Sortal concepts are at the center of certain logical discussions and have played a significant role in solutions to particular problems in philosophy. Apart from logic and philosophy, the study of sortal concepts has found its place in specific fields of psychology, such as the theory of infant cognitive development and the theory of human perception. In this monograph, different formal logics for sortal concepts and sortal-related logical notions are characterized. Most of these logics are intensional in nature and possess, (...) in addition, a bidimensional character. That is, they simultaneously represent two different logical dimensions. In most cases, the dimensions are those of time and natural necessity, and, in other cases, those of time and epistemic necessity. Another feature of the logics in question concerns second-order quantification over sortal concepts, a logical notion that is also represented in the logics. Some of the logics adopt a constant domain interpretation, others a varying domain interpretation of such quantification. Two of the above bidimensional logics are philosophically grounded on predication sortalism, that is, on the philosophical view that predication necessarily requires sortal concepts. Another bidimensional logic constitutes a logic for complex sortal predicates. These three sorts of logics are among the important novelties of this work since logics with similar features have not been developed up to now, and they might be instrumental for the solution of philosophically significant problems regarding sortal predicates. The book assumes a modern variant of conceptualism as a philosophical background. For this reason, the approach to sortal predicates is in terms of sortal concepts. Concepts, in general, are here understood as intersubjective realizable cognitive capacities. The proper features of sortal concepts are determined by an analysis of the main features of sortal predicates. Posterior to this analysis, the sortal-related logical notions represented in the above logics are discussed. There is also a discussion on the extent to which the set-theoretic formal semantic systems of the book capture different aspects of the conceptualist approach to sortals. These different semantic frameworks are also related to realist and nominalist approaches to sortal predicates, and possible modifications to them are considered that might represent those alternative approaches. (shrink)

This paper investigates a limitation of the model of belief and knowledge prevailing in mainstream economics, namely the state-space model. Because of its set-theoretic nature, this model has difficulties in capturing the difference between expressions that designate the same object but have different meanings, i.e., expressions with the same extension but different intensions. This limitation generates puzzling results concerning what individuals believe or know about the world as well as what individuals believe or know about what other individuals believe or (...) know about the world. The paper connects these puzzling results to two issues that are relevant for economic theory beyond the state-space model, namely, framing effects and the distinction between the model-maker and agents that appear in the model. Finally, the paper discusses three possible solutions to the limitations of the state-space model, and concludes that the two alternatives that appear practicable also have significant drawbacks. (shrink)

The author defends the view that the notion of concept, if used in the logical tradition, should be explicated procedurally . He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts.

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates (...) and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (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)

This is part I of a two-part essay introducing case-intensional first order logic, an easy-to-use, uniform, powerful, and useful combination of first-order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus. CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions are context-independent terms, and lambda-predicates (...) and -operators can be introduced without constraints. These logical resources allow one to define, within CIFOL, important properties of properties, viz., extensionality and absoluteness, Bressan’s chief innovation that allows tracing an individual across cases without recourse to any notion of “rigid designation” or “trans-world identity.” Thereby CIFOL abstains from incorporating any metaphysical principles into the quantificational machinery, unlike extant frameworks of quantified modal logic. We claim that this neutrality makes CIFOL a useful tool for discussing both metaphysical and scientific arguments involving modality and quantification, and we illustrate by discussing in diagrammatic detail a number of such arguments involving the extensional identification of individuals via absolute properties, essential properties, de re vs. de dicto, and the results of possible tests. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

The aim of this chapter is to explore to some extent the relationship between identity and necessity in logic and metaphysics. First, I provide a historically-based summary of proofs of the necessity of identity, highlighting the importance of the role that self-identity plays. Second, I introduce two examples of metaphysical topics where the necessity of identity has played a pivotal role: the necessary a posteriori, and the coincidence of material objects. I argue that important aspects of these debates rest on (...) how we represent identity. Third, I consider some recent work on generalized identity. This opens up new prospects for explaining why identity is necessary. (shrink)

