There is a tendency to assume otherwise, to take authenticity for a real predicate, and this is true not only of proponents of existentialism. We find even prominent interpreters of Heidegger using "authenticity" as a real predicate, as a quality applied to a referent present at hand. Let a couple instances suffice.

This chapter has two main aims. First, it reconstructs the ontological arguments of Descartes, Leibniz, and Baumgarten to show that they do, in fact, implicitly presuppose that existence is a real predicate. Kant is correct about the presuppositions of ontological arguments. It then reconstructs and critically evaluates Kant’s arguments in _Only Possible Ground_ that existence is not a real predicate. It argues that these arguments have little force against a sophisticated defender of the ontological argument, like (...) Leibniz. While Kant’s rejection of the view that existence is a real predicate will have decisive consequences for the development of his modal theory, this rejection is not backed up by a strong argument. (shrink)

Two real-valued deduction schemes are introduced, which agree on $\vdash \triangle$ but not on $\Gamma \vdash \triangle$ , where Δ and ▵ are finite sets of formulae. Using the first scheme we axiomatize real-valued equality so that it induces metrics on the domains of appropriate structures. We use the second scheme to reduce substitutivity of equals to uniform continuity, with respect to the metric equality, of interpretations of predicates in structures. This continuity extends from predicates to arbitrary formulae (...) and the appropriate models have completions resembling analytic completions of metric spaces. We provide inference rules for the two deductions and discuss definability of each of them by means of the other. (shrink)

It is a commonly held view that Dedekind's construction of the real numbers is impredicative. This naturally raises the question of whether this impredicativity is justified by some kind of Platonism about sets. But when we look more closely at Dedekind's philosophical views, his ontology does not look Platonist at all. So how is his construction justified? There are two aspects of the solution: one is to look more closely at his methodological views, and in particular, the places in (...) which predicativity restrictions ought to be applied; another is to take seriously his remarks about the reals as things created by the cuts, instead of considering them to be the cuts themselves. This can lead us to make finer-grained distinctions about the extent to which impredicative definitions are problematic, since we find that Dedekind's use of impredicative definitions in analysis can be justified by his philosophical views. (shrink)

We study a predicate extension of an unbounded real valued propositional logic that has been recently introduced. The latter, in turn, can be regarded as an extension of both the abelian logic and of the propositional continuous logic. Among other results, we prove that our predicate extension satisfies the property of weak completeness (the equivalence between satisfiability and consistency) and, under an additional assumption on the set of premisses, the property of strong completeness (the equivalence between logical (...) consequence and provability). Eventually we discuss some topological properties of the space of types in our logic. (shrink)

We critically investigate and refine Dunn's relevant predication, his formalisation of the notion of a real property. We argue that Dunn's original dialectical moves presuppose some interpretation of relevant identity, though none is given. We then re-motivate the proposal in a broader context, considering the prospects for a classical formalisation of real properties, particularly of Geach's implicit distinction between real and ''Cambridge'' properties. After arguing against these prospects, we turn to relevance logic, re-motivating relevant predication with Geach's (...) distinction in mind. Finally we draw out some consequences of Dunn's proposal for the theory of identity in relevance logic. (shrink)

We claim that Kant's doctrine of the "transcendental ideal of pure reason" contains, in an anticipatory sense, a second-order theory of reality (as a second-order property) and of the highest being. Such a theory, as reconstructed in this paper, is a transformation of Kant's metatheoretical regulative and heuristic presuppositions of empirical theories into a hypothetical ontotheology. We show that this metaphysical theory, in distinction to Descartes' and Leibniz's ontotheology, in many aspects resembles Gödel's theoretical conception of the possibility of a (...) supreme being. The proposed second-order modal formalization of the Kantian doctrine of the "transcendental ideal" of the supreme being includes some specific features of Kantian general logic like "categorical", "hypothetical", and exclusive disjunctive propositions as basic forms. (shrink)

The paper presents a simple proof of an early result by Dana Scott that the modal predicate logic of real time cannot be recursively axiomatized. © 2011 Elsevier B.V., All rights reserved.

In 1985, van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretical argument, which provides no apparent bounds on the complexity of a decision procedure. We provide a syntactical argument that yields a procedure that is primitive recursive, although not elementary.

