One of the advantages of my account in the essay “Instantiation as Partial Identity” was capturing the contingency of instantiation—something David Armstrong gave up in his experiment with a similar view. What made the contingency possible for me was my own non-standard account of identity, complete with the apparatus of counts and aspects. The need remains to lift some obscurity from the account in order to display its virtues to greater advantage. To that end, I propose to respond (...) to those who have grappled with it in print. There are various criticisms by commentators: that it is rendered absurd by the transitivity of identity, that it makes instantiation necessary instead of contingent, that it is unclear what counts are, that aspects are simply tropes, that my view does not capture multiple location, that I make an unclear reference to a theory of composition as identity, that the account suffers from problems with polyadicity, and that it is not a realist account of universals after all. I give responses to these objections. (shrink)

Many familiar forms of property realism identify properties with sui generis ontological categories like universals or tropes and posit a fundamental instantiation relation that unifies objects with their properties. In this paper, I develop and defend locationism, which identifies properties with locations and holds that the occupation relation that unifies objects with their locations also unifies objects with their properties. Along with the theoretical parsimony that locationism enjoys, I argue that locationism resolves a puzzle for actualists regarding the ontological (...) status of uninstantiated properties. I also note some promising applications of the locationist framework to the metaphysics of quantities and possible worlds. (shrink)

This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness by a new normal form technique. In addition, we (...) relate INL to other modal logics by means of translations, and determine its precise SAT complexity. Finally, we discuss proof-theoretic fine-structure of INL in terms of semantic tableaux and some expressive fine-structure in terms of fragments, while discussing concrete illustrations of the instantial neighborhood language in topological spaces, in games with powers for players construed in a new way, as well as in dynamic logics of acquiring or deleting evidence. We conclude with some coalgebraic perspectives on what is achieved in this paper. Many of these final themes suggest follow-up work of independent interest. (shrink)

Instantiation Theory presents a new, general unification algorithm that is of immediate use in building theorem provers and logic programming systems. Instantiation theory is the study of instantiation in an abstract context that is applicable to most commonly studied logical formalisms. The volume begins with a survey of general approaches to the study of instantiation, as found in tree systems, order-sorted algebras, algebraic theories, composita, and instantiation systems. A classification of instantiation systems is given, (...) based on properties of substitutions, degree of type strictness, and well-foundedness of terms. Equational theories and the use of typed variables are studied in terms of quotient homomorphisms and embeddings, respectively. Every instantiation system is a quotient system of a subsystem of first-order term instantiation. The general unification algorithm is developed as an application of the basic theory. Its soundness is rigorously proved, and its completeness and efficiency are verfied for certain classes of instantiation systems. Appropriate applications of the algorithm include unification of first-order terms, order-sorted terms, and first-order formulas modulo alpha-conversion, as well as equational unification using simple congruences. (shrink)

This article proposes to recontextualize Tractarian ethics within the anthropological frame that develops through Wittgenstein’s Philosophical Grammar to the Philosophical Investigations. The Tractarian vision of absolute value, ethical propositions as nonsense, and the transcendentality of ethics seems incapable of being instantiated within the particulars that surround human action. This difficulty is resolved by showing that the Tractarian theme of the coextension of ethics and language (and of ethics and life) combined with Wittgenstein’s later ideas of language-games, rule-following, and forms of (...) life instantiates Tractarian ethics within this later anthropological frame. (shrink)

The rule of universal instantiation appears to be subject to counterexamples, although the rule of existential generalization is not subject to the same doubts. This paper is a survey of ways of responding to this problem, both conservative and revisionist. The conclusion drawn is that logical validity should be defined in terms of assertibility in a context rather than in terms of truth on an interpretation. Contexts are here defined, not in terms of the attitudes of the interlocutors, but (...) in terms of the goals of conversation, and assertibility is explained in terms of cooperation. (shrink)

While each Form is what it is to be F, some Forms also instantiate F (or “self-instantiate”). Here I consider whether the explanation for a Form’s instantiating F should be the Form’s participating in itself. First, I motivate the need for an explanation of self-instantiation. Second, I consider the advantages and disadvantages of self-participation alongside an alternative explanation—that the Form’s being what it is to be F is a sufficient explanation of its instantiation of F. The result is (...) not a conclusive case for self-participation, but only some initial considerations in favor of it. (shrink)

We agree that treating rules and similarity as dichotomous opposites is unproductive. However, describing all categorization operations as a continuum of varied similarity process obscures a multidimensional contrast. We describe two processes, instantiated rules and abstract analogy, both of which have aspects of rules and similarity, and question whether they can be compared informatively as points on a continuum.

