole is captured both by means of second-order and by means of first-order related notions. (shrink)

In this paper, I will defend the claim that there are three existence properties: the second-order property of being instantiated, a substantive first-order property (or better a group of such properties) and a formal, hence universal, first-order property. I will first try to show what these properties are and why we need all of them for ontological purposes. Moreover, I will try to show why a Meinong-like option that positively endorses both the former and the latter first-order property is the (...) correct view in ontology. Finally, I will add some methodological remarks as to why this debate has to be articulated from the point of view of reality, i.e., by speaking of properties, rather than from the point of view of language, i.e., by speaking of predicates (for such properties). (shrink)

The collapse models of arithmetic are inconsistent, nontrivial models obtained from ℕ and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom system for (...) the finite collapse models. I present some standard arithmetical axioms in addition to a cyclic axiom and prove that these axioms are sound and complete for the cyclic models, reporting a similar result for the heap models. The state of the situation for the each of the kinds of infinite collapse model is, however, left an open question. (shrink)

A logic is said to be paraconsistent if it does not allow everything to follow from contradictory premises. There are several approaches to paraconsistency. This paper is concerned with several philosophical positions on paraconsistency. In particular, it concerns three ‘schools’ of paraconsistency: Australian, Belgian and Brazilian. The Belgian and Brazilian schools have raised some objections to the dialetheism of the Australian school. I argue that the Australian school of paraconsistency need not be closed down on the basis of the Belgian (...) and Brazilian schools’ objections. In the appendix of the paper, I also argue that the Brazilian school’s view of logic is not coherent. (shrink)

There is a tension in Santayana's ontological system, one that is generated by the interactions of his doctrine of existence, doctrine of systematization, and critical agnosticism on the infinity of material substance. From and, in conjunction with what will be called the expansionist postulate, an infinite material expansion is generated, one that is in conflict with. This tension is remediated by a coherentist proposal regarding Santayanan existence, the relevant feature of which is that existents at distinct orders of organization are (...) in symmetrical dependence relations. "Metaphysical coherentism," which has recently been described as "one of the least explored areas in contemporary... (shrink)

The claim that nature is self-consistent has recently been contested by a number of paraconsistent logicians. In this paper I will survey the arguments which paraconsistent logicians have presented for the thesis that nature is actually inconsistent. My conclusion is that these arguments all fail.The paraconsistency programme has to date been concerned primarily with outlining the philosophical inadequacy of classical logic, and detailed discussions of issues bearing upon the philosophical adequacy of the paraconsistency position itself are not to be found (...) as yet in the literature. This inadequacy will be illustrated here with respect to the question of the self-consistency of nature. (shrink)

Alexius Meinong is one of the foremost, most independent-minded, most distinctive, most misunderstood and most unjustly maligned of all philosophers. He was pilloried by his own teacher Brentano and his one-time admirer Bertrand Russell as what Gilbert Ryle called “perhaps the supreme entity-multiplier in the history of philosophy.” It is often enough to employ the adjective ‘Meinongian’ to cast a philosopher’s views into the outer darkness. But as supreme commentator J. N. Findlay observes, Meinong was a painstakingly careful and methodical (...) thinker, who inched his way forward to his radical ontological views. Meinong maintained a running interest in ethics and value theory, and the subjective experiences of feeling and desire that correlate to these spheres, from his 1894 Psychological-ethical investigations in value theory to his late works Emotional presentation and the posthumous On the foundation of general value theory. In the process he graduated from value subjectivism to value objectivism. In this paper we will survey Meinong’s mature theory of intentionality and its objects, with particular attention to the otherwise neglected dignitatives and desideratives. (shrink)

Przedmiotem artykułu jest status ontologiczny światów możliwych oraz niemożliwych. Zgodnie z jedną ze współczesnych wersji meinongianizmu, o ile świat aktualny jest przedmiotem istniejącym, o tyle światy czysto możliwe oraz niemożliwe uznawane są za przedmioty nieistniejące. Zwolennicy tego podejścia twierdzą ponadto, że światom nieaktualnym nie przysługuje żaden inny rodzaj istnienia.Celem artykułu jest wskazanie na problematyczne konsekwencje wspomnianego stanowiska oraz zarysowanie poglądu alternatywnego, który oparty jest na pluralizmie ontologicznym, tj. na poglądzie uznającym wielość rodzajów istnienia.

