Extensional articulations of physicalism define what it means to be physical relative to the properties of a set of entities, such that physicalism is true if the fundamental properties which compose the entities in this set are the same sorts of fundamental properties which compose everything that exists. Here I present a novel problem for these articulations of physicalism: they are consistent with phenomenal idealism, which is the view that only phenomenal properties exist. Under this view, paradigm physical objects (...) such as tables and chairs are constructed out of more basic phenomenal properties. Since this view says that everything—including paradigm physical entities—is ultimately constituted by phenomenal properties, it follows that this view is consistent with extensional definitions of physicalism, since such definitions only require that there be no fundamental difference between paradigm physical entities and everything else. Yet a good definition of physicalism should not be consistent with phenomenal idealism. (shrink)

Extensionalist theories of the specious present suggest that every perceptual experience is extended in time for a short while, such that they are co-extensive in time with the time experienced in them. Thus, there can be no experience of time, unless the experience itself is extended in time. Accordingly, there must be something that unites the temporal parts of a perceptual experience into temporally extended wholes. I call this the “glue-problem for extensionalism”. In this paper I suggest three desiderata (...) that an extensionalist theory should meet in order to solve the glue-problem. I also distinguish between different versions of extensionalism, and argue that none of them can solve the glue-problem without violating at least one desideratum. (shrink)

In the present paper, I examine how Michael Devitt's proposal as to how to understand the notion of rigidity for general terms fares as regards what I have called the 'criterion of extensional adequacy' for any such notion -namely, the condition according to which any notion of general term rigidity should make the class of rigid terms coincide with that of natural kind terms. I try to show that Devitt's defense of his view from the usual objections raised in the (...) literature fails. In the first place, the proposal seems to overgeneralize, as terms such as 'television set' or 'table', would also be rigid appliers; as I try to show here, the arguments presented by Devitt in order to show that that is not the case are based on some alleged properties of those terms that are also true of some of the expressions he does consider as rigid. In the second place, the proposal also undergeneralizes; even though Devitt himself accepts that this is so, I try to show that his strategy to lessen the disappointment this causes also fails. En este trabajo examino el desempeño de la propuesta acerca de cómo entender la noción de rigidez para términos generales defendida por Michael Devitt respecto de lo que denomino el 'criterio de adecuación extensional' para una noción de rigidez -a saber, la condición según la cual una noción de rigidez para términos generales debería hacer coincidir la clase de términos rígidos con la clase de términos de género natural. Intento mostrar que las estrategias desplegadas por Devitt para defender su postura de las objeciones usuales no son exitosas. En primer lugar, la propuesta parece sobregeneralizar, dado que términos como 'televisor' o 'mesa' también serían aplicadores rígidos; en efecto, según intento defender aquí, los argumentos de Devitt tendientes a mostrar que no lo son se basan en supuestas características de estos términos que son igualmente válidas respecto de las expresiones que él considera rígidas. En segundo lugar, la propuesta también subgeneraliza; si bien Devitt acepta esto, hago notar que su estrategia para quitar dramatismo a este resultado también falla. (shrink)

Quine’s “New Foundations” (NF) was first presented in Quine [1937] and later on in Quine [1963]. Ernst Specker [1958, 1962], building upon a previous result of Ehrenfeucht and Mostowski [1956], showed that NF is consistent if and only if there is a model of the Theory of Negative (and positive) Types (TNT) with full extensionality that admits of a “shifting automorphism,” but the existence of a such a model remains an open problem.

If one takes seriously the idea that a scientific language must be extensional, and accepts Quine’s notion of truth-value-related extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ‘extensionality’, so that it would not be (...) the truth-value that had to be preserved under the substitution of co-extensional expressions, but the state of affairs that the sentence described. The question is whether or not elementary sentences containing empty singular terms, such as ‘Vulcan rotates’, are extensional in the substitutivity sense. Five conditions are specified under which extensionality in the substitutivity sense of such sentences can be secured. It is demonstrated that such sentences are state-of-affairs-as-extension-related extensional. This implies that such sentences are also truth-value-related extensional in Quine’s sense, but not truth-value-as-extension-related extensional. (shrink)

The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set (...) theory, leads to triviality. (shrink)

It has been argued that prototypes cannot compose, and that for this reason concepts cannot be prototypes (Osherson and Smith in Cognition 9:35–58, 1981; Fodor and Lepore in Cognition 58:253–270, 1996; Connolly et al. in Cognition 103:1–22, 2007). In this paper I examine the intensional and extensional approaches to prototype compositionality, arguing that neither succeeds in their present formulations. I then propose a hybrid extensional theory of prototype compositionality, according to which the extension of a complex concept is determined as (...) a function of what triggers its constituent prototypes. I argue that the theory escapes the problems traditionally raised against extensional theories of compositionality. (shrink)

The problems that Millikan addresses in theories of concepts arise from an extensional view of concepts and word meaning. If instead one assumes that concepts are psychological entities intended to explain human behavior and thought, many of these problems dissolve.