The aim of this paper is to defend a naturalistic approach to instantiation and the Principle of Instantiation. I argue that the instantiation of an ordinary property F consists of two coordinated relationships at the levels of the manifest and scientific images, namely, constituency and entailment. Also, I offer an account of the Principle of Instantiation related to this conception of instantiation based on the notion of scientific prediction.

Realists about mental disorder have been hasty about dismissing social explanations of how mental disorder is constituted. However, many social ontologies are realist ontologies. In order to create a meaningful distinction between realism and social metaphysics about mental disorder, I propose that realism about mental disorder is best understood as Individual Trait Realism (ITR) about them. For ITR, mental disorders exist in virtue of traits. I defend the view that ITR is compatible with social metaphysics, arguing that, in asking whether (...) constituents in the social sphere figure the metaphysics of psychopathology, we are asking questions on three different strata of explanation: the strata of demarcation, instantiation, and individual traits. Distinguishing between these strata allows for nuanced realism that need not reject the social constitution of mental disorder. (shrink)

ellucci, C., Existential instantiation and normalization in sequent natural deduction, Annals of Pure and Applied Logic 58 111–148. A sequent conclusion natural deduction system is introduced in which classical logic is treated per se, not as a special case of intuitionistic logic. The system includes an existential instantiation rule and involves restrictions on the discharge rules. Contrary to the standard formula conclusion natural deduction systems for classical logic, its normal derivations satisfy both the subformula property and the separation (...) property and allow to establish a version of the midsequent theorem and Herbrand's theorem. (shrink)

The problem of many-over-one asks how it can be thatmanyproperties are ever instantiated byoneobject. A putative solution might, for example, claim that the properties are appropriately bundled, or somehow tied to a bare particular. In this essay, the author argues that, surprisingly, an extant candidate solution to this problem is at the same time an independently developed candidate solution to the mind-body problem. Specifically, what is argued here to be the best version of the relata-specific bundle theory—the thesis that each (...) instance of compresence has a special intrinsic nature in virtue of which it necessarily bundles its specific bundle-ees—is also a species of Russellian monism, labeled by David Chalmers as ‘constitutive Russellian panprotopsychism’. The upshot of this connection is significant for the metaphysics of the mind-body problem: a credible theory of property instantiation turns out to have a built-in account of how consciousness is grounded in certain (broadly) physical systems. (shrink)

In order to avoid the problems faced by standard realist analyses of the “relation” of instantiation, Baxter and, following him, Armstrong each analyze the instantiation of a universal by a particular in terms of their partial identity. I introduce two related conceptions of partial identity, one mereological and one non-mereological, both of which require at least one of the relata of the partial identity “relation” to be complex. I then introduce a second non-mereological conception of partial identity, which (...) allows for both relata to be simple. I take these three conceptions to exhaust the plausible ways of construing two entities as being partially identical. I then argue that there is no analysis (including those offered by Baxter and Armstrong) of a universal and a particular as being partially identical consistent with any of these three conceptions that (i) is coherent, (ii) is consistently realist, (iii) does not lead to absurd consequences, and (iv) offers a “solution” to the problem of instantiation that avoids the problems with the other standard realist responses. In so arguing, I offer a criticism of the analysis of instantiation as partial identity that is independent of the standard criticism that it entails the necessity of predication. (shrink)

We study instantiated abstract argumentation frames of the form, where is an abstract argumentation frame and where the arguments x of S are instantiated by I as well formed formulas of a well known logic, for example as Boolean formulas or as predicate logic formulas or as modal logic formulas. We use the method of conceptual analysis to derive the properties of our proposed system. We seek to define the notion of complete extensions for such systems and provide algorithms for (...) finding such extensions. We further develop a theory of instantiation in the abstract, using the framework of Boolean attack formations and of conjunctive and disjunctive attacks. We discuss applications and compare critically with the existing related literature. (shrink)

The concept of instantiation is realized differently across a variety of metaphysical theories. A certain realization of the concept in a given theory depends on what roles are specified and associated with the concept and its corresponding term as well as what entities are suited to fill those roles. In this paper, the classic realization of the concept of instantiation in a one-category ontology of abstract particulars or tropes is articulated in a novel way and defended against unaddressed (...) objections. (shrink)