In chapter one I firstly critique some contemporary family-resemblance approaches to the category woman, and claim that they do not take sufficient account of dis-semblance, that is, resemblances that people have in common with members of the contrast category man. Second, I analyze how the concept of woman is semantically contestable: resemblance/dissemblance structures give rise to vagueness and to borderline cases. Borderline cases can either be included in the category or excluded from it. The factors which incline parties in a (...) dispute about membership to include or exclude depend on metaphysical, ethical, or political background assumptions. In chapter two, I begin by considering the harms suffered by transgender persons through “misgendering”, the deployment of gender terms which inflict psychological harms upon transgender persons, place them in situations of injustice, or diminish their self-respect. Such deployments are morally contestable: they can be challenged on ethical grounds. Several characterisations of the term ‘woman’ proposed in the feminist literature are critiqued from this perspective. In chapter three, I elaborate a broadly liberal approach to gender pluralism. The approach involves: i) the public toleration of gender practices and beliefs which contest prevalent gender norms; and ii) state-gender neutrality. Public toleration allows gender non-conforming practices and beliefs within public space. State gender-neutrality consists mainly in the removal from law and government policy of provisions which assume compliance with prevalent conceptions of gender. (shrink)

In this article, I consider the harms inflicted upon transgender persons through “misgendering,” that is, such deployments of gender terms that diminish transgender persons’ selfrespect, limit the discursive resources at their disposal to define their own gender, and cause them microaggressive psychological harms. Such deployments are morally contestable, that is, they can be challenged on ethical or political grounds. Two characterizations of “woman” proposed in the feminist literature are critiqued from this perspective. When we consider what would happen to transgender (...) women upon the broad implementation of these characterizations within transgender women’s social context, we discover that they suffer from two defects: they either exclude at least some transgender women, or else they implicitly foster hierarchies among women, marginalizing transgender women in particular. In conclusion, I claim that the moral contestability of gender-term deployments acts as a stimulus to regularly consider the provisionality and revisability of our deployments of the term “woman.”. (shrink)

Tarski's analysis of the concept of truth gives rise to a hierarchy of languages. Does this fragment the concept all the way to philosophical unacceptability? I argue it doesn't, drawing on a modification of Kaplan's theory of indexicals.

The two main features of this thesis are (i) an account of contextualized (context indexed) counterfactuals, and (ii) a non-vacuist account of counterpossibles. Experience tells us that the truth of the counterfactual is contingent on what is meant by the antecedent, which in turn rests on what context is assumed to underlie its reading (intended meaning). On most conditional analyses, only the world of evaluation and the antecedent determine which worlds are relevant to determining the truth of a conditional, and (...) consequently what its truth value is. But that results in the underlying context being fixed, when evaluating distinct counterfactuals with the same antecedent on any single occasion, even when the context underlying the evaluation of each counterfactual may vary. Alternative approaches go some of the way toward resolving this inadequacy by appealing to a difference in the consequents associated with counterfactuals with the same antecedent. That is, in addition to the world of evaluation and the antecedent, the consequent contributes to the counterfactual’s evaluation. But these alternative approaches nevertheless give a single, determinate truth value to any single conditional (same antecedent and consequent), despite the possibility that this value may vary with context. My reply to these shortcomings (chapter 4) takes the form of an analysis of a language that makes appropriate explicit access to the intended context available. That is, I give an account of a contextualized counterfactual of the form ‘In context C: If it were the case that … , then it would be the case that …’. Although my proposal is largely based on Lewis’ (1973, 1981) analyses of counterfactuals (the logic VW and its ordering semantics), it does not require that any particular logic of counterfactuals should serve as its basis – rather, it is a general prescription for contextualizing a conditional language. The advantage of working with ordering semantics stems from existing results (which I apply and develop) concerning the properties of ordering frames that facilitate fashioning and implementing a notion of contextual information preservation. Analyses of counterfactuals, such as Lewis’ (1973), that cash out the truth of counterfactuals in terms of the corresponding material conditional’s truth at possible worlds result in all counterpossibles being evaluated as vacuously true. This is because antecedents of counterpossibles are not true at any possible world, by definition. Such vacuist analyses have already been identified and challenged by a number of authors. I join this critical front, and drawing on existing proposals, I develop an impossible world semantics for a non-vacuist account of counterpossibles (chapter 5), by modifying the same system and semantics that serve the basis of the contextualized account offered in chapter 4, i.e. Lewis’ (1986) ordering semantics for the logic VW. I critically evaluate the advantages and disadvantages of key conditions on the ordering of worlds on the extended domain and show that there is a sense in which all of Lewis’ analysis of mere counterfactuals can be preserved, whilst offering an analysis of counterpossibles that meets our intuitions. The first part of chapter 1 consists of an outline of the usefulness of impossible worlds across philosophical analyses and logic. That outline in conjunction with a critical evaluation of Lewis’ logical arguments in favour of vacuism in chapter 2, and his marvellous mountain argument against impossible worlds in chapter 3, serves to motivate and justify the impossible world semantics for counterpossibles proposed in chapter 5. The second part of chapter 1 discusses the limitations that various conditional logics face when tasked to give an adequate treatment of the influence of context. That introductory discussion in conjunction with an overview of conditional logics and their various semantics in chapter 2 – which includes an in-depth exposition of Stalnaker-Lewis similarity semantics for counterfactuals – serves as the motivation and conceptual basis for the contextualized account of counterfactuals proposed in chapter 4. (shrink)