The subject of this article is the Principle of Characterization—the most controversial principle of Alexius Meinong’s Theory of Objects. The aim of this text is twofold. First of all, to show that Bertrand Russell’s well-known objection to the Principle of Characterization can be reformulated against contemporary unrestricted interpretations of it. Second, to propose an alternative formulation of this principle. This refers to the methodology of metaphysics and is based on the distinction between pre-theoretical and theoretical languages. The proposed formulation fits (...) well with every type of contemporary interpretation of the Theory of Objects and helps to overcome Russell’s criticism. (shrink)

The subject of this article is the Principle of Characterization—the most controversial principle of Alexius Meinong’s Theory of Objects. The aim of this text is twofold. First of all, to show that Bertrand Russell’s well-known objection to the Principle of Characterization can be reformulated against contemporary unrestricted interpretations of it. Second, to propose an alternative formulation of this principle. This refers to the methodology of metaphysics and is based on the distinction between pre-theoretical and theoretical languages. The proposed formulation fits (...) well with every type of contemporary interpretation of the Theory of Objects and helps to overcome Russell’s criticism. (shrink)

The subject of my article is the principle of characterization – the most controversial principle of Meinong’s Theory of Objects. The aim of this text is twofold. First of all, I would like to show that Russell’s well-known objection to Meinong’s Theory of Objects can be reformulated against a new modal interpretation of Meinongianism that is presented mostly by Graham Priest. Secondly, I would like to propose a strategy which gives uncontroversial restriction to the principle of characterization and which allows (...) to avoid Russell’s argument. The strategy is based on the distinction between object- and metalanguage, and it applies to modal Meinongianism as well as to other so-called Meinongian theories. (shrink)

A central problem for any truthmaker theory is the problem of negative truths. In this paper, I develop a novel, piecemeal strategy for solving this problem. The strategy puts central focus on a truth-relevant notion of aboutness within a metaphysically modest version of truthmaker theory and uses key conceptual tools gained by taking a deeper look at the best attempts to solve the problem of intentionality. I begin this task by critically discussing past proposed solutions to P-NEG in light of (...) Russell’s debate with Demos. This reveals a central difficulty with addressing the problem, specifically that one cannot be committed to incompatibility facts in one’s account of negation and of the truth of negative truths. I then present an aboutness-based version of truthmaker theory. Utilising what I call the strict and full account of aboutness, I extract aboutness-based theories of truth and falsity. I use this machinery to present a promising new strategy for solving P-NEG which does not have the problems of alternative approaches. Finally, I present and respond to some potential objections. (shrink)

Relevantism, as a matter of definition, rejects classical logic as incorrect and adopts instead a relevant logic as encapsulating correct inference. It rejects classical logic on the grounds that the rule of Material Detachment, from A and not A or B to infer B,, sometimes leads from truth to falsity. Relevantism — although promoted by some relevant logicians, and an integral part of ultralogic — has recently encountered heavy, but interesting, criticism from relevance logicians themselves.

