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)

We describe a knowledge representation and inference formalism, based on an intensional propositional semantic network, in which variables are structures terms consisting of quantifier, type, and other information. This has three important consequences for natural language processing. First, this leads to an extended, more natural formalism whose use and representations are consistent with the use of variables in natural language in two ways: the structure of representations mirrors the structure of the language and allows re-use phenomena such as pronouns and (...) ellipsis. Second, the formalism allows the specification of description subsumption as a partial ordering on related concepts (variable nodes in a semantic network) that relates more general concepts to more specific instances of that concept, as is done in language. Finally, this structured variable representation simplifies the resolution of some representational difficulties with certain classes of natural language sentences, namely, donkey sentences and sentences involving branching quantifiers. The implementation of this formalism is called ANALOG (A NAtural LOGIC) and its utility for natural language processing tasks is illustrated. (shrink)

The theory that Kit Fine calls 'semantic relationism' replaces standard semantic compositionality with an alternative according to which statements of the form '... A … A ...’ and ‘... A … B ...’ (e.g., ‘Cicero admires Cicero’ and ‘Cicero admires Tully’) differ in semantic content—even where the two terms involved are exactly synonymous—simply in virtue of the recurrence that is present in the former statement and absent from the latter. A semantic-relationist alternative to standard compositionality was first explicitly proffered by (...) Hilary Putnam in 1954 and later by others in the latter part of the 20th Century. However, semantic relationism had already been implicitly rejected in Frege’s 1892 landmark masterpiece "Über Sinn und Bedeutung" (“On Sense and Reference”). The present compilation of three previously published essays cuts through the hype and thoroughly rebuts semantic relationism, particularly Fine’s more developed version (2007). A fatal fallacy is exposed in Fine's high-flown purported formal disproof of Millianism with standard compositionality. Standard Millianism does not implode; Fine's overzealous attempt to demolish it does. The failure of his purported disproof renders Fine's central notion of coordination either redundant or empty. So-called coordination is non-semantic if it is anything real. (shrink)

The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural (...) contexts of application. We introduce in this paper a first-order formal system that captures the notion of grounding and avoids the paradoxes in a novel and non-trivial way. The system we present formally develops Bolzano’s ideas on grounding by employing Hilbert’s ε-terms and an adapted version of Fine’s theory of arbitrary objects. (shrink)

Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all properties of the numbers, achieving a key (...) neofregean advantage, while preserving the key structuralist advantage, which objects play the number role does not matter. (shrink)

It is argued that truth value of a sentence containing free variables in a context of use, just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. (...) On letting, say, x be such that \, the sentence ‘Either \ or \’ is true but the sentence ‘\’ has an indeterminate truth value: it is determinate that the variable x refers to either 2 or \, but it is indeterminate which of the two it refers to, as a result ‘\’ has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a ‘radically’ supervaluational semantic framework closely analogous to the treatment of vagueness in McGee and McLaughlin and Smith, which saves bivalence, the T-schema and the truth-functional analysis of the boolean connectives. It is shown that on such an analysis the modality ‘determinately’ is quite clearly not an epistemic modality, avoiding a potential objection raised by Williamson against such ‘radically’ supervaluational treatments of vagueness, and that determinate truth is the semantic value preserved in classically valid arguments. The analysis is contrasted with the epistemicist proposal of Breckenridge and Magidor which implies that ‘\’ has a determinate but unknowable truth value. (shrink)

Situation theorists such as John Barwise, John Etchemendy, John Perry and François Recanati have put forward the hypothesis that linguistic representations are situated in the sense that they are true or false only relative to partial situations which are not explicitly represented as such. Following Recanati's lead, I explore this hypothesis with respect to mental representations. First, I introduce the notion of unarticulated constituent, due to John Perry. I suggest that the question of whether there really are such constituents should (...) divide in two issues, one concerning language and the other concerning thought. Then I formulate a dilemma that any friend of cognitive unarticulated constituents must face: alleged unarticulated constituents seem to be either articulated or non-constituents after all. The dilemma is strengthened by the fact that unarticulated constituents cannot be inferentially relevant. In §4, three constraints on entertaining situated representations are spelled out. First, although the situation within which one is immersed is not represented as such, there must be cognitive facts that make immersion possible, and explain why one is implicitly related to a particular situation as opposed to another. Second, the move from a given representation to one which articulates the situation requires the capacity to contrast the latter with others in the same range. Third, I suggest that conceptual representations differ from non-conceptual ones in the permanent possibility of detachment that they allow. I then illustrate how these constraints work in three sorts of cases. In the first, thoughts like It's raining and It's over are implicitly related to their situations via some practical capacity of keeping track of particular places or times. In the second sort of cases, the relevant situations are not given, but stipulated, like in In Constance, it's raining. Cases of the third sort are those in which an unarticulated constituent is relevant to a whole system of representations, for instance the perceptual system. In the last section, I use the notion of ad hoc representation to defend the cognitive application of situation semantics against an important objection. (shrink)