The study of reference often leads to addressing fundamental issues in semantics, metaphysics and epistemology; this suggests that reference is closely linked to the three realms. The overall purpose of this study is to elucidate the structure of some of these links, through a close examination of the “mechanism” of reference. As in many other enquiries, considering the possible (i.e., the modal,) in addition to the actual proves very helpful in clarifying and explicating insights. The reference of a term with (...) respect to possible worlds is commonly called “intension”; so this is a study of intensions. The main contribution of the study is an outline for a “calculator” of intensions. It is argued that the intension of a term is a function of three variables: (a) the way in which the term “picks out” its referent in different possible worlds (semantics); (b) criteria of identity (metaphysics); and (c) the actual state of affairs (actuality). While considering different possible values for these variables, it is demonstrated how the variables combine to generate the term’s intension. In other words, the result is a calculator that when provided with the required values, yields the reference of the term in different possible worlds. By taking into account the possible gap between what we take the values of these variables to be and what they may in fact be, we also gain important insights into the epistemic aspect of reference. In addition, since a rigid designator is a term with constant intension, the proposed thesis provides an elaborate account of rigidity. The first chapter is devoted to the development of the calculator of intensions. Each of the following three chapters elaborates on one aspect of intensions, namely, the semantic, metaphysical and epistemic aspects. In the course of these chapters, various familiar puzzles pertaining to the respective philosophical realms are addressed (many of these puzzles are discussed in Kripke’s Naming and Necessity – a work that considerably inspired this study). In the fifth and last chapter the analysis of intensions is applied to two case-studies from relatively recent philosophical literature: the Kripke-Lewis debate over the identity theory of mind, and the debate over the significance of Donnellan’s referential/attributive distinction. The novel accounts that these applications generate purport to illustrate the importance and originality of the proposed thesis. (shrink)

Is identity fundamental to every conceptual systems? In this article I intend to present reasons against the claim that every conceptual system presupposes the notion of identity. To address this debate I analyze the positions of Bueno (2014; 2016) and Krause and Arenhart (2015). While Bueno argues that identity is necessary for all conceptual systems, Krause and Arenhart present a series of objections against such position, thus defending that identity is not fundamental. I intend to show that the main objections (...) presented by Krause and Arenhart do not affect Bueno’s theory because of a misinterpretation of his arguments. Finally, I will present some objections against Bueno that, hopefully, does not miss the target. (shrink)