One feature of vague predicates is that, as far as appearances go, they lack sharp application boundaries. I argue that we would not be able to locate boundaries even if vague predicates had sharp boundaries. I do so by developing an idealized cognitive model of a categorization faculty which has mobile and dynamic sortals (`classes', `concepts' or `categories') and formally prove that the degree of precision with which boundaries of such sortals can be located is inversely constrained by (...) their flexibility. Given the literature, it is plausible that we are appropriately like the model. Hence, an inability to locate sharp boundaries is not necessarily because there are none; boundaries could be sharp and it is plausible that we would nevertheless be unable to locate them. (shrink)
In a recent article, Harold Noonan argues that application conditions and criteria of identity are not distinct from one another. This seems to threaten the standard approach to distinguishing sortals from adjectival terms. I propose that his observation, while correct, does not have this consequence. I present a simple scheme for distinguishing sortals from adjectival terms. I also propose an amended version of the standard canonical form of criteria of identity.
It is argued that there are ways of individuating the objects of perception without using sortal concepts. The result is an moderate anti-sortalist position on which one can single out objects using demonstrative expressions without knowing exactly what sort of thing those objects are.
This paper reviews the role of sortals in the syntax and semantics of proper names and the related question of a mass-count distinction among proper names. The paper argues that sortals play a significant role with proper names and that that role matches individuating or ‘sortal’ classifiers in languages lacking a mass-count distinction. Proper names do not themselves classify as count, but may classify as mass or rather number-neutral. This also holds for other expressions or uses of expressions (...) that lack a syntactic mass-count distinction, namely that-clauses, predicative phrases, intensional NPs, quotations, as well as verbs with respect to their event arguments. In all those cases, the relevant diagnostics show a number-neutral status, rather than a division into mass and count. This is remarkable because it means that count status is independent of the nature of the semantic values of an expression or its conceptual content. It also means that even languages such as English or German are classifier languages when it comes to expressions or uses of expressions to which a syntactic mass-count distinction is inapplicable. (shrink)
Advocates of sortal essentialism have argued that concepts like “thing” or “object” lack the unambiguous individuative criteria necessary to play the role of genuine sortals in reference. Instead, they function as “dummy sortals” which are placeholders or incomplete designations. In disqualifying apparent placeholder sortals, however, these philosophers have posed insuperable problems for accounts of childhood conceptual development. I argue that recent evidence in psychology demonstrates that children do possess simple or basic sortals of physical objects or (...) things. I contend that these concepts provide the genuine individuative criteria necessary for reference. As a consequence, sortalism can be made compatible with the developmental facts of conceptual development. (shrink)
We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.
With the past and future tense propositional operators in its syntax, a formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. A completeness proof for the system is constructed and its absolute consistency proved. The completeness proof is given relative to a notion of logical validity provided by an intensional semantic system, which assumes an approach to sortals from a modern form of conceptualism.
The neo-Fregean account of arithmetical knowledge is centered around the abstraction principle known as Hume’s Principle: for any concepts X and Y , the number of X ’s is the same as the number of Y ’s just in case there is a 1–1 correspondence between X and Y . The Caesar Problem, originally raised by Frege in §56 of Die Grundlagen der Arithmetik , emerges in the context of the neo-Fregean programme, because, though Hume’s Principle provides a criterion of (...) identity for objects falling under the concept of Number–namely, 1–1 correspondence—the principle fails to deliver a criterion of application. That is, it fails to deliver a criterion that will tell us which objects fall under the concept Number, and so, leaves unanswered the question whether Caesar could be a number. Hale and Wright have recently offered a neo-Fregean solution to this problem. The solution appeals to the notion of a categorical sortal. This paper offers a reconstruction of their solution, which has the advantage over Hale and Wright’s original proposal of making clear what the structure of the background ontology is. In addition, it is shown that the Caesar Problem can be solved in a framework more minimal than that of Hale and Wright, viz . one that dispenses with categorical sortals. The paper ends by discussing an objection to the proposed neo-Fregean solutions, based on the idea that Leibniz’s Law gives a universal criterion of identity. This is an idea that Hale and Wright reject. However, it is shown that a solution very much in keeping with their own proposal is available, even if it is granted that Leibniz’s Law provides a universal criterion of identity. (shrink)
A formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. The absolute consistency of the system is proved. A completeness proof for the system is also constructed. This proof is relative to a concept of logical validity provided by a semantics, which assumes as its philosophical background an approach to sortals from a modern form of conceptualism.