This essay presents a philosophical and computational theory of the representation of de re, de dicto, nested, and quasi-indexical belief reports expressed in natural language. The propositional Semantic Network Processing System (SNePS) is used for representing and reasoning about these reports. In particular, quasi-indicators (indexical expressions occurring in intentional contexts and representing uses of indicators by another speaker) pose problems for natural-language representation and reasoning systems, because--unlike pure indicators--they cannot be replaced by coreferential NPs without changing the meaning of the (...) embedding sentence. Therefore, the referent of the quasi-indicator must be represented in such a way that no invalid coreferential claims are entailed. The importance of quasi-indicators is discussed, and it is shown that all four of the above categories of belief reports can be handled by a single representational technique using belief spaces containing intensional entities. Inference rules and belief-revision techniques for the system are also examined. (shrink)

This paper articulates Sylvan's theory of mathematical objects as non-existent, by improving (arguably) his treatment of the Characterisation Postulate. It then defends the theory against a number of natural objections, including one according to which the account is just platonism in disguise.

Meinongians in general, and Routley in particular, subscribe to the principle of the independence of Sosein from Sein. In this paper, I put forward an interpretation of the independence principle that philosophers working outside the Meinongian tradition can accept. Drawing on recent work by Stephen Yablo and others on the notion of subject matter, I offer a new account of the notion of Sosein as a subject matter and argue that in some cases Sosein might be independent from Sein. The (...) question whether numbers exist, for instance, is not part of the question of how numbers are, which is the topic mathematicians are interested in. (shrink)

ABSTRACTI propose a different account of fictional objects from the ones already present in the literature. According to my account, fictional objects are culturally created abstract objects dependent for their existence on the pretence attitude adopted by a group of people towards a single fictional content. My work is divided into three parts: in the first one, I present how fictional objects come into existence according to my proposal; in the second part, I illustrate how the existence of fictional objects (...) so conceived may be ontically indeterminate; in the last part, I consider what happens when vague existence and indeterminate identity are claimed within fictional texts. (shrink)

It is usually taken for granted that a necessary condition for knowing that P is the truth of P. It may therefore be claimed that if we assume that we gain some kind of knowledge through fiction (let us call it fictional knowledge) of P*, then P* should be true—in at least a certain sense. My hypothesis is that this assumption grounds the different ways adopted by philosophers for attributing truth-conditions to fictional sentences. My claim in this work is that (...) fictional sentences do not have truth-values and truth-conditions, but I want to maintain that we gain some kind of knowledge through fiction: to this aim, I will characterize the objective content of fictional sentences not in terms of truth-conditions (which are usually described by appealing to rules of the language or rules of interpretation of language independent of the actual users), but in dispositional terms and I will define a necessary condition for fictional knowledge accordingly. (shrink)

Philosophers have found postulating possible worlds to be very useful in a number of areas, including philosophy of language and mind, logic, and metaphysics. Impossible worlds are a natural extension to this use of possible worlds, and can help resolve a number of difficulties thrown up by possible‐worlds frameworks.

Anselm's Ontological Argument fails, but not for any of the various reasons commonly adduced. In particular, its failure has nothing to do with violating deep Kantian principles by treating ‘exists’ as a predicate or making reference to ‘Meinongian’ entities. Its one fatal flaw, so far from being metaphysically deep, is in fact logically shallow, deriving from a subtle scope ambiguity in Anselm's key phrase. If we avoid this ambiguity, and the indeterminacy of reference to which it gives rise, then his (...) argument is blocked even if his supposed Meinongian extravagances are permitted. Moreover it is blocked in a way which is straightforward and compelling (by contrast with the Kantian objections), and which generalizes easily to other versions of the Ontological Argument. A significant moral follows. Fear of Anselm's argument has been hugely influential in motivating ontological fastidiousness and widespread reluctance to countenance talk of potentially non-existing entities. But if this paper is correct, then the Ontological Argument cannot properly provide any such motivation. Some of the most influential contributions to ontology, from Kant to Russell and beyond, rest on a mistake. (shrink)

Meinongian 'objects' are evoked in an effort to critique and expand upon traditional theories of reference. The argument stems from an account of Peirce's categories of meaning in light of vague, contradictory, inconsistent, general, incomplete, and incompleteable signs. In addition to signs as either 'true', 'false', or meaningless, the function of imaginary numbers reveals the possibility of a sign's being both 'true' and 'false' or neither 'true' nor 'false', over time, and dialogically speaking. This demands a tolerance for vagueness, ambiguity, (...) contradiction, and incessantly changing meaning. (shrink)