We shall try to defend two non-standard views that run counter to two well-entrenched familiar views. The standard views are the universal and existential quantifiers of first-order logic are not modal operators, and the quantifiers are extensional. If that is correct then the counterclaims create genuine problems for some traditional philosophical doctrines.

A number of Christian theologians and philosophers have been critical of overly moralizing approaches to the doctrine of sin, but nearly all Christian thinkers maintain that moral fault is necessary or sufficient for sin to obtain. Call this the “Moral Consensus.” I begin by clarifying the relevance of impurities to the biblical cataloguing of sins. I then present four extensional problems for the Moral Consensus on sin, based on the biblical catalogue of sins: (1) moral over-demandingness, (2) agential unfairness, (3) (...) moral repugnance, and (4) moral atrocity. Next, I survey several partial solutions to these problems, suggested by the recent philosophical literature. Then I evaluate two largely unexplored solutions: (a) genuine sin dilemmas and (b) defeasible sinfulness. I argue that (a) creates more problems than it solves and that, while (b) is well-motivated and solves or eases each of the above problems, (b) leaves many biblical ordinances about sin morally misleading, creating (5) a pedagogical problem of evil. I conclude by arguing that (5) places hefty explanatory burdens on those who would appeal to (b) to resolve the four extensional problems discussed in this paper. So Christian thinkers may need to consider a more radical separation of sin and moral fault. (shrink)

We state the consistency problem of extensional partial set theory and prove two complementary results toward a definitive solution. The proof of one of our results makes use of an extension of the topological construction that was originally applied in the paraconsistent case.

The original interest of this article lies in existential import. It provides a broader view on the problem by reference to modern, symbolic logic (ch.1). Gradually, however, our interest will change into the amalgamated expressions often used in logic; that is, why are such expressions as “x is a round triangle” applied in logic? We critically discuss this question from an extensional viewpoint, namely model theoretic semantics (ch.2). We also touch on Church’s λ-calculus in the appendix (app.2).

In a recent paper, Michael Levin argues that both statements reporting causal relations and causal explanatory statements are extensional. We show that his argument for the extensionality of causal explanatory statements fails to establish that conclusion. His claim that certain 'because' statements are elliptical for statements of what he terms the 'causal explanatory' form is unsubstantiated. The argument for the referential transparency of the allegedly explanatory form, regardless of whether it is a distinct explanatory form, fails because of scope (...) problems. Finally, we argue that the apparent referential opacity of explanations, the attribution of certain kinds of properties to explanations, and our satisfaction with explanations in what appear to be disparate forms are best accounted for, not by the assumption of ellipticality of statements in various forms for statements in some inherently explanatory form, but rather by an account of explanation as a speech act, the success or failure of which may be affected by which of several co-referring expressions is employed. (shrink)

This paper argues that ordinary object languages for fundamental physics are incomplete, essentially because they are extensional, and consequently lack any adequate formal representation of contingency. It is shown that it is impossible to formulate adequate deduction systems for general transformations in such languages. This is argued in detail for the time reversal transformation. Two important controversies about the application of time reversal in quantum mechanics are summarized at the start, to provide the context of this problem, and show (...) its serious implications, but the aim here is not to solve these problems. The flaw is not special to quantum mechanics: it is a general feature traced to extensionality, and demonstrated through a simple example in classical physics. It is proposed that this defect can be overcome by extending to an intensional semantics, but this involves extending the usual formalism of physics. A detailed proposal for such an extension is given in Part 2. (shrink)

Two straightforward “extensionalisations” of Kleene's realizability are considered; denoted re and e. It is shown that these realizabilities are not equivalent. While the re-notion is a subset of Kleene's realizability, the e-notion is not. The problem of an axiomatization of e-realizability is attacked and one arrives at an axiomatization over a conservative extension of arithmetic, in a language with variables for finite sets. A derived rule for arithmetic is obtained by the use of a q-variant of e-realizability; this rule (...) subsumes the well-known Extended Church's Rule. The second part of the paper focuses on toposes for these realizabilities. By a relaxation of the notion of partial combinatory algebra, a new class of realizability toposes emerges. Relationships between the various realizability toposes are given, and results analogous to Robinson and Rosolini's characterization of the effective topos, are obtained for a topos generalizing e-realizability. (shrink)