It has long been debated whether objects are ‘sortally’ individuated. This paper begins by clarifying some of the key terms in play—in particular, ‘sortal’, ‘individuation’, and ‘object’. The term ‘individuation’ is taken to have both a cognitive and a metaphysical sense, in the former denoting the singling out of an object in thought and in the latter a determination relation between entities. ‘Sortalism’ is defined as the doctrine that only as falling under some specific sortal concept can an object be (...) successfully singled out in thought. It is argued that such a view is too strong, but that a weaker one, ‘categorialism’, can be defended, this implying that a thinker cannot successfully single out an object in thought without having at least an implicit grasp of the criterion of identity that the object satisfies. (shrink)
In recent decades, a view of identity I call Sortalism has gained popularity. According to this view, if a is identical to b, then there is some sortal S such that a is the same S as b. Sortalism has typically been discussed with respect to the identity of objects. I argue that the motivations for Sortalism about object-identity apply equally well to event-identity. But Sortalism about event-identity poses a serious threat to the view that mental events are token identical (...) to physical events: A particular mental event m is identical with a particular physical event p only if there is a sortal S such that m and p are both Ss. If there is no such sortal, the doctrine of token-identity is not true. I argue here that we have no good reason for thinking that there is any such sortal. (shrink)
In the past few years, deflationary positions in the debate on the nature of composite material objects have become prominent. According to Ted Sider these include the thesis of quantifier variance, against which he has defended ontological realism. Recently, Sider has considered the possibility of rejecting his arguments against the vagueness of the unrestricted quantifiers in terms of translation functions. Against this strategy, he has presented an intuitive complaint and has argued that it can only be resisted if quantifier variance (...) is accepted. But this is false. In this paper I argue, against Sider, that there is a coherent way to combine the rejection of quantifier variance with the vagueness of the unrestricted quantifiers. I sketch a model to show this, and then I consider, on the basis of it, several versions of the indeterminacy argument against the vagueness of the unrestricted quantifiers that Sider has formulated over the years. (shrink)
The paper discusses sortal essentialism': the view that some sortal concepts represent essential properties of the things that fall under them. Although sortal essentialism is widely accepted, there is a dearth of theories purporting to explain why some sortals should have this characteristic. The paper examines two theories that do attempt this explanatory task, theories proposed by Baruch Brody and David Wiggins. It is argued that Brody's theory rests on an untenable principle about "de re" modality, while Wiggins' theory (...) appeals to a thesis about principles of individuation that is either unjustified, or vacuous and incapable of supporting sortal essentialism. (shrink)
Spatiotemporal and qualitative continuity are not sufficient to trace the career or path of one and the same object through its history. One needs sortal continuity, guaranteed by the form-token of the object. In this paper I concentrate on the question of sortal continuity linked to the problem of the cohabitation of objects. I intend to test whether it is possible to stick to the belief in continuants or endurers as well as the sortal dependence of identity and at the (...) same time avoid an undesirable multiplication of spatially coinciding objects, i.e., avoid the thesis of cohabitation. I abandon the philosophical view – this is the price to be paid – that the set of the material constituents making up an object is an object proper. The basic units of reality are the objects falling under sortals and not the ultimate components thereof. That a determinate piece of copper is not identical with the statue made from it, therefore, does not imply that we have a cohabitation of two numerically different objects. (shrink)
An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system (...) is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system. (shrink)
This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment (...) is part of. This framework allows us to define the familiar Ockhamist temporal/modal connectives, most notably for past, future, and settledness. The novelty of our framework becomes visible in our discussion of substances in branching histories, i.e., in its first-order part. That discussion shows how the basic idea of tracing an individual thing from case to case via an absolute property is applicable in a branching histories framework. We stress the importance of keeping apart extensionality and moment-definiteness, and give a formal account of how the specification of natural sortals and natural qualities turns out to be a coordination task in BH-CIFOL. We also provide a detailed answer to Lewis’s well-known argument against branching histories, exposing the fallacy in that argument. (shrink)
: ‘Sortalism about demonstrative reference’ is the view that the capacity to refer to things demonstratively rests on the capacity to classify them according to their kinds. This paper argues for one form of sortalism. Section 1 distinguishes two sortalist views. Section 2 argues that one of them is false. Section 3 argues that the other is true. Section 4 uses the argument from Section 3 to develop a new response to the objection to sortalism from examples where we seem (...) to succeed in referring even though we get sortal classification wrong, or do not attempt to classify at all. (shrink)
Recent work in natural language semantics leads to some new observations on generalized quantifiers. In § 1 we show that English quantifiers of type $ $ are booleanly generated by their generalized universal and generalized existential members. These two classes also constitute the sortally reducible members of this type. Section 2 presents our main result--the Generalized Prefix Theorem (GPT). This theorem characterizes the conditions under which formulas of the form Q1x 1⋯ Qnx nRx 1⋯ xn and q1x 1⋯ qnx nRx (...) 1⋯ xn are logically equivalent for arbitrary generalized quantifiers Qi, qi. GPT generalizes, perhaps in an unexpectedly strong form, the Linear Prefix Theorem (appropriately modified) of Keisler & Walkoe (1973). (shrink)
Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of counting, to them is (...) associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described. (shrink)