Given a theory T of a polynomially bounded o-minimal expansion R of $${\bar{\mathbb{R}} = \langle\mathbb{R}, +,., 0, 1, < \rangle}$$ with field of exponents $${\mathbb{Q}}$$, we introduce a theory $${\mathbb{T}}$$ whose models are expansions of dense pairs of models of T by a discrete multiplicative group. We prove that $${\mathbb{T}}$$ is complete and admits quantifier elimination when predicates are added for certain existential formulas. In particular, if T = RCF then $${\mathbb{T}}$$ axiomatises $${\langle\bar{\mathbb{R}}, \mathbb{R}_{alg}, 2^{\mathbb{Z}}\rangle}$$, where $${\mathbb{R}_{alg}}$$ denotes the (...) class='Hi'>real algebraic numbers. We describe types and definable sets in our models and prove that $${\mathbb{T}}$$ is dependent. (shrink)

The ontological argument fails because of an operator order switch between (1) “necessarily there is an perfect being” and (2) “there is a being which necessarily is perfect”. Here (1) is trivially true logically but (2) problematic. Since Kant's criticisms were directed at the notion of existence, not at the step from (1) to (2), they are misplaced. They are also wrong, because existence can be a predicate. Moreover, Kant did not anticipate Frege's claim that “is” is ambiguous between (...) existence, predication, identity, and class‐inclusion. To restore the ontological argument, an extra premise is needed to the effect that it is known who the existentially perfect being is. The question is raised whether Kant could have meant the failure of this extra premise by his thesis that existence is not a real predicate. (shrink)

This paper contrasts the scholastic realisms of David Armstrong and Charles Peirce. It is argued that the so-called 'problem of universals' is not a problem in pure ontology (concerning whether universals exist) as Armstrong construes it. Rather, it pertains to which predicates should be applied where, issues which Armstrong sets aside under the label of 'semantics', and which from a Peircean perspective encompass even fundamentals of scientific methodology. It is argued that Peirce's scholastic realism not only presents a more nuanced (...) ontology (distinguishing existence and reality) but also illuminates why scholastic realism is a position worth fighting for. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of Whitehead (...) (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

Sainsbury argued that exact extensions for predicates entails the unacceptable infinite tower of higher order vagueness so that exact extensions must be rejected. I offer a second argument: The exact extensions arise when semantic values are assumed to be (exact) properties. But no assignment of unique properties to predicates could arise from any real-world finite basis. How, then, is talk of properties as semantic values to be understood? We distinguish the precise compositional rules of semantics from the operation of (...) messy, imprecise rules at the word/world interface for applicability of minimal predicates. When such application is sufficiently clear it is idealized as property instantiation and semantic composition proceeds in familiar ways. These imprecise rules for application of minimal predicates provide the proper locus for study of vagueness. The conclusions thus far apply to show that higher order vagueness is not forced and that classical logic can generally be retained. I discuss implications for the sorites paradox. Abandoning properties entails abandoning simple correspondence truth understood as Pa is true just in case a has the property signified by P. As an alternative I outline a pragmatist approach to truth, the spirit of which is conveyed by the slogan, “To be true enough is to work well enough.”. (shrink)

Identity, existence, predication, necessity, and truth are fundamental philosophical concerns. Colin McGinn treats them both philosophically and logically, aiming for maximum clarity and minimum pointless formalism. He contends that there are real logical properties that challenge naturalistic metaphysical outlooks. These concepts are not definable, though we can say a good deal about how they work. The aim of Logical Properties is to bring philosophy back to philosophical logic.

According to a widely held view, people's commitments to laws are dependent on the existence in their community of a conventional practice of complying with certain fundamental laws. This conventionalism has significantly hampered our attempts to explain the normative practice of law. Ronald Dworkin has argued against conventionalism by bringing up the phenomenon of persistent fundamental legal controversies, but neither Dworkin nor his legal positivist respondents have correctly understood the real significance of such controversies. This article argues that such (...) controversies pose a deep challenge to any conception of our legal practice as a genuinely normative, rule-mediated, practice. The article also argues that what is needed to deflect this challenge is a new understanding – different from the widely held conventionalist understanding – of how people's commitments to laws are predicated on their fellows’ like commitments. (shrink)

