In a number of essays published over the last decade or so, W. V. Quine has made some interesting suggestions concerning the ontology of theories. If I understand him correctly, one of his principal objects has been to formulate a criterion by means of which one can correctly decide what are the ontological commitments of any given theory. My aim in this paper is to reveal what I think are inadequacies in Quine's criterion and to indicate the direction in which (...) a proper formulation lies. (shrink)

Non-Relational Realism is a popular solution to the Bradleyan regress of facts or truths. It denies that there is a relational universal of exemplification; for an object a to exemplify a universal F-ness, on this view, is not for a relation to subsist between a and F-ness. An influential objection to Non-Relational Realism is that it is unacceptably obscure. The author argues that Non-Relational Realism can be understood as a selective application of satisfaction semantics to predicates like ‘exemplify’, and that (...) so understood, it is not obscure. This kind of selective use of satisfaction semantics may be feasible in other contexts as a means of making theories more parsimonious. (shrink)

One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...) the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...) difficulties while still being able to put abstraction principles to a foundational use. (shrink)

This paper tries to unleash the nature of the paradox of nonexistence or non-being or negative singular existentials by using a General Metalogical Theory. In the first section, this paper explains in detail the paradox of negative singular eixistentials and explains how Alexius Meinong and Bertrand Russell respond to this paradox. Russell resolves the paradox using quantification method which Quine extends to formulate a criterion of ontological commitments. In the second section, a General Metalogical Theory is explained, and it is (...) shown that how the developed General Metalogical Theory is useful in unleashing the paradox of nonexistence. The principles of General Metalogical Theory is developed from Quine’s criterion: to be is to be the value of bound variable. In Quine’s criterion, the notion of the bound variable is significant. The General Metalogical Theory in unleashing the nature of the paradox mainly focuses on the question: from where does the binding of the bound variable come? The paper argues that it is not enough to say that the binding of the bound variable comes from the existentially loaded use of the particular quantifier. General Metalogical Theory attempts to show that the binding of the bound variable comes from somewhere else, so that we attach the particular quantifier to the variable and use the particular quantifier in an existentially loaded sense. Explaining the binding nature of the bound variable in the above-mentioned manner will unleash the nature of the paradox. (shrink)

On a widespread reading, the Carnap-Quine debate about ontology concerns the objectivity and non-triviality of ontological claims. I argue that this view mischaracterizes Carnap’s aims in “Empiricism, Semantics, and Ontology” : Carnap’s fundamental goal is to free up decisions about scientific language from constraints deriving from ontological doctrine. The contention, based on his internal/external distinction, that ontological claims are either meaningless or trivial was Carnap’s means to achieving this more fundamental goal. Setting the record straight on this point brings out (...) three important and often overlooked features of Carnap’s views on ontology. First, the target of Carnap’s critique in ESO is not Quine’s mature views on ontology, as laid out in “On What There Is”. Rather, Carnap is responding to arguments for nominalism that were given by Tarski, Goodman, and Quine in the 1940s. Second, a more general rejection of conservatism in theory choice is essential to Carnap’s aims and is implicit in his fundamental views on language. Third, even if it turns out to be tenable, the i/e distinction is not adequate for Carnap’s aim in ESO. Drawing on his basic conception of scientific language, I will suggest an alternative approach on his behalf. (shrink)

This article deals with a question of a most general, comprehensive and profound content as it is the nature of mathematical–logical objects insofar as these are considered objects of knowledge and more specifically objects of formal mathematical theories. As objects of formal theories they are dealt with in the sense they have acquired primarily from the beginnings of the systematic study of mathematical foundations in connection with logic dating from the works of G. Cantor and G. Frege in the last (...) decades of the nineteenth century. Largely motivated by a phenomenologically founded view of mathematical objects/states-of-affairs, I try to consistently argue for their character as objects shaped to a certain extent by intentional forms exhibited by consciousness and the modes of constitution of inner temporality and at the same time as constrained in the form of immanent ‘appearances’ by what stands as their non-eliminable reference, that is, the world as primitive soil of experience and the mathematical intuitions developed in relations of reciprocity within-the-world. In this perspective and relative to my intentions I enter, in the last section, into a brief review of certain positions of G. Sher’s foundational holism and R. Tieszen’s constituted platonism, among others, respectively presented in Sher and Tieszen. (shrink)

In this article I am going to argue for the possibility of a transcendental source of logic based on a phenomenologically motivated approach. My aim will be essentially carried out in two succeeding steps of reduction: the first one will be the indication of existence of an inherent temporal factor conditioning formal predicative discourse and the second one, based on a supplementary reduction of objective temporality, will be a recourse to a time-constituting origin which has to be assumed as a (...) non-temporal, transcendental subjectivity and for that reason as possibly the ultimate transcendental root of pure logic. In the development of the argumentation and taking into account W.V. Quine’s views in his well-known Word and Object, a special emphasis will be given to the fundamentally temporal character of universal and existential predicative forms, to their status in logical theories in general, and to their underlying role in generating an inherently non-finitistic character reflected, for instance, in the undecidability of certain infinity statements in formal mathematical theories. This is shown also to concern metatheorems of such vital importance as Gödel’s incompleteness theorems in mathematical foundations. Moreover in the course of the discussion the quest for the ultimate limits of predication will lead to the notions of separation and intentional correlation between an ‘observing’ subject and the object of ‘observation’ as well as to the notion of syntactical individuals taken as the irreducible non-analytic nuclei-forms within analytical discourse. (shrink)