Within Linguistics the semantic analysis of natural languages (English, Swahili, for example) has drawn extensively on semantical concepts first formulated and studied within classical logic, principally first order logic. Nowhere has this contribution been more substantive than in the domain of quantification and variable binding. As studies of these notions in natural language have developed they have taken on a life of their own, resulting in refinements and generalizations of the classical quantifiers as well as the discovery of new types (...) of quantification which exceed the expressive capacity of the classical quantifiers. We refer the reader to Keenan and Westerståhl (1997) for an overview of results in this area. Here, we focus on one property of quantification in natural language?its inherently sortal nature?which distinguishes it from quantification in classical logic. (shrink)
Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of 'sortal' as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates 'quantum-sortal predicates' and, instead of a process of counting, to them is (...) associated a 'criterion of cardinality'. After their general characterization, it is discussed how these predicates can be formally described. (shrink)
A lot of people believe that distinct objectscan occupy precisely the same place for theentire time during which they exist. Suchpeople have to provide an answer to the`grounding problem' – they have to explain howsuch things, alike in so many ways, nonethelessmanage to fall under different sortals, or havedifferent modal properties. I argue in detailthat they cannot say that there is anything invirtue of which spatio-temporally coincidentthings have those properties. However, I alsoargue that this may not be as bad (...) as it looks,and that there is a way to make sense of theclaim that such properties are primitive. (shrink)
I examine John Campbell’s claim that the determination of the reference of a perceptual demonstrative requires conscious visual object-based selective attention. I argue that although Campbell’s claim to the effect that, first, a complex binding parameter is needed to establish the referent of a perceptual demonstrative, and, second, that this referent is determined independently of, and before, the application of sortals is correct, this binding parameter does not require object-based attention for its construction. If object-based attention were indeed required (...) then the determination of the referent would necessarily involve the application of sortal concepts, since object-based attention initiates top-down cognitive effects on visual processing. I also examine Mohan Matthen’s claim that reference to objects is established only through the visual processing in the dorsal visual stream and argue that although it is true that processing in the dorsal stream can determine reference, a thesis that goes against Campbell’s view that the determination of the referent requires conscious attention, processing along the ventral visual stream can also establish the reference of perceptual demonstratives. It also claim that Matthen’s account of dorsal processing underestimates the kind of information processed along the dorsal stream and this has some implications regarding perceptual demonstratives reference fixing. (shrink)
I am now typing on a computer I bought two years ago. The computer I bought is identical to the computer on which I type. My computer persists over time. Let us divide our subject matter in two. There is first the question of criteria of identity, the conditions governing when an object of a certain kind, a computer for instance, persists until some later time. There are secondly very general questions about the nature of persistence itself. Here I include (...) the question of temporal parts, as well as certain familiar paradoxes (e.g., the statue and the lump). Following John Perry (1975, Introduction), let us characterize a criterion of identity over time for F s as a way of filling in φ in the following schema: Stages S1 and S2 belong to some continuing F iff φ Defenders of temporal parts (see below) regard S1 and S2 as being temporal parts of the continuing F ; others regard S1 and S2 as different stages in the life history of the continuing F . Thus each camp can make use of Perry’s formula. It is traditional to divide such criteria into those governing persons and those governing anything else. It is further traditional to say that the criterion of identity over time for non-persons involves spatiotemporal continuity. An excellent discussion is Eli Hirsch’s The Concept of Identity1, which utilizes the notion of continuity under a sortal. Kind-terms, or sortals, are terms that specify what kind of or sort of thing an object is. Examples include ‘tree’, ‘car’, and ‘mountain’. Where F is a sortal, Hirsch’s analysis is roughly that stages belong to the same F iff they are connected by a spatiotemporally and qualitatively continuous sequence of F -stages. Unmodified, this analysis prohibits temporally discontinuous entities, such as a watch that is taken apart and then reassembled. Hirsch discusses the necessary modifications. Spatiotemporal continuity analyses face a problem when applied to the persistence of matter. The literature here has been dominated by discussion of examples provided by David Armstrong (1980) and Saul Kripke (unpublished.... (shrink)
John Campbell argues that visual attention to objects is the means by which we can refer to objects, and that this is so because conscious visual attention enables us to retrieve information about a location. It is argued here that while Campbell is right to think that we visually attend to objects, he does not give us sufficient ground for thinking that consciousness is involved, and is wrong to assign an intermediary role to location. Campbell’s view on sortals is (...) also queried, as is his espousal of the so-called Referential View of Experience. (shrink)
This paper is an informal presentation of the ideas presented formally in (”Relative-Sameness Counterpart Theory”. Relative-sameness relations -- such as being the same person as -- are like David Lewis’s “counterpart” relations in the following respects: (i) they may hold over time or across worlds between objects that aren’t cross-time or cross-world identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different contexts. They differ from his counterpart relations, however, (...) in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis’s Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). The use of sameness as opposed to similarity relations in the analysis of de-re temporal and modal predication renders the resulting truth conditions as statable in terms that proponents of Kripke’s identity-based analysis can accept. (shrink)
I defend a version of color subjectivism — that colors are sortals for certain neural events — by arguing against a sophisticated form of color objectivism and by showing how a subjectivist can legitimately explain the phenomenal fact that colors seem to be properties of external objects.