According to a widely held view, people's commitments to laws are dependent on the existence in their community of a conventional practice of complying with certain fundamental laws. This conventionalism has significantly hampered our attempts to explain the normative practice of law. Ronald Dworkin has argued against conventionalism by bringing up the phenomenon of persistent fundamental legal controversies, but neither Dworkin nor his legal positivist respondents have correctly understood the real significance of such controversies. This article argues that such (...) controversies pose a deep challenge to any conception of our legal practice as a genuinely normative, rule-mediated, practice. The article also argues that what is needed to deflect this challenge is a new understanding – different from the widely held conventionalist understanding – of how people's commitments to laws are predicated on their fellows’ like commitments. (shrink)

ON A GENERAL READING of the Metaphysics and the treatises of the so-called Organon, the types of assertion which Aristotle would allow as genuine predications seem relatively straightforward. According to the Categories, for instance, a species is characteristically predicated of the individuals falling under it, while genera and differentiae are predicated both of the relevant species and their associated individuals. The predicates are, in these instances, universals in a familiar Aristotelian sense. Furthermore, these intra-categorial predications, such as "Socrates is a (...) man" and "white is a color," are not the only instances of categorial acts. Aristotle also admits certain cross-categorial predications as logically well-formed; for example, "Socrates is white" and "Socrates is in the marketplace". These latter predications are at first glance also intelligible enough, though there are in both cases questions yet to be faced about the logical structure and ontological commitments of such ways of speaking. For Aristotle, one metaphysical theme presented even on the face of these linguistic appearances is the possibility that being a substrate for predication counts as a criterion for ontological primacy or, more generally, that being an ultimate substrate for meaningful discourse is grounds for being primarily real. An obvious corollary to this line of thought is the thesis that whatever might be said of or predicated of such primary substrata is ontologically dependent upon them. Just such a criterion seems to be at work in disqualifying universals from their claim to be substance in a significant sense. Therefore, it would be somewhat surprising to find primary substance appearing anywhere as a predicate. (shrink)

Identity, existence, predication, necessity, and truth are fundamental philosophical concerns. Colin McGinn treats them both philosophically and logically, aiming for maximum clarity and minimum pointless formalism. He contends that there are real logical properties that challenge naturalistic metaphysical outlooks. These concepts are not definable, though we can say a good deal about how they work. The aim of Logical Properties is to bring philosophy back to philosophical logic.

When we speak of a predicate's extension, we intend to delineate the class of objects of which it is true.' Unfortunately, in some common situations the proper ground for determining whether a predicate is true of a particular individual becomes uncertain or ambiguous. One kind of situation in which this can happen — the kind of situation I will be particularly concerned with in this paper — is one in which the linguistic community is unaware of the existence (...) of kinds of objects to which a predicate might be thought to apply. It is frequently indeterminate whether such un-expected objects should be assigned to the extension or to the counter-extension of the predicate. This common phenomenon suggests deeper issues concerning the rationale for our intuitive extension assignments, I shall discuss some real life examples of this phenomenon, but it will be convenient to begin with a simple fictional case. (shrink)

This paper introduces an interesting class of predicates that come in pairs, so-called total and partial predicates. It will be shown that such predicates contribute to an explanation for the weak and strong interpretations of donkey sentences. This paper proposes that the phenomenon of weak and strong interpretations is real, and that whether a sentence receives the weak or the strong interpretation depends on the predicate in the nuclear scope of the sentence. It also proposes that sum individuals (...) are calculated at some level before the nuclear scope of the sentence is processed. Once the sum individuals are calculated, it will be decided whether the nuclear scope is true of at least one element of the sum individual (weak interpretation) or true of all elements of the sum individual (strong interpretation). (shrink)

Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This (...) is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields real-valued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)

In this book about metaphysics the author defends a realistic view of universals, characterizing the notion of universal by considering language and logic, the idea of possibility, hierarchies of universals, and causation. He argues that neither language nor logic is a reliable guide to the nature of reality and that basic universals are the fundamental type of universal and are central to causation. All assertions and predications about the natural world are ultimately founded on these basic universals. A distinction is (...) drawn between unified particulars and arbitrary particulars ; unified particulars are the terms of causal relations and thus the real constituents of the world. The world is not made up of events but of unified particulars and basic universals. (shrink)

The aim of this short book is to discuss the traditional topics of philosophical logic without the “formalistic fetishism and scholasticism” that McGinn associates with recent work in the field. The writing is indeed crisp, engaging, and free of formalisms. The book consists of five separate essays—one each on identity, existence, predication, necessity, and truth—loosely united by the general theme that these “logical properties” are real and irreducible. “These concepts,” McGinn says, “form a conceptual bedrock; they stand, as it (...) were, underneath all our other concepts. They have no analysis”. (shrink)