Construing the instantiation of a universal by a particular in terms of my theory of aspects resolves the basic mystery of this "non-relational tie", and gives theoretical unity to the four characteristics of instantiation discerned by Armstrong. Taking aspects as distinct in a way akin to Scotus's formal distinction, I suggest that instantiation is the sharing of an aspect by a universal and a particular--a kind of partial identity. This approach allows me to address Plato's multiple location (...) and One over Many problems, Bradley's problem concerning the instantiation of relations, and the problem of change. (shrink)

According to traditional universalism, properties are instantiated by objects, where instantiation is a ‘tie’ that binds objects and properties into facts. I offer two arguments against this view. I then develop an alternative higher-order account which holds that properties are primitively predicated of objects yet, unlike traditional nominalism, are nevertheless genuinely real. When it’s a fact that Fo, it’s not because object o instantiates F-ness, but just that Fo – where F still exists. Against orthodox higher-order approaches, however, my (...) arguments against instantiation also serve to support a sparse conception of properties. In developing the view, I introduce an extension of ontological and ideological commitment in the form of syntactic commitment. (shrink)

The co-instantiation thesis is pivotal to a significant solution to the problem of causal exclusion. But this thesis has been subject to some powerful objections. In this paper, I argue that these difficulties arise because the thesis lacks the necessary metaphysical framework in which its claims should be interpreted and understood. Once this framework is in place, we see that the co-instantiation thesis can answer its critics. The result is a rehabilitated co-instantiation solution to the troubling problem (...) of causal exclusion. But questions remain concerning the viability of certain of its applications. (shrink)

According to Lowe’s Four-Category Ontology, the general nature of the entities belonging to the four fundamental categories is determined by the basic formal ontological relations (instantiation and characterization) that they bear to other entities. I argue that, in closer analysis, instead of one formal relation of characterization, this category system introduces two, one connecting particulars and another universals. With regard to the characterization relation connecting particulars, it remains an open issue whether it would need further analysis. By contrast, the (...) status of instantiation as an internal relation is comparatively clear. Nevertheless, because of holding by virtue of the essences of particulars, the holding of instantiation between universals and particulars rules out the possibility of kind change and entails that particulars are essentially rigidly dependent on universals. Finally, Lowe’s analysis of necessary exemplification gives us some reasons to suspect that some property universals need not have any instances in order to exist. (shrink)

This work presents and discusses the conception of instantiation as ‘partial identity’. The theory has been previously proposed in two different guises by Baxter and Armstrong . Attention will be paid mostly to Baxter’s presentation, which seems the best de veloped, and where instantiation is understood as identity of ‘aspects’ of a universal and a particular. The theory seems to offer a solution to the vexed question of Bradley’s Regress, because instantiation is no longer conceived as a (...) relation between numerically different entities. The proposed solution requires an ontology of ‘aspects’ in order to work. Aspects are presented in the form [ x insofar as j] where x is filled by the entity to which the aspect pertains and j is filled by the respect in which the entity in question is considered. Aspects are numerically identical with the entity to which they pertain and with the other aspects of the same entity. Aspects, nonetheless, are not mere ways in which one can conceive an entity. Aspects are objective. Rejection of the principle of indiscernibility of identicals is crucial to this theory. The attributions of one aspect are not also attributions to the other aspects of the same entity. Hence, aspects offer ways to deal with seemingly incoherent attributions to the same entity. Baxter uses them to solve the problem of the multi-location of universals, temporary intrinsics and trans-world identity, besides the nature of instantiation. Several difficulties are presented, both to the general metaphysics of aspects, and to the conception of instantiation as identity of aspects. In general: it is not clear how to distinguish objective aspects from the mere forms in which we conceive an entity; it is not clear what are the conditions of identity of an aspect; and although the necessity of identity is rejected in general, it reappears as necessity of ‘aspectual’ identity. The necessity of aspectual identity raises concerns about the stability of the view. In respect to the specific conception of instantiation as identity of aspects, it will be pointed out that the theory implies the complete identity of universals and particulars that instantiate them and, further, that it implies the identity of everything with everything. (shrink)