Many believe that, if true, reason-statements of the form ‘that X is F is a reason to φ’ describe a ‘favouring-relation’ between the fact that X is F and the act of φing. This favouring-relation has been assumed to share many features of other, more concrete relations. This combination of views leads to immediate problems. Firstly, unlike statements about many other relations, reason-statements can be true even when the relata do not exist, i.e., when the relevant facts do not obtain (...) and the relevant acts are not done. Secondly, the previous combination of views also makes it very difficult to draw the distinction between agent-relative and agent-neutral reasons. I argue that we should think that the predicate ‘is a reason to’ creates non-extensional contexts in the statements in which it is used. This would both solve the previous problems and avoid the awkward consequences of the so-called slingshot argument. (shrink)

Framing effects occur when different descriptions of the same decision problem give rise to divergent decisions. They can be seen as a violation of the decisiontheoretic version of the principle of extensionality (PE). The PE in logic means that two logically equivalent sentences can be substituted salva veritate. We explore what this notion of extensionality becomes in decision contexts. Violations of extensionality may have rational grounds. Based on some ideas proposed by the psychologist Craig McKenzie and (...) colleagues, we contend that framing effects are justified when the selection of one particular frame conveys choice relevant information. We first discuss this idea from a philosophical point of view, and proceed next to formalize it first in the context of the Bolker–Jeffrey decision theory. Finally, we extend the previous analysis to non-expected utility theories using the Biseparable Preference model introduced by Ghirardato and Marinacci (2001) and therefore show that the analysis is independent of the assumptions of Bayesian decision theory. (shrink)

My central concern is to show that attempts to resolve problems of non-extensionality in abstraction from speech act theory are unsatisfactory. Generally, I shall argue that speech act theory identifies the various units, levels, and dimensions of analysis which are relevant to the problem of non-extensionality. To ignore or underplay this results in interpretations of non-extensionality which are counter-intuitive and plagued with counter-examples. In what follows, I shall first distinguish what I take to be the essential (...) ingredients of the problem of non-extensionality and restrict the primary scope of my discussion to a certain kind of paradigm case, viz., that kind of non-extensional context generated by the use of so-called verbs of propositional attitude. Although other kinds of context must also be reckoned with, I am especially interested in the attitudinal context, because it is here, as I shall try to show, that recent interpretations exhibit a significant philosophical mistake. Then I shall isolate the kind of interpretation I want to emphasize and criticize—one which I label "soft extensionalism." Finally, I shall differentiate those aspects of speech act theory which pertain to non-extensionality and apply them to the paradigm case. This will require a clarification of the role which the locutionary act, the propositional act, and the illocutionary act respectively play in the determination of the referential status of singular terms in linguistic contexts. (shrink)

This continues from Part 1. It is shown how an intensional interpretation of physics object languages can be formalised, and how a syntactic compositional time reversal operator can subsequently be defined. This is applied to solve the problems used as examples in Part 1. A proof of a general theorem that such an operator must be defineable is sketched. A number of related issues about the interpretation of theories of physics, including classical and quantum mechanics and classical EM theory are (...) discussed. (shrink)

This paper critiques the All-Subjected Principle. The All-Subjected Principle is one of the most prominent answers to the Boundary Problem, which consists in determining who should be entitled to participate in which democratic decision. The All-Subjected Principle comes in many versions, but the general idea is that all people who are subjected in a relevant sense with regard to a democratic decision should be entitled to participate in that decision. One respect in which versions of the All-Subjected Principle differ (...) concerns how to best understand ‘subjectedness’. One view spells out ‘subjectedness’ in terms of legal bindingness. Another view understands ‘subjectedness’ in terms of coercion. I argue that the All-Subjected Principle is extensionally inadequate on both views in that it yields verdicts that are at odds with our considered judgements about certain cases. These cases involve legal norms of referral or international administrative assistance. (shrink)

This paper offers an extensional account of Aristotle’s theory of perceptual content. To do so I make use of an extensional account of Aristotle’s notion of universals and related notions. I argue that this view avoids certain problems recently posed by Caston by showing how it can accept a distinction between intrinsic and extrinsic perception. I also show how perception of individuals is related to knowledge and universals.