The article provides a linguophilosophical analysis of theoretical approaches to the symbolism of Vyacheslav Ivanov and Andrei Bely using the predicative concept of Lyudmila Gogotishvili. It is shown that the consideration of the category of symbol in the dimensions of the unmanifest and the manifest makes it possible to expand the problematics of symbolism into phenomenological and linguophilosophical perspectives. In this case, symbolization turns out to be associated with reference, determined by the specifics of the “participation” in it of the (...) linguistic subject and predicate and the status of the referent as a phenomenon of consciousness. The antinomy of the unmanifest and the manifest presupposes in symbolic reference the allocation of a special extra-linguistic category of the most real, which is fundamentally outside the field of natural language and is energetically associated with it through verbal myth. It is shown that the ratio of myth, name and the most real in the reference allows using Gogotishvili’s predicative concept to evaluate the linguophilosophical features of this or that approach to the symbol. It is concluded that the symbolism of Vyacheslav Ivanov presupposes the prevailing role of the predicate in the reference to the unmanifest most real and can be designated as mythological, while the symbolism of Andrei Bely presupposes the prevailing role of the subject in the reference to the real, manifested in language, and can be designated as metaphorical. (shrink)

We suggest a new framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory P ZF which resembles ZF, and is suitable for mechanization. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. The language of P ZF is type-free, and it reflects real mathematical practice in making an extensive use of statically (...) defined abstract set terms. Another important feature of P ZF is that its underlying logic is ancestral logic (i.e. the extension of first-order logic with a transitive closure operation). (shrink)

We present correct and natural development of fundamental analysis in a predicative set theory we call PZFU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf {PZF}^{\mathsf {U}}}$$\end{document}. This is done by using a delicate and careful choice of those Dedekind cuts that are adopted as real numbers. PZFU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf {PZF}^{\mathsf {U}}}$$\end{document} is based on ancestral logic rather than on first-order logic. Its key feature is that it is definitional in the (...) sense that every object which is shown in it to exist is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented model of it, and makes it very suitable for MKM and ITP. The development of analysis in PZFU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf {PZF}^{\mathsf {U}}}$$\end{document} does not involve coding, and the definitions it provides for the basic notions are the natural ones, almost the same as one can find in any standard analysis book. (shrink)

This article explores the intricate relationship between Schelling, Being, and Predication, framed by two core themes that shape its argumentation. The first theme addresses the continuity between the System of Identity and Schelling’s System of Freedom, particu­larly through a critique of Fichte’s idealistic conception of Being. Schelling counters Fichte’s inadvertent dualism between consciousness and its real content by affirming the primacy of nature and proposing a realist unity. Drawing from Hölderlin’s thesis on the trans-reflexive nature of Being, Schelling asserts (...) the identity of ideal and real grounds as the foundation of a unified reality. The second theme, concerning the theory of the bond, marks a profound shift in Schelling’s metaphysical framework, challenging the legitimacy of a system grounded solely in reason. The notion that no being can fully coincide with itself, thereby undermining the establishment of an identity in absolute terms, destabilizes the systematic vision of philosophy as the identity of principle and de­velopment. This critique extends to the conception of reason as a substantive principle, disrupting the foundational assumptions of other systematic thinkers of modernity. Through these interconnected themes, the article reveals how Schelling’s thought recon­figures the metaphysical and epistemological foundations of modern philosophy. (shrink)

This article explores the intricate relationship between Schelling, Being, and Predication, framed by two core themes that shape its argumentation. The first theme addresses the continuity between the System of Identity and Schelling’s System of Freedom, particu­larly through a critique of Fichte’s idealistic conception of Being. Schelling counters Fichte’s inadvertent dualism between consciousness and its real content by affirming the primacy of nature and proposing a realist unity. Drawing from Hölderlin’s thesis on the trans-reflexive nature of Being, Schelling asserts (...) the identity of ideal and real grounds as the foundation of a unified reality. The second theme, concerning the theory of the bond, marks a profound shift in Schelling’s metaphysical framework, challenging the legitimacy of a system grounded solely in reason. The notion that no being can fully coincide with itself, thereby undermining the establishment of an identity in absolute terms, destabilizes the systematic vision of philosophy as the identity of principle and de­velopment. This critique extends to the conception of reason as a substantive principle, disrupting the foundational assumptions of other systematic thinkers of modernity. Through these interconnected themes, the article reveals how Schelling’s thought recon­figures the metaphysical and epistemological foundations of modern philosophy. (shrink)