It is argued that instantiation, i.e. the relation between particular objects and properties (conceived as universals or tropes) is indeed an ontologically robust relation. The relation of instantiation is required to explain the difference between a state of affairs of, for example, a being F, and the mereological fusion [ a + F]. If instantiation is a true relation, then Bradley’s Regress ensues. It is argued, nevertheless, that the regress cannot be taken as a reason to reject (...) the existence of instantiation or to reject the existence of properties as entities numerically different from particular objects to which the properties should be related. All the nominalist alternatives suffer from similar regresses. Bradley’s Regress should, therefore, be addressed head-on. After dismissing all the applicable ways in which an infinite regress may be deemed vicious, it is argued that Bradley’s Regress is — in a sense — harmless. (shrink)

Some people object to realism about universals because they think that instantiation, the connection between something and the universals that characterize it, is too mysterious. Baxter and Armstrong try to make instantiation less mysterious by taking it to be a kind of partial identity. However, I argue that their accounts of instantiation, and any similar ones, fail.

We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number of predicates in the overlying language.

Discovery proceeds in stages of construction, evaluation, and revision. Each of these stages is constrained by what is known or conjectured about what is being discovered. A new characterization of mechanism aids in specifying what is to be discovered when a mechanism is sought. Guidance in discovering mechanisms may be provided by the reasoning strategies of schema instantiation, modular subassembly, and forward/backward chaining. Examples are found in mechanisms in molecular biology, biochemistry, immunology, and evolutionary biology.

In Lowe’s Four-Category Ontology, instantiation is a basic formal ontological relation between particulars (objects, modes) and their kinds (kinds, attributes). Therefore, instantiation must be considered as a metaphysically necessary relation, which also rules out the metaphysical possibility of kind change. Nevertheless, according to Lowe, objects obtain their identity conditions in a more general level than specific natural kinds, which allows for kind change. There also seems to be actual examples of kind change. The advocate of Four-Category Ontology is (...) obliged to resolve the tension between these mutually incompatible claims. In this article, we argue that the only viable option for the advocate of Four-Category Ontology is to bite the bullet and stick to the necessity of each of the most specific natural kind to the object instantiating it. As a major drawback, the four-category ontologist does not have any credible means to allow for kind change or determination of the identity conditions in a more general level. (shrink)

Existential instantiation is a rule of inference that allows us infer, from the proposition that there are some p things, the proposition that a is a p thing. What role does 'a' play here? According to one account, recently defended by Breckenridge and Magidor, we use 'a' to refer to a p thing. I argue that this cannot be right. I propose an alternative account, according to which we use 'a' to refer to a supposedly p thing.

What is it, metaphysically, for a universal to be instantiated in a concrete particular? Philosophical controversy has been ongoing since the beginning of philosophy itself. I here contribute a novel account of instantiation developed on the basis of Aristotelian premises (but departing from the mainstream interpretation according to which Aristotelian universals are instantiated by ‘combining’ hylomorphically with matter). The key stance is that for Aristotle each substance is one, i.e. single (in addition to also being a non-recurrent particular). I (...) show that for Aristotle, the oneness of substances is primitively assumed, and, importantly, cannot be derived from composition of parts, not even holistic composition. Parts undermine oneness. It follows that instantiated properties are 'not parts' of substances. However, if not parts of the substances they are in, what are they? Aristotle shows they are 'qualifications' of the substances they are in. Don’t qualifications undermine the singleness of a substance? I show that Aristotle makes sure they do not. The way he does it is new, then and now. Instantiated properties are ‘hybrid’ entities: they sacrifice their own discreteness 'qua' properties, while adopting the discreteness of the metaphysical subject they qualify, i.e. the substance. But then, how can a universal quality recur in many substances, if, when instantiated, it assimilates the discreteness of each of these substances? This is a key Aristotelian stance: 'the quality recurs, not its qualifications'. Qualities are abstracted from their instances in similar objects, e.g. ‘wisdom’ is abstracted from many ‘wise’ people; ‘wisdom’ is individuated bottom-up from its instances, by abstraction. (shrink)