Neste artigo daremos principal atenção aos dois critérios de identidade de conteúdo conceitual que estão presentes nos §§ 3 e 8 da Conceitografia de Gottlob Frege. Nosso propósito é analisar as características destes critérios da notação conceitual de Frege porque pretendemos delimitar a discussão em torno dos problemas relacionados às noções de identidade intensional e extensional. Dessa forma, pretendemos: analisar os critérios de identidade de conteúdo conceitual presentes nos §§ 3 e 8 da Conceitografia com o objetivo de mostrar que (...) Frege apresentou uma caracterização híbrida da noção de conteúdo conceitual e fazer considerações a respeito de relações que podemos estabelecer entre os critérios intensionais e extensionais de Frege e Richard Kirkham presentes no livro Teorias da Verdade: Uma Introdução Crítica. Com tais comparações pretendemos averiguar: se o critério de identidade do § 8 da Conceitografia é idêntico ao critério extensional de equivalência material de Kirkham e se o critério de identidade do § 3 da Conceitografia é mais forte, mais fraco ou idêntico aos critérios intensionais de equivalência essencial e de equivalência de sinonímia de Kirkham.: In this paper we will give primary attention to two identity criteria of conceptual content that are present in §§ 3 and 8 of Gottlob Frege's Begriffsschrift. Our purpose is to analyze the characteristics of these criteria of conceptual notation of Frege because we want to delimit the discussion around problems related to the notions of intensional and extensional identity. Thus, we intend to: analyze the identity criteria of conceptual content present in §§ 3 and 8 of Begriffsschrift aiming to show that Frege introduced a hybrid characterization of the notion of conceptual content and make considerations about the relationships that we establish between intensional and extensional criteria of Frege and Richard Kirkham present in the book Theories of Truth: A Critical Introduction. With such comparisons we intend to investigate: if the identity criterion of § 8 of Begriffsschrift is identical to the extensional criterion of material equivalence in Kirkham and if the identity criterion of § 3 of Begriffsschrift is stronger, weaker or identical to intensional criteria of essential equivalence and of synonyms equivalence of Kirkham. Key words: Identity, Intensional Criterion, Extensional Criterion. (shrink)

The present century has seen renewed interest in characterizing cognition, the object of inquiry of the cognitive sciences. In this paper, I describe the problem of cognition—the absence of a positive characterization of cognition despite a felt need for one. It is widely recognized that the problem is motivated by decades of controversy among cognitive scientists over foundational questions, such as whether non-neural parts of the body or environment can realize cognitive processes, or whether plants and microbes have (...) cognitive processes. The dominant strategy for addressing the problem of cognition is to seek a dichotomous criterion that vindicates some set of controversial claims. However, I argue that the problem of cognition is also motivated by ongoing conceptual development in cognitive science, and I describe four benefits that a characterization of cognition could confer. Given these benefits, I recommend an alternative criterion of success, ecumenical extensional adequacy, on which the aim is to describe the variation in expert judgments rather than to correct this variation by taking sides in sectarian disputes. I argue that if we had an ecumenical solution to the problem of cognition, we would have achieved much of what we should want from a “mark of the cognitive”. (shrink)

In this paper we consider the problem of the existence of a λ-theory T such that:–T is recursive enumerable;–the ω-rule holds in T .We solve affirmatively this problem.Some related questions are also discussed.

In ”Formal Problems about Knowledge,” Roy Sorensen examines epistemological issues that have logical aspects. He uses Fitch's proof for unknowables and the surprise test paradox to illustrate the hopes of the modal logicians who developed epistemic logic, and he considers the epistemology of proof with the help of the knower paradox. One solution to this paradox is that knowledge is not closed under deduction. Sorensen reviews the broader history of this maneuver along with the relevant alternatives model of knowledge which (...) assumes that ”know” is an absolute term like ”flat.” Sorensen argues that the difference between epistemic absolute terms and extensional absolute terms gives rise to an asymmetry that undermines recent claims that there is a structural parallel between the supervaluational and epistemicist theories of vagueness, and he suggests that we have overestimated the ability of logical demonstration to produce knowledge. (shrink)

There are a number of different versions of Reductive Nominalism, versions distinguished by the way in which each accounts for facts about having and sharing properties. This chapter discusses three broad varieties of Reductive Nominalism: Predicate Nominalism, Class Nominalism, and Resemblance Nominalism. Class Nominalism identifies properties with classes or sets. Resemblance Nominalists come in two sub‐varieties, depending on whether they take the resemblance relation to hold between particular properties (called 'tropes') or particular things that have properties (ordinary particulars). Trope Theory (...) comes in two varieties depending on whether one plumps for universals. It should not be difficult to see that Extreme Resemblance Nominalism is faced with Class Nominalism's extensionality problems, both the problem of contingent predication and the co‐extensive property problem. Resemblance Nominalists can reply by insisting on a distinction between a priori or conceptual equivalence and metaphysical equivalence. The chapter focuses on the extensionality problems for Class Nominalism. (shrink)