The paper defines truth-value assignment predicates T i (ϕ^) in multi-valued logics, generalising the classical truth-predicate T(ϕ^) The meaning of this predicate is that ϕ has the truth-value v i. The paper studies deflational truth-value assignments and their transparency in the form of natural-deduction proof-system. The main technical tool used is poly-sequents of the form Γ 1 | ∙∙∙ |Γ n : Δ 1 | ∙∙∙ |Δ n, interpreted as follows: if for every 1 ≤ i ≤ n (...) every α ∈ Γ i has truth value v i, then for some 1 ≤ j ≤ n, β ∈ Δ j has truth-value vj. The paper proposes a way to identify real truth and real falsity among the n truth-values. © 2019 Elsevier B.V., All rights reserved. (shrink)

The idea that temporal propositions are vague predicates is examined with attention to the nature of the objects over which the predicates range. These objects should not, it is argued, be identified once and for all with points or intervals in the real line (or any fixed linear order). Context has an important role to play not only in sidestepping the Sorites paradox (Gaifman 2002) but also in shaping temporal moments/extent (Landman 1991). The Russell-Wiener construction of time from events (...) (Kamp 1979) is related to a notion of context given by a string of observations, the vagueness in which is brought out by grounding the observations in the real line. With this notion of context, the context dependency functions in Gaifman 2002 are adapted to interpret temporal propositions. (shrink)

In this article we give an overview, from a philosophical point of view, of Lorenzen’s construction of the natural and the real numbers. Particular emphasis is placed on Lorenzen’s classification in the tradition of predicative approaches that stretches from Poincaré to Feferman.

Kant famously declared that existence is not a (real) predicate. This famous dictum has been seen as echoed in the doctrine of the founders of modern logic, Gottlob Frege and Bertrand Russell, that existence isn’t a first-order property possessed by individuals, but rather a second-order property expressed by the existential quantifier. Russell in 1905 combined this doctrine with his new theory of descriptions and declared the paradox of nonexistence to be resolved without resorting to his earlier distinction between (...) existence and being. In recent years, however, logicians and philosophers like Saul Kripke, David Kaplan, and Nathan Salmon have argued that there is no defensible reason to deny that existence is a property of individuals. Kant’s dictum has also been re-evaluated, the result being that the paradox of nonexistence has not, after all, disappeared. Yet it’s not clear how exactly Kripke et al. propose to resolve the paradox. (shrink)

This work presents a version of the correspondence theory of truth based on Wittgenstein's Tractatus and Russell's theory of truth and discusses related metaphysical issues such as predication, facts and propositions. Like Russell and one prominent interpretation of the Tractatus it assumes a realist view of universals. Part of the aim is to avoid Platonic propositions, and although sympathy with facts is maintained in the early chapters, the book argues that facts as real entities are not needed. It includes (...) discussion of contemporary philosophers such as David Armstrong, William Alston and Paul Horwich, as well as those who write about propositions and facts, and a number of students of Bertrand Russell. It will interest teachers and advanced students of philosophy who are interested in the realistic conception of truth and in issues in metaphysics related to the correspondence theory of truth, and those interested in Russell and the Tractatus. (shrink)

The paper examines the Cartesian and the Strawsonian answers to the question of why self-applied and other-applied mental predicates mean the same. While these answers relate to different, complementary aspects of this question, they seem and are usually considered as incompatible. Indeed, their apparent incompatibility constitutes a major objection to the Cartesian answer. A primary aim of the paper is to show that the Strawsonian answer does not pose a real problem to the Cartesian answer. Unlike other attempts to (...) show this, the paper does not seek to undermine the Strawsonian answer. Indeed, its second aim is to defend this answer against these other attempts. The paper’s strategy in defending the Cartesian answer is to show that the framework underlying this answer can — indeed, for internal reasons, must — accommodate the Strawsonian answer. By showing this, the paper also shows that a Cartesian framework can provide a comprehensive answer to the aforementioned question, which is its third aim. (shrink)