Argumentation Frameworks provide a fruitful basis for exploring issues of defeasible reasoning. Their power largely derives from the abstract nature of the arguments within the framework, where arguments are atomic nodes in an undifferentiated relation of attack. This abstraction conceals different senses of argument, namely a single-step reason to a claim, a series of reasoning steps to a single claim, and reasoning steps for and against a claim. Concrete instantiations encounter difficulties and complexities as a result of conflating these senses. (...) To distinguish them, we provide an approach to instantiating AFs in which the nodes are restricted to literals and rules, encoding the underlying theory directly. Arguments in these senses emerge from this framework as distinctive structures of nodes and paths. As a consequence of the approach, we reduce the effort of computing argumentation extensions, which is in contrast to other approaches. Our framework retains the theoretical and computational bene.. (shrink)

In an effort to refute Avicenna’s real distinction between essence and existence, Averroes argues for an Instantiation Analysis of existence which thinks of existence not as an accidental addition to an essence, but rather as the recognition that there is an instance in extramental reality which matches a concept in the mind of a knower. In this study, I argue that Averroes’s Instantiation Analysis fails to refute Avicenna’s real distinction by showing that Avicenna himself endorses the Instantiation (...) Analysis and, in fact, makes use of it to motivate his real distinction. To show this, I review several texts where Avicenna makes the puzzling claim that substances are found to be in subjects. These texts reveal how Avicenna discovers the real distinction with Aristotle’s help—not, as Averroes relates, against the view of Aristotle. (shrink)

In a recent paper, Breckenridge and Magidor argue for an interesting and counterintuitive account of instantial reasoning. According to this account, in arguments such as one beginning with 'There is some x such that x is mortal. Let O be such an x. ...', the 'O' refers to a particular object, although we cannot know which. I give and defend a simple counterexample involving the notion of an unreferred-to object.

This paper is a commentary on the target article by Michael Arbib, “Levels of modeling of mechanisms of visually guided behavior”, in the same issue of the journal, pp. 407–465. -/- I focus on the importance of the inclusion of an ability of a system to entertain, at a given time, multiple instantiations of a given schema (situation template, frame, script, action plan, etc.), and complications introduced into neural/connectionist network systems by such inclusion.

ABSTRACT An apparent objection against my theory of instantiation as partial identity is that identity is necessary, yet instantiation is often contingent. To rebut the objection, I show how it can make sense that identity is contingent. I begin by showing how it can make sense that identity is temporary. I rely heavily on Andre Gallois’s formal theory of occasional identity, but argue that there is a gap in his explanation of how his formalisms make sense that needs (...) to be filled by appeal to my theory of Aspects. (shrink)

Working with the assumption that properties depend for their instantiation on substances, I argue against a unitary analysis of instantiation. On the standard view, a property is instantiated just in case there is a substance that serves as the bearer of the property. But this view cannot make sense of how properties that are mind-dependent depend for their instantiation on minds. I consider two classes of properties that philosophers often take to be mind-dependent: sensible qualities like color (...) and bodily sensations like itches. Given that the mind is never itself literally red or itchy, we cannot explain the instantiation of these qualities as a matter of their having a mental bearer. Appealing to insights from Berkeley, I defend a view on which a property can be instantiated not in virtue of having a bearer—mental or material—but rather in virtue of being the object of a conscious act of perception. In the second half of the paper, I suggest that the best account of sensible qualities and bodily sensations ultimately makes use of both varieties of instantiation. (shrink)

In many domains of public discourse such as arguments about public policy, there is an abundance of knowledge to store, query, and reason with. To use this knowledge, we must address two key general problems: first, the problem of the knowledge acquisition bottleneck between forms in which the knowledge is usually expressed, e.g., natural language, and forms which can be automatically processed; second, reasoning with the uncertainties and inconsistencies of the knowledge. Given such complexities, it is labour and knowledge intensive (...) to conduct policy consultations, where participants contribute statements to the policy discourse. Yet, from such a consultation, we want to derive policy positions, where each position is a set of consistent statements, but where positions may be mutually inconsistent. To address these problems and support policy-making consultations, we consider recent automated techniques in natural language processing, instantiating arguments, and reasoning with the arguments in argumentation frameworks. We discuss application and “bridge” issues between these techniques, outlining a pipeline of technologies whereby: expressions in a controlled natural language are parsed and translated into a logic (a literals and rules knowledge base), from which we generate instantiated arguments and their relationships using a logic-based formalism (an argument knowledge base), which is then input to an implemented argumentation framework that calculates extensions of arguments (an argument extensions knowledge base), and finally, we extract consistent sets of expressions (policy positions). The paper reports progress towards reasoning with web-based, distributed, collaborative, incomplete, and inconsistent knowledge bases expressed in natural language. (shrink)