How should political power and influence be allocated in democratic systems? That is, roughly, the core of the boundary problem in democratic theory. As of late, some authors have begun paying increased attention to the methodological aspects of this dispute. This paper attempts to make a twofold contribution to this ‘methodological turn’. On the one hand, it identifies and analyzes five desiderata of a successful principle of democratic inclusion. Any such principle, I argue, must be grounded in a clearly (...) identifiable set of values, must provide a clear standard of inclusion, must specify the relevant modalities of inclusion, must provide sound bridging principles, and must be extensionally adequate. In the first half of the paper, these desiderata are developed and critically scrutinized. On the other hand, I also extract three lessons from the previous discussion. First, that a unique answer to the boundary problem (i.e. one grounded in one single principle) is unlikely. Second, that a satisfactory answer to the boundary problem need not necessarily appeal, as some have argued, to distinctively democratic values. And third, that intuitions about political exclusion (i.e. those requiring or permitting the exclusion of some individuals) should be treated with special caution. (shrink)

The aim of the paper is to distinguish two common notions of the expression “to see” – objective and subjective without attributing beliefs to the observer. Thus, the main aim can be characterized as extensional explication. This gives us the ability to describe visual perception without assuming anything about higher cognitive abilities of the agent. Subsequent addition of the notion of belief enables me to characterize more visual categories present in the literature of the subject.

The division of the problems about Meaning in an extensional and an intensional theory was accused of unnecessarily duplicating the theoretical problems involved in the knowledge of Meaning. The result was either 1. an aggressive rejection of the intensional part of the problem or 2. the adoption of non-classical semantics to account for intensions. This paper suggests a reading of Frege's theory of Meaning that preserves the contribution of the intensional aspect of the question without sacrificing the benefits of (...) the classical insights. For this, however, we need to expand his theory to cases of semantic values which are not directly assertive, that is, what Micheal Dummett called ingredient value. This solution preserves the direct and intuitive insights of classical semantics, expanding it to cases where the designation of truth or falsehood does not have a unified interpretation: speculative, modal, ambiguous, relative cases or cases in which theories disputing Meaning is not straightforwardly mapped to the truth or the not-truth. The paper is a contribution to support the pragmatic interpretation of Frege's legacy by Micheal Dummett. (shrink)

Resumo: O projeto semântico de Davidson toma a forma de reducionismo que visa explicar as noções intencionais com base em noções puramente extensionais. O objetivo desse trabalho consiste na investigação do fracasso do projeto de Davidson como um argumento indireto contra sua suposição segundo a qual a chamada interpretação radical seria o fundamento do significado linguístico e do pensamento. Abstract: Davidson's semantic program is a form of semantic reductionism that aims to account for intensional notions on a purely extensional basis. (...) My aim in this paper is not to show that Davidsons fails in addressing the so-called extensionality problem. That is no novelty. Even Davidsonians recognize Davidson's failure. My main goal is to explore Davidson's failure as an indirect argument against his key assumption that the radical interpretation is the basis of sense and hence the possibility of thought. There is no priority of language over thought. This is a remnant of the so-called linguistic turn that Davidson inherited from the analytical tradition. The moral is the following: we must come back to Lockean common sense that to learn a natural language and to translate an alien tongue into our own is merely to learn a vehicle for communicating and expressing thoughts we have already had. (shrink)

:Self-ownership theorists argue that many of our most morally urgent and enforceable rights stem from the fact that we own ourselves. Critics of self-ownership argue that the claim that people own their bodies commits self-ownership theorists to several implausible conclusions because self-ownership theory relies on several vague moral predicates, and any precisification of the required predicates is seemingly too permissive or too restrictive. I argue that this line of criticism does not undermine the case for self-ownership theory because self-ownership theory (...) does not require precisification of each moral concept that it is based on and, even if it did, the theory’s alleged extensional inadequacy does not undermine its justification. (shrink)

It is argued that, in the traditional subject-predicate sentence, two interpretations of the subject term coexist, one intensional and the other extensional, which explains the superficial difference between the traditional S-P relation and the predication of predicate logic. Data from psychological studies of syllogistic reasoning support the view that the contrast between predicate and argument is carried over to the traditional S-P sentence.