Thomistic commentators agree that Thomas Aquinas at least nominally allows for 'to be' (esse) to signify not only an act contrasted with essence in creatures, but also the essence itself of those creatures. Nevertheless, it is almost unheard of for any author to interpret Thomas's use of the word 'esse' as referring to essence. Against this tendency, this paper argues that Thomas's In V Metaphysics argument that every predication signifies esse provides an important instance of Thomas using esse to signify (...) essence. This reading of In V Metaphysics, which this paper defends against an alternative interpretation, entails significant reinterpretations of Thomas's technical terms 'esse substantiale' and 'esse in rerum natura' as well as Thomas's use of 'is,' both as a copula and as a principal predicate. (shrink)

We present correct and natural development of continuity theory in a predicative set theory called ${\textsf{PZF}^{\textsf{U}}}$. This is done by using a delicate and careful choice of those Dedekind cuts that are taken as real numbers. ${\textsf{PZF}^{\textsf{U}}}$ is based on ancestral logic rather than on first-order logic. Its key feature is that it is definitional in the sense that every object that is shown in it to exist is defined by some closed term of the theory. This allows for (...) a very concrete, computationally oriented model of it. The development of analysis in ${\textsf{PZF}^{\textsf{U}}}$ does not involve coding, and the definitions it provides for the basic notions are the natural ones. (shrink)

Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. But (...) it is well known that 〈ℝ, <, +, · ℚ 〉 defines every real Borel set, in particular, every open subset of any finite cartesian power of ℝ and every subset of any finite cartesian power of ℚ. To put this another way, the definable open sets in models ofTare essentially as simple as possible, whileT′ has a model where the definable open sets are as complicated as possible, as is the structure induced on the new predicate.In contrast to the preceding example, if ℝalgis the set of real algebraic numbers andT′ Th, then no model ofT′ defines any open set that is not definable in the underlying model ofT. (shrink)

The subject of this rich and wide-ranging book is old-fashioned metaphysics: its aim is to give an account of "the real constituents of the world". But its idiom and methodology are those of late twentieth-century analytic philosophy. Newman works out his own positions in constant dialogue with such philosophers as Frege and Wittgenstein, Geach and D. M. Armstrong, Keith Campbell and David Lewis; and he has an impressive mastery of modern formal logic and contemporary philosophy of language. He also (...) makes effective use of a quite detailed understanding of recent work in mathematics and physics. For all his reliance on the concepts and techniques of logic and philosophy of language, however, Newman does not believe that either language or logic "is a reliable guide to the nature of reality". On his view, metaphysics is an autonomous intellectual discipline, at least some of whose convictions and concepts are primitive. (shrink)

Immanent realism is a justly popular theory of universals which is incomplete. It is not good enough to say that all universals are equally real and all equally inhere in objects. Concepts come in hierarchies, For example: "colored," "red" and "claret," where "claret" is a shade of red. Only those at the very bottom of the hierarchy exist in objects, And are rightly called properties. Only properties have causality as a criterion of identity. Frege's functional account of concepts can (...) be adapted to explain how higher level concepts apply to objects. Between two concepts at different levels there is a relationship called 'essential subordination', Which is different from all other relationships. That a person is said to possess a concept of a property is to be explained in terms of a person possessing certain mental capacity, Which enables him to make certain judgments. Properties are concepts which exist in objects. (shrink)

The topic of our analysis is the argument for the existence of substances given by Bernard Bolzano in Athanasia, where he essentially employs two ontological categories: substance and adherence. Bolzano considers the real and conditioned Inbegriff of all adherences, which are wirklich and nicht selbst bestehen. He claims that the formed collection is dependent on something external and non-adherential, which therefore is a substance. Bolzano’s argumentation turns out to be structurally similar to his argument for the existence of God (...) from Lehrbuch der Religionswissenschaft, but in each of these reasonings, we find different plausible interpretations of the key concept “Inbegriff”. The latter argumentation refers to the mereological totality of existentially conditioned objects. We propose the explication of the Bolzanian Inbegriff of all adherences using two types of predication: we consider its extension as composed of certain intensional counterparts of adherences. In our approach, we use a fragment of the theory of abstract objects formulated by E. Zalta, describing two different relations between individuals and properties: extensional exemplification and intensional encoding. We put our reconstruction in a wider context of Bolzano’s ontology, formulating the needed axioms with two primitive predicates of second order... is an adherence,... is conditioned by something real as well as the conditionally introduced first order predicate constant \ for Inbegriff of all adherential ideas. Finally, we sketch a model for our theory. (shrink)