There is disagreement over the notion of representation in cognitive science. Many investigators equate representations with symbols, that is, with syntactically defined elements in an internal symbol system. In recent years there have been two challenges to this orthodoxy. First, a number of philosophers, including many outside the symbolist orthodoxy, have argued that "representation" should be understood in its classical sense, as denoting a "stands for" relation between representation and represented. Second, there has been a growing challenge to orthodoxy under (...) the banner of connectionism. Although this connectionist challenge has evoked emotionally-charged rebukes from the symbolist camp, connectionists as a group have not articulated a conception of representation to replace the symbolist view. Nonetheless, most agree on the need for a nonsymbolic notion of representation. This paper advances a "stands for" sense of representation as primary by incorporating it into a general approach to cognitive science consonant with the connectionism. The idea is to marry connectionism to a particular version of functionalism, viz., one that builds its notion of "function" on the similarity between functional analysis in biology and in psychology. It builds on my earlier work adapting and revising Marr's tri-level approach to cognition. My proposal frees Marr's analysis from its moorings in the orthodox symbolic view of representation and allies it with a notion of functional analysis akin to that proposed by Cummins, developed further by Haugeland, and invoked by Millikan and Dretske. Unlike these authors, however, I do not wed representation to a general belief-desire analysis of behavior. Rather, I follow what I take to be the lesson of psychological practice, according to which the investigator does not seek to explain behavior in general but seeks to analyze the cognitive capacities that underlie behavior, such as vision, memory, learning, and linguistic capacities. Accordingly, ascriptions of representational content are made not by working back from belief-desire ascriptions, but in the context of forming psychological models to account for specific cognitive capacities. Because conceptions of representation in cognitive science typically are embedded in a general approach to the study of cognition, arguments for the comparative plausibility of a particular conception of representation must scout these larger frameworks. I therefore begin by characterizing the interlocking set of assumptions that gave life to the orthodox symbolist approach, paying special attention to the complementarity between representation and process that naturally arises from those assumptions. I then consider two versions of an alternative approach to representation: Dretske's and my own. Finally, I urge the merits of the "cognitive capacities" over the "belief-desire" approach to the subject-matter of cognitive science. (shrink)

This paper is concerned with English noun phrases that denote generalized instances: they do not refer to actual spatio-temporal instances, but to virtual ones that are abstracted from a limited number of actual instances, e.g., a student in Three times, a student complained (Langacker, Foundations of Cognitive Grammar. Volume II: Descriptive application, Stanford University Press, 1991, Dynamicity, fictivity, and scanning: The imaginative basis of logic and linguistic meaning, Cambridge University Press, 2005, forthcoming). Langacker likens generalized instances to generic ones, which (...) constitute “global” generalizations over all actual instances of a type. On the basis of authentic data, I argue that, even though the profiled instance denoted by generic and generalized noun phrases is similar, the way the respective instances are accessed in discourse is very different. My data set consists of English noun phrases that are explicitly marked for generalized instantiation by the addition of a secondary determiner such as same in The twin brothers bought the same car or kind of in There was no way we could match that kind of offer. I compare noun phrases of four sets of secondary determiners, viz. adjectives of multiple exposure (usual), of identity (same, identical), of similarity (similar, comparable) and type noun constructions (kind of/type of/sort of). These data also allow me to refine the concept of generalized instantiation in terms of its semantic subtypes, the semantic interaction between secondary determiner and primary determiner, and the selection criteria for secondary determiners that can express it. (shrink)

Ante rem structures were posited as the subject matter of mathematics in order to resolve a problem of referential indeterminacy within mathematical discourse. Nevertheless, ante rem structuralists are inevitably committed to the existence of indiscernible entities, and this commitment produces an exactly analogous problem. If it cannot be sorted out, then the postulation of ante rem structures is futile. In a recent paper, Stewart Shapiro argued that the problem may be solved by analysing some of the singular terms of mathematics (...) not as genuinely referring expressions, but as instantial terms. In this paper, I discuss several competing accounts of the semantics of terms of this kind, and argue that they are all untenable for the ante rem structuralist. Shapiro, then, still owes us an account of the semantics of instantial terms that suits the ante rem structuralist project. Without it, the ante rem structuralist is still unable to determine the reference of the singular terms of mathematics. (shrink)