For the events "e" and "f" to be identical, They must have the same subject and spatio-Temporal location, And their (participial) property-Descriptions must belong to the same "modification set" (e.G., Reddening, Reddening slowly, Reddening in july). The same criterion applies to actions, Which are here treated strictly as a proper subclass of events (john's closing the door = the door's being closed by john = the door's becoming closed). Actions related by goldman's "causal generation" are therefore distinct, But those related (...) by his other three types of act-Generation are not. This conclusion requires abandonment of the view--Questionable on other grounds--That causal contexts are thoroughly extensional. (shrink)

This article constitutes an attempt to reexamine a crucial issue of legal theory from the perspective of philosophy of language and of social ontology: by analyzing a jurisprudential case recently decided by the U.S. Supreme Court, we explain how Searle's account on rules in The Construction of Social Reality constitutes an important starting point for the clarification of the old jurisprudential debate between conventionalism and interpretivism. In a nutshell, we show that Searle's framework, while strictly conventionalist, makes it possible to (...) conceive of the distinction between the semantic content of rules and their extension, by drawing a parallel with the idea of “deep conventions” as well as with the semantic conventions in natural language. The paper thus touches on the broader problem of the relations between legal concepts and nonlegal values. (shrink)

It has often been remarked that the metatheory of strong reduction $\succ$ , the combinatory analogue of βη-reduction ${\twoheadrightarrow_{\beta\eta}}$ in λ-calculus, is rather complicated. In particular, although the confluence of $\succ$ is an easy consequence of ${\twoheadrightarrow_{\beta\eta}}$ being confluent, no direct proof of this fact is known. Curry and Hindley’s problem, dating back to 1958, asks for a self-contained proof of the confluence of $\succ$ , one which makes no detour through λ-calculus. We answer positively to this question, by (...) extending and exploiting the technique of transitivity elimination for ‘analytic’ combinatory proof systems, which has been introduced in previous papers of ours. Indeed, a very short proof of the confluence of $\succ$ immediately follows from the main result of the present paper, namely that a certain analytic proof system G e [ $\mathbb {C}$ ] , which is equivalent to the standard proof system CL ext of Combinatory Logic with extensionality, admits effective transitivity elimination. In turn, the proof of transitivity elimination—which, by the way, we are able to provide not only for G e [ $\mathbb {C}$ ] but also, in full generality, for arbitrary analytic combinatory systems with extensionality—employs purely proof-theoretical techniques, and is entirely contained within the theory of combinators. (shrink)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the standard (...) meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

This dissertation argues for a metaethical theory I call "Expressive-Assertivism." Expressive-Assertivism is a distinctive, substantial refinement of dual-use metaethical theories traditionally associated with R. M. Hare, C. L. Stevenson, and, more recently, with David Copp. If true, Expressive-Assertivism clarifies, resolves, or dissolves---without, in turn, raising additional difficulties---a number of philosophical problems, including what Michael Smith calls "The Moral Problem," which many consider to be the central organizing problem in contemporary metaethics. The following are the three most important features (...) of Expressive-Assertivism. ;1. The central tenet. The proper, literal use of an ethical sentence, such as 'Donating to charity is right', is the performance of a direct expressive illocutionary act and a direct assertive illocutionary act. Recognizing that ethical sentences can be used to both directly express a speaker's attitude and directly assert something about the world captures what is intuitively compelling about "expressivist" theories---namely, that there is some strong connection between a speaker's sincere moral utterance and his or her motivations to act---and what is intuitively compelling about "descriptivist" theories---namely, that moral utterances appear to have descriptive or cognitive content and, therefore, are truth-evaluable. The Central Tenet is the feature of Expressive-Assertivism that dissolves The Moral Problem. ;2. The generality principle. The proper, literal use of an ethical sentence directly expresses an attitude, not toward the subject of the sentence, but toward things of a more general kind, namely, things that have the property picked out by the ethical predicate . ;3. The extensionality principle. A speaker directly expresses an attitude toward things that have the property picked out by an ethical predicate whenever that predicate appears in any extensional context. Together, the Extensionality and Generality Principles shield Expressive-Assertivism from many objections to traditional expressivist theories, including "The Embedding Objection," which many consider to be the most difficult problem faced by expressivists. (shrink)