According to what Jonathan Bennett calls the Kant–Frege view of existence, Frege gave solid logical foundations to Kant’s claim that existence is not a real predicate. In this article I will challenge Bennett’s claim by arguing that although Kant and Frege agree on what existence is not, they agree neither on what it is nor on the importance and justification of existential propositions. I identify three main differences: first, whereas for Frege existence is a (non-relational) property of a (...) concept, for Kant it is a relational property pertaining between the concept and intuition of an object. Second, whereas for Frege truth about individuals presupposes their existence, for Kant truth is in many cases (including judgments about individuals) independent of the (possible) existence of objects. Third, whereas Frege binds logic to existence and removes modalities from logic, for Kant existence is a modal category that is emphatically removed from the domain of (general) logic and set in the core of metaphysics. Due to these differences in Kant’s and Frege’s theories of existence, Frege cannot be seen as giving logical clarity to Kant’s view. (shrink)

How is it possible that a thing singled out not exist? How is it possible that two things singled out be numerically identical? How is one to understand the relationship between, say, a quality of a thing and what this quality is? And how is one to understand the relation between this quality and the thing which happens to be thus qualified? Trying to answer these four questions involves investigation of the four senses of the verb "to be," or of (...) the concepts of existence, identity, essential and accidental predication. Butchvarov’s thesis is that these four questions admit of a common answer, that the cornerstone of this comprehensive theory is an answer to the second question, and that this crucial answer depends on making some such distinction as his between "objects" and "entities." The bare bones of his argument are these: We commonly make statements of the form "a is b" where "a" and "b" are used referringly. A "material identity" statement of this form may be true. If true, it is about one thing; yet what it is about appears to be distinct things. This distinctness is not a real distinction among existents, nor does it arise solely or primarily from features of language. Butchvarov’s account is based on a distinction "of reason" between objects and entities. An entity is an existent, a constituent of the world. An object is whatever can be singled out once, and only once, in perception or imagination or in "thought". Entities as such cannot be singled out, yet they may be recognized through applications of a conceptual apparatus to objects. A material identity statement, then, states that two objects are one entity. If true, it is both about two distinct objects and about the one entity which each is. When two objects are judged to be one entity, then indiscernibility is enforced. Seeming counterexamples to the indiscernibility of identicals are explained in terms of the distinction between objects and entities. Though some applications of the concept of identity are relative to sortal characteristics, others are not. The latter are prior to the former. These primary judgments constitute the backbone of "thought" and discourse. They are governed by impersonal, nonhuman "paradigms." There are entities, of course; and there are objects, though as objects none exists. Some objects are entities, some are not. The notion of existence, like the notion of identity in its material role, is then a principle of classification, a concept. Butchvarov examines nine objections to this claim, and elaborates his distinction between objects and entities. He concludes that identifiability, hence indefinite reidentifiability, is the logically sufficient condition of applicability of the concept of existence. A statement such as "Socrates is white" is a disguised conjunction, viz., "Socrates has this color, and this color is white." The second conjunct is an "essential" statement; it says of an object singled out that it is a certain entity; or, to allow for essences of nonexistent objects, it states what entity the object would be were it an entity. An essential statement is not a material identity statement, for only one of its terms is used referringly. The essence of an object is not a property of it, for it is what the object is or would be. Whereas logically prior consciousness of objects is intentional and non-conceptual, consciousness of entities is conceptual and nonintentional; it consists in recognizing that a thing can be identified by oneself or by others. What is accidentally white, say, cannot be a material substance or bare particular; therefore it is a "cluster" of qualities. The Resemblance Theory, according to which qualities are particulars, is not a coherent alternative to the Identity Theory; therefore the qualities an individual happens to have are themselves universals. The Bradleyan critique of ontological atomism is cogent; therefore an individual is a cluster of qualities each of which depends for its "formal identity" on its being together with the rest. An individual’s having qualities is then to be understood in terms of the necessary togetherness of the qualities constitutive of it. Since in addition each of these qualities is essentially a universal, and specific universals are contingently coinstantiated, the predication in question is properly regarded as accidental. The problem of identifying quality-clusters through space and time is discussed. (shrink)

According to modems interpreters, there are two differents accounts of the doctrine of predicables in Aristotle's Topics: the exclusive and the inclusive one. The shift between these two accounts it is generally explained with genetic criteria. This paper shows that not all the contradictions found between book A of Topics and its central books are real, and gives a non genetic explanatión of the authentic incoherences. It is also shown that in the whole text of Topics there is no (...) trace of an inclusive account of genus. (shrink)