The paper defends a combination of perdurantism with mereological universalism by developing semantics of temporary predications of the sort ’some P is/was/will be (a) Q’. We argue that, in addition to the usual application of causal and other restrictions on sortals, the grammatical form of such statements allows for rather different regimentations along three separate dimensions, according to: (a) whether ‘P’ and ‘Q’ are being used as phase or substance sortal terms, (b) whether ‘is’, ‘was’, and ‘will be’ (...) are the ‘is’, ‘was’, ‘will be’ of identity or of constitution, and (c) whether ‘Q’ is being used as a subject or predicate term. We conclude that this latitude is beneficial, as it conforms with linguistic reality (i.e., the multiple uses actually in place) and also enables one to turn what is ordinarily perceived as a problem for universalist perdurantism viz., a commitment to all sorts of weird and gerrymandered temporally extended entities, into an advantage, for the richness in questions allows us to make sense of the many different readings of sentences of the same grammatical form. (shrink)
Coincidence (e.g., of a statue and the piece of bronze which constitutes it) comes in two varieties – permanent and temporary. Moderate monism (about coincidence) is the position that permanent coincidence, but not temporary coincidence, entails identity. Extreme monism (also known as the stage theory) is the position that even temporary coincidence entails identity. Pluralists are opponents of monism tout court. The intuitively obvious, commonsensical position (= my own position) is moderate monism. It is therefore important to see if it (...) can be sustained. (shrink)
The whole-part relationship is generally considered transitive, but there are some apparent exceptions. Componential sortals create some apparent problems. Homo sapiens, the Pope, and his heart are all individuals. A human being, such as the Pope, is an organism-level component of Homo sapiens. The Pope’s heart is an organ-level component of both Homo sapiens and the Pope. Although the Pope is a part, and not an instance, of the Roman Catholic Church, it seems odd to say that his heart (...) is a part of that church. This is largely because the Pope’s heart does not have a place in the ecclesiastical government. However, it does contribute to the functioning of the organization. One popular alternative to the view that Homo sapiens is an individual is the notion that it is a natural kind. This has been done by redefining ‘natural kind’ in such a manner that not just the Roman Catholic Church, but the Pope and every other human being is a natural kind as well. (shrink)
Jointly, separately, and in collaboration with others, Steven French and Décio Krause have been central to recent debates about identity and individuality in modern physics; their new book draws together many threads, and is interesting in all sorts of ways. It’s not an easy read, because it ranges wide and digs deep: you’ll need some knowledge of physics to get anywhere, you’ll need an idea of Who Was Who amongst the Great Physicists to follow the historical sections, and you’ll need (...) plenty of formal know-how to get the most out of the chapters on set theory and logic. But even if you’re not fully-equipped for all this, it is well worth persisting conscientiously, skimming, or cherry-picking, according to your temperament. The book contains valuable insights into the philosophy of quantum physics; the metaphysics of spacetime; the metaphysics, epistemology and semantics of identity, indiscernibility and naming; the logic of indeterminacy; and the nature of sortals. There are thought-provoking methodological asides about the relationships between science and philosophy, between formal theory and interpretation, and between set theory and contingent facts. Moreover, the historical sections show the Great Physicists grappling with these substantive philosophical issues. (Tip: if you’re only going to read one chapter, make it chapter 4, where the philosophical juice is especially concentrated.). (shrink)