In this essay I offer a theory of the outward directedness of intentional states, namely, an account of what makes intentional states directed at their respective intentional objects. The theory is meant to be complementary to the canonical interactivist account of mental content in that the latter emphasizes the predicative, intensional, and internal aspects of representation whereas here I shall focus on its denotative, extensional, and external aspects. Thus, the aim is to establish that the two projects are not only (...) consistent but mutually supportive. Further, it is hoped that supplementing the interactivist conception of representation with a theory of intentional directedness along such lines will increase its overall appeal to critical readers. Based on the core idea that the directedness of a representation is a function of the manner in which it is constructed within, and contributes to the ongoing unfolding of a dynamical interactive loop connecting information to focused action, the theory is subsequently extended to cover many problem domains familiarly associated with representation and reference. (shrink)

The person-affecting restriction, in its slogan form, states that an outcome can be better than another only if it is better for someone. It has a strong intuitive appeal and several theorists have suggested that it avoids certain counterintuitive implications in population ethics. At the same time, the restriction has highly counterintuitive implications and yields non-transitive orderings in some nonidentity cases. Many theorists have taken this criticism to be decisive. Recently, however, there have been some reformulations of the restriction, suggesting (...) that the restriction survives this “old” criticism. This paper investigates the viability of those reformulations, which are versions of “Comparativism,” and argues that most of them either have counterintuitive implications or are extensionally equivalent with impersonal theories, but that “Soft Comparativism” seems to have an advantage over impersonal theories. (shrink)

Carnap in the 1930s discovered that there were non-normal interpretations of classical logic - ones for which negation and conjunction are not truth-functional so that a statement and its negation could have the same truth value, and a disjunction of two false sentences could be true. Church ar-gued that this did not call for a revision of classical logic. More recent writers seem to disa-gree. We provide a definition of "non-normal interpretation" and argue that Church was right, and in fact, (...) the existence of non-normal interpretations tells us something important about the condi-tions of extensionality of the classical logical operators. (shrink)

This paper critically discusses two points concerning some recent views about the concept of truth. Firstly, contrary to Davidson, it shows that meaning of sentences cannot be explicated by T-equivalences. In particular, “is true” is an extensional predicate, but “means that” an intensional one. Secondly, the minimalist account of truth does not provide a satisfactory analysis of the concept of falsity. In this respect, minimalism does not satisfy Russell’s claim that any adequate truth-theory must be a theory of falsity as (...) well. (shrink)

According to epistemic utility theory, epistemic rationality is teleological: epistemic norms are instrumental norms that have the aim of acquiring accuracy. What’s definitive of these norms is that they can be expected to lead to the acquisition of accuracy when followed. While there’s much to be said in favor of this approach, it turns out that it faces a couple of worrisome extensional problems involving the future. The first problem involves credences about the future, and the second problem (...) involves future credences. Examining prominent solutions to a different extensional problem for this approach reinforces the severity of the two problems involving the future. Reflecting on these problems reveals the source: the teleological assumption that epistemic rationality aims at acquiring accuracy. (shrink)

In his tripartite theory of corporate responsibility, Kenneth Goodpaster argues for the inclusion of “Comprehensive Moral Thinking (CMT)” as the third part alongside shareholder and stakeholder thinking. CMT requires managers sometimes to act for reasons of dignity or a just community, against what shareholder and stakeholder thinking recommend. To address concerns about the demandingness of CMT, Goodpaster argues that the responsibilities it imposes are significant but qualified or conditional: they require only that managers make efforts to address problems of dignity (...) and justice, especially in cooperation with other willing firms. If extreme efforts are required or if other firms are unwilling to cooperate, managers can be justified in deciding in favor of shareholder or stakeholder values, even when dignity or justice is at stake. I raise two problems for the appeal to qualified responsibility—an extensional problem about the inability of the account to yield the correct judgment in important cases and an internal problem about the coherence of the account when qualified responsibility is included. I conclude by considering the prospects of a theory that includes CMT but rejects qualified responsibility. (shrink)

In this paper, I briefly outline the notion of a truth-conditional meaning-theory and introduce two prominent problems it faces. The“extensionality problem” arises because not all correct specifications of truth-conditions are meaning-giving. The “explanatory problem”concerns the extent to which truth-conditional meaning-theories can contribute to the task of clarifying the nature of linguistic meaning.The “principle of humanity” is supposed to resolve both issues simultaneously. I argue that it fails to do so.