This long-awaited volume is a must-read for anyone with a serious interest in philosophy of mathematics. The book falls into two parts, with the primary focus of the first on ontology and structuralism, and the second on intuition and epistemology, though with many links between them. The style throughout involves unhurried examination from several points of view of each issue addressed, before reaching a guarded conclusion. A wealth of material is set before the reader along the way, but a reviewer (...) wishing to summarize the author's views crisply will be frustrated. The chapter-by-chapter survey below conveys at best a very incomplete and imperfect impression of the work's virtues, and even of its contents, falling short even of supplying a full menu for the banquet of food for thought that Parsons serves up to his readers. (shrink)

. Fresh evidence from Free Choice Items (FCIs) in French question the current perception of the class. The role of some standard distinctions found in the literature is weakened or put in a new perspective. The distinction between universal and existential is no longer an intrinsic property of FCIs. Similarly, the opposition between variation-based vs intension-based analyses is relativized. We show that the regime of free choiceness can be characterized by an abstract constraint, that we call Non-Individuation (NI), and which (...) can be satisfied in different ways that match current distinctions. NI says that the information conveyed by a sentence containing a FCI should not be reducible to a referential situation, that is a situation in which particular individuals satisfy the sentence in the current world. The widely used resource of modal variation becomes a particular scenario of free-choiceness, not its essence. In fact, we show that under certain conditions, FCIs can occur in episodic, non-modal sentences, a fact that NI can accommodate. We also discuss more fine-grained aspects of the semantics of FCIs, such as their emotional colour. (. . .) the tripod fell spontaneously, because, though it stood on its feet so as to serve for a seat, it did not fall so as to serve for a seat. Aristotle, Physics II,6. (shrink)

In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper, and others proper. Improper inference rules are more complicated and are often harder to understand than the proper ones. In the present paper, we distinguish between proper and improper derivations by using sequent systems. Specifically, we introduce a sequent system \(\vdash_{\bf Sc}\) for classical propositional logic with only structural rules, (...) and prove that \(\vdash_{\bf Sc}\) does not allow improper derivations in general. For instance, the sequent \(\Rightarrow p \to q\) cannot be derived from the sequent \(p \Rightarrow q\) in \(\vdash_{\bf Sc}\). In order to prove the failure of improper derivations, we modify the usual notion of truth valuation, and using the modified valuation, we prove the completeness of \(\vdash_{\bf Sc}\). We also consider whether an improper derivation can be described generally by using \(\vdash_{\bf Sc}\). (shrink)

This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, (...) and the ontological commitments underlying the stylistic practice. (shrink)

Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.

There are several innocuous or trivial ways in which to explicate Aristotle’s hylomorphism. For example: objects are characterisable in terms of matter and form; or analysable into matter and form; or understood on the basis of matter and form. Serious problems arise when we seek to specify the sorts of relation holding among the different contributors to the hylomorphic picture. Here are some central general questions: a. What types of relation are most suitable for each n-tuple of contributors? b. What (...) direction and modal profile should each relation have? In addressing such questions we find that the types, directions, or modal character of the relations that we or Aristotle may favour are often in tension with each other, or clearly lead to inconsistencies. The paper focuses on the Modal Question, also known as ‘Ackrill’s problem’: is form essentially or contingently related to matter? I outline a hylomorphic model, what I label the ‘causal-explanatory’ model, and show how it can tackle M. (shrink)

In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.

In a recent paper, Kit Fine offers a reconstruction of Cantor's theory of ordinals. It avoids certain mentalistic overtones in it through both a non-standard ontology and a non-standard notion of abstraction. I argue that this reconstruction misses an essential constructive and computational content of Cantor's theory, which I in turn reconstruct using Martin-Löf's theory of types. Throughout, I emphasize Kantian themes in Cantor's epistemology, and I also argue, as against Michael Hallett's interpretation, for the need for a constructive understanding (...) of Cantorian ?existence principles? (shrink)

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I argue that the interaction between the multi-dimensional intensional framework and intensional plural quantification enables epistemic possibilities to target the haecceitistic properties of individuals. I outline the elements of plural logic, and I specify, then, a multi-dimensional intensional formula encoding the relation between the epistemic possibility of haecceity comprehension and its metaphysical possibility. I conclude by addressing objections from the indeterminacy (...) of ontological principles relative to the space of epistemic possibilities, and from the consistency of epistemic modal space. (shrink)

Husserlian Essentialism is the view, maintained byEdmundHusserl throughout his career, that necessary truths obtain because essentialist truths obtain. In this thesis I have two goals. First, to reconstruct and flesh out Husserlian Essentialism and its connections with surrounding areas of Husserl's philosophy in full detail – something which has not been done yet. Second, to assess the theoretical solidity of the view. As regards the second point, after having presented Husserlian Essentialism in the first two chapters, I raise a serious (...) problem for it in Chapter 3. In the remainder of the thesis I endeavour to solve the problem. In order to do so, I propose to amend both Husserl's theory of essence and his theory of predication. The bulk of the emendation consists in working out an account of essence and an account of predication that do not presuppose, or in any way imply, the claims that: 1) for a universal to be in the essence of an object, either the object or one of its parts must instantiate the universal; 2) for a universal to be truly predicated of an object, either the object or one of its parts must instantiate the universal. These claims, notice, apart from being what gets Husserl in trouble, are well entrenched not only in Husserl's, but in most theories of essence and predication. It is thus interesting to see what an alternative option may be – even regardless of the Husserlian setting in which I work it out. (shrink)