In this article my primary intention is to engage in a discussion on the inherent constraints of models, taken as models of theories, that reaches beyond the epistemological level. Naturally the paper takes into account the ongoing debate between proponents of the syntactic and the semantic view of theories and that between proponents of the various versions of scientific realism, reaching down to the most fundamental, subjective level of discourse. In this approach, while allowing for a limited discussion of physical (...) and positive science models, I am primarily focused on the structure and ontology of mathematical models, in particular Cohen’s forcing models and to a lesser extent Gödel’s constructible universe, to the extent that these were designed to answer questions bearing on the scope, the capacity and ultimately the ontology of models themselves, therefore influencing in one or the other way the status of models in general. This status, it is argued, is largely defined by the way models subsume a set-theoretical structure whose constraints, reducible to an extra-linguistic level of discourse, may implicitly condition the epistemic status of models as representations of axiomatic theories. In the last section I deal extensively with the inner constraints of theories as subjectively originated in a less technical philosophically oriented discussion with certain prompts from phenomenology. (shrink)

A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis, by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention is to primarily (...) address ontological multiversism as advocated, for instance, by Hamkins or Väätänen, precisely for the reason that they proclaim, to the one or the other extent, ontological preoccupations for the introduction of respective multiverse theories. Taking also into account Woodin’s and Steel’s multiverse versions, I take up an argumentation against multiversism, and in a certain sense against platonism in mathematical foundations, mainly on subjectively founded grounds, while keeping an eye on Clarke-Doane’s concern with Benacerraf’s challenge. I note that even though the paper is rather technically constructed in arguing against multiversism, the non-negligible philosophical part is influenced to a certain extent by a phenomenologically motivated view of the matter. (shrink)

This paper traces the development of Quine's ontological ideas throughout his early logical work in the period before 1948. It shows that his ontological criterion critically depends on this work in logic. The use of quantifiers as logical primitives and the introduction of general variables in 1936, the search for adequate comprehension axioms, and problems with proper classes, all forced Quine to consider ontological questions. I also show that Quine's rejection of intensional entities goes back to his generalisation of Principia (...) Mathematica in 1932. (shrink)

When we use a directly referential expression to denote an object, do we incur an ontological commitment to that object, as Russell and Barcan Marcus held? Not according to Quine, whose regimented language has only variables as denoting expressions, but no constants to model direct reference. I make a case for a more liberal conception of ontological commitment—more wide-ranging than Quine’s—which allows for commitment to individuals, with an improved logical language of regimentation. The reason for Quine’s prohibition on commitment to (...) individuals, I argue, is that his choice of regimented language is heavily informed by his holist epistemology, in which objects are introduced via a description of their explanatory role. But non-holists can coherently attempt to commit to individuals using directly referential expressions, modelled in a formal language as constants. While holding on to the insight that a logical language is a helpful medium for ontology, I propose instead a more permissive language of regimentation, one expanded to permit the use of constants to record attempts to commit to individuals, which allows us to make sense of non-holist theories with alternative name-based or name-and-variable-based criteria of ontological commitment as well as Quinean theories. (shrink)

In Parts of Classes David Lewis argued that mereology is ‘ontologically innocent’, mereological notions not incurring additional ontological commitments. Unfortunately, though, Lewis’s argument for this is not fully spelled out. Here we use some formal results concerning translations between formal languages to argue for the ontological innocence of mereology directly.

With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...

What is it for an utterance of an expression to lack meaning? In this paper I address the issue along the lines of Carnap’s seminal article “Empiricism, Semantics and Ontology”. Carnap provides there an answer to the above question, which he then uses to argue that certain claims of metaphysics are meaningless. In the first section of the paper I present Carnap’s argument for the meaninglessness of certain metaphysical claims. In the second section I argue that, although the argument is (...) not compelling, the main virtue of Carnap’s proposal is the strategy he develops for generating meaningless uses of language. In the third section I propose an externalist criterion of meaningless uses of expressions that relies on semantic externalist considerations. This, I argue, bears significant resemblances to Carnap’s proposal. In the last section I discuss the applicability of the new criterion to the question concerning the meaning of metaphysical claims. (shrink)

This paper consists of two parts. Part I contains a precise model-theoretic reconstruction of Quine's criterion for the ontological presuppositions of a theory. Two versions (K1), (K2) of the criterion are elaborated, (K2) being the more adequate one which is shown through a number of theorems for each version. Part II contains a critical discussion of (K2), in particular of the question wether (K2) is a criterion for ontological presuppositions, i.e. for entities existing independently of the theory. Its answer depends (...) on the meaning of the quantifiers used in (K2). It is shown that this meaning, contrary to Quine's opinion, does not commit one to the existence of entities. Quine's criterion is therefore not a criterion for ontological presuppositions of theories. If theories at all presuppose independently existing entities, then it is not by using the standard quantifiers of classical logic. One of the consequences of this result is that there is no need for a free logic, which is shown by discussing a system of Lambert and Meyer. Another consequence is that there is no problem about negative existentials. (shrink)