This paper defends the possibility of admitting occurrents in a presentist ontology. Two ways of doing so are proposed, the first one involves Meinongian presentism. By using the notion of non-existent object and coherently modifying some mereological principle, it is argued, the presentist can allow for occurrents. The second proposal involves ex-concrete objects. Ex-concrete objects, i.e. objects that are contingently not concrete, have been used by Linsky and Zalta, 431-458, 1994), Williamson in the modal metaphysics debate, by Orilia, 589-607, 2016) (...) in the presentism-eternalism debate, and by Longenecker, 5091-5111, 2018) in the debate about material constitution. I argue that, just by admitting ex-concrete objects, it is possible to have occurrents even for the presentist. Of course, in order to do so we must modify our definitions of occurrent and continuant. Nevertheless, I argue that my theory is metaphysically sound, at least for the presentist persuaded by the intuitive claim that there are occurrents, which otherwise she must reject. (shrink)

I examine the basic logical character of ‘the last man example’, as well as the logical character of one of its more important variants. Although it has one striking antecedent in recent philosophy – of which more later – it’s fair to regard it as an example first presented to a contemporary audience by Richard Routley in his 1973 paper, ‘Is There a Need for a New, an Environmental, Ethic?’. I want to determine exactly how the example goes and what (...) it shows. I want to determine what it does not show. One reason for engaging in this exercise is the striking and engaging character of the last man example itself. Another is that a large number of environmental philosophers have since referred to the last man but have drawn different, sometimes contrary, lessons from it – though we won’t have time here to visit any but the earliest of these responses. It seems to me time to patiently revisit the example and time to attempt a conclusive understanding of its significance. A second, and broader, purpose I have is to describe the meta-ethical views it led Routley to adopt – or manufacture! – in an attempt to philosophically position his normative stance within a more fundamental, explanatory, framework. (shrink)

Attempts to analyze negative existential statements face the following familiar problem. If a negative existential statement—say, “Hamlet does not exist” or “the golden mountain does not exist”—is true, its subject term must lack an object of reference. But, absent such an object, it seems that nothing true or false can be said about “it.” In particular, if there is no Hamlet to talk about, we surely cannot truthfully say that “he” does not exist. Hence, the truth of true negative existentials—and (...) there are many—seems to preclude their truth and falsity. Call this “the negative existential problem.”. (shrink)

In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...) to other philosophically problematic entities. The moral is that puzzle avoidance fails to motivate deflationary nominalism. (shrink)

In this paper I want to examine Meinong’s account of what it is to think about a particular object in the context of issues that have preoccupied twentieth-century philosophy of language. The central interpretive task is to determine what Meinong might have said about cases of intending where the object is referred to by means of a proper name. The two theoretical notions at the heart of Meinong’s account of intending, intending by way of being and intending by way of (...) being-so, are a species of singling an object out by means of an associated description. Since Kripke’s landmark discussion, it is widely denied that descriptive accounts furnish an adequate account of intending. I will consider whether Meinong’s account has the resources to provide reassurance on this matter and whether the descriptive nature of his account raises other difficulties. (shrink)

An elementary exercise in symbolizing an existential to universal relation reveals expressive limitations in standard first-order predicate-quantificational logic. Alternative translations of a sample some-every sentence are considered and rejected after criticism, leaving as the best choice a particular structure that demonstrably does not serve for all predicates available to the ordinary language to which the sample sentence belongs. We explain the difficulties encountered in trying to arrive at an adequate translation of the sentence in classical logic, as background to examining (...) five alternative nonclassical logics to resolve the problem. We settle finally if only provisionally in the process on a version of intensional logic that permits reference and true predication of constitutive properties to nonexistent as well as existent objects. (shrink)