This paper concerns the apparent fact — discussed by Sinan Dogramaci and Brian Weatherson — that inductive reasoning often interacts in disastrous ways with patterns of reasoning that seem perfectly fine in the deductive case. In contrast to Dogramaci's and Weatherson's own suggestions, I argue that these cases show that we cannot reason inductively about arbitrary objects. Moreover, as I argue, this prohibition is neatly explained by a certain hypothesis about the rational basis of inductive reasoning — namely, the hypothesis (...) that inductive reasoning is fundamentally reasoning about what normally happens. (shrink)

HorstenLeon* * _ The Metaphysics and Mathematics of Ordinary Objects. _Cambridge University Press, 2019. Pp. xviii + 231. ISBN: 978-1-107-03941-4 ; 978-1-10860177-1. doi: 10.1017/9781139600293.

The role of intuition in Kant's theory of mathematics is similar to instantiation rules in first-order logic according to Jaakko Hintikka. This paper is a critical examination of Hintikka's interpretation and reconstruction of Kant's theory. It is argued that Kant's position is question-begging on this interpretation.

In this article I present HYPER-REF, a model to determine the referent of any given expression in First-Order Logic. I also explain how this model can be used to determine the referent of a first-order theory such as First-Order Arithmetic. By reference or referent I mean the non-empty set of objects that the syntactical terms of a well-formed formula pick out given a particular interpretation of the language. To do so, I will first draw on previous work to make explicit (...) the notion of reference and its hyperintensional features. Then I present HYPER-REF and offer a heuristic method for determining the reference of any formula. Then I discuss some of the benefits and most salient features of HYPER-REF, including some remarks on the nature of self-reference in formal languages. (shrink)

According to common judicial standard, judgment in favor ofplaintiff should be made if and only if it is more probable than not thatthe defendant''s action was the cause for the plaintiff''s damage (or death). This paper provides formal semantics, based on structural models ofcounterfactuals, for the probability that event x was a necessary orsufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient)causation can be learned from statistical data, and (...) shows how data fromboth experimental and nonexperimental studies can be combined to yieldinformation that neither study alone can provide. Finally, we show thatnecessity and sufficiency are two independent aspects of causation, andthat both should be invoked in the construction of causal explanations for specific scenarios. (shrink)

Alex Oliver; XI*—A Few More Remarks on Logical Form, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 247–272, https://doi.org/10.

The paper offers a new understanding of induction in the empirical sciences, one which assimilates it to induction in geometry rather than to statistical inference. To make the point a system of notions, essential to logically sound induction, is defined. Notable among them are arbitrary object and particular property. A second aim of the paper is to bring to light a largely neglected set of assumptions shared by both induction and deduction in the empirical sciences. This is made possible by (...) appealing to the logic of common nouns and applying it to the logic of natural-kind terms.This strategy yields a new insight into the concept of natural kinds. While the strategy reveals deep affinity between empirical induction and deduction it also reveals two problems peculiar to induction. This helps to explain the intuition that induction is the more problematic of the two. The paper does not set out ‘to solve the problem of induction’. 1The paper has benefited from the support and critical comments of several friends: Steven Davis, Kevin Dunbar, Anil Gupta, Michael Hallett, Ray Jackendoff and Storrs McCall. Two friends, however, deserve special thanks, Michael Makkai and Gonzalo Reyes. Many of the points made in the paper, otherwise unacknowledged, are due to their generosity and patience. In fact, the paper can be seen as an application of the logic of kinds on which Gonzalo Reyes has been working for several years. (shrink)

I am grateful to Nathan Salmon [in Salmon (2012)] for being willing to spill so much ink over my monograph on semantic relationism (2007), even if what he has to say is not altogether complimentary. There is a great deal in his criticisms to which I take exception but I wish to focus on one point, what he calls my ‘formal disproof’ of standard Millianism. He believes that ‘the alleged hard result is nearly demonstrably false’ (p. 420) and that the (...) disproof contains a ‘serious error’ (p. 407). Neither claim is correct; and it is the aim of this short note to explain why.First some background. In some cases, we are justified (from an internalist standpoint) in inferring the singular proposition F&G(x) from F(x) and G(x) (as when I learn more and more about Obama, for example); and in other cases, we are not so justified (as when Peter, in Kripke’s puzzle case, knows that Paderewski is a pianist and that Paderewski is a politician but does not know that anyone is both a pianist and a poli. (shrink)

Motivated by avoiding a difficulty confronting the usual formulations of identity criteria, Fine has proposed and developed a generic account of grounding. In this paper, I examine two versions of the account. I argue that both proposals fail, as it is difficult to see how the strategy of ‘going generic’ can really solve the problem. I conclude that the idea of generic grounding is mysterious and unmotivated.