Structural properties are properties something has in virtue of its mereological structure in that they are properties whose instantiation by a particular involves the parts of the particular being propertied and related in the appropriate way. Most of the literature on structural properties has focused on problems that arise from the pairing of two assumptions: (1) structural properties are universals and (2) structural properties are, in some sense, composed of the properties they involve. Chief among these difficulties is David Lewis’ (...) claim that the conjunction of (1) and (2) require non-unique composition and hence entail the denial of the extensionality of parthood: butane, as well as methane, is composed of the universals carbon, hydrogen and bonded, yet they are distinct properties. This is the extensionality problem. In this paper I discuss a different problem for the conjunction of (1) and (2) and propose a single solution to both problems. First, in section two, I introduce the idea of multiple decomposition and suggest that at least some structural properties are multiply decomposable. In section three, I introduce the “problem of multiple decompositions.” This problem arises when it seems possible for a structural property to be composed of some xs and some ys even when the xs ≠ ys. Finally, in section four I show how both problems admit of a single solution by focusing on the parthood relation that holds between structural properties and their constituents. While the solution I propose is theoretically costly, I argue that this cost should be paid to retain both (1) and (2). (shrink)

This article argues that existing systems on the Web cannot approach human‐level intelligence, as envisioned by Descartes, without being able to achieve genuine problem solving on unseen problems. The article argues that this entails committing to a strong intensional logic. In addition to revising extant arguments in favor of intensional systems, it presents a novel mathematical argument to show why extensional systems can never hope to capture the inherent complexity of natural language. The argument makes its case by focusing (...) on representing, with increasing degrees of complexity, knowledge in a first‐order language. Nevertheless, the attempts at representation fail to achieve consistency, making the case for an intensional representation system for natural language clear. (shrink)

This paper is about both an application of virtue ethics, and about virtue ethics itself. A popular application of neo-Aristotelian virtue ethics to environmental issues is called interpersonal extensionism. It argues that we should view the normative range of traditional interpersonal virtues, such as compassion and humility, as extending beyond our interactions with people to also include our interactions with non-human environments. This paper uncovers an unaddressed problem for this view, then proposes a solution by revising how we understand (...) neo-Aristotelian virtue ethics itself. The tenet in question, defended by virtue ethicists such as Hursthouse and Foot, claims that a character trait counts as a virtue only if it is strictly necessary for human flourishing. This tenet threatens interpersonal extensionism because, as I show, the extended or environment-regarding aspects of virtues such as compassion and humility are not strictly speaking necessary for human flourishing: people can in principle flourish without those. But I then argue that diversities across both people and environments give us good, seldom acknowledged, reasons to revise neo-Aristotelian virtue ethics so that it no longer imposes the tenet that led to this problem. Neither a trait nor an aspect of it need be necessary for human flourishing in order to count as a neo-Aristotelian virtue. Indeed, marked variation between people and between environments can be complementary with respect to flourishing. Sometimes, for instance, part of the reason an environment-regarding aspect of compassion is virtuous is because of its distinct role in creating conditions that increase the chance that others will flourish. To show these things, I draw from work in philosophy of science on cluster approaches to categories and constitution, and from experiences working with diverse people in Canada's diverse national and provincial parks. (shrink)

Certain philosophers have held the thesis of the unity of science. As often conceived, the thesis has two parts: the thesis of physicalism and the thesis of extensionality. For each of these two parts there is an outstanding problem, i.e. the problem of intentionality and the problem of intensionality respectively. The purpose of this paper is twofold: first, to make explicit the nature of these two problems, and second, to show to what extent they can be (...) said to be the same problem. Thus I am not at all interested here either to defend or attack this thesis or either of its parts. (shrink)

This chapter argues that existing systems on the Web cannot approach human‐level intelligence, as envisioned by Descartes, without being able to achieve genuine problem solving on unseen problems. The chapter argues that this entails committing to a strong intensional logic. In addition to revising extant arguments in favor of intensional systems, it presents a novel mathematical argument to show why extensional systems can never hope to capture the inherent complexity of natural language. The argument makes its case by focusing (...) on representing, with increasing degrees of complexity, knowledge in a first‐order language. Nevertheless, the attempts at representation fail to achieve consistency, making the case for an intensional representation system for natural language clear. (shrink)

Philosophical problems about the part-whole relation have been discussed throughout the history of philosophy, at least since Plato and Aristotle. In contemporary philosophy, the understanding of these issues has benefited from the formal tools of Classical Extensional Mereology. This paper aims is to defend mereological restrictivism against some constraints imposed by the vagueness argument. To achieve this, the paper is divided into three parts. In the first, I introduce the special composition question (hereafter SCQ) as formulated by [Van Inwagen, 1990] (...) and briefly present the three sets of theories that proffer answers to it. In the second part, I focus on the vagueness argument, that was presented by [Lewis, 1986, ] and [Sider, 2007, ] to defend mereological universalism. In the third section, I introduce the theory of natural properties by David Lewis. From this theory, I propose a new mereological operation labeled as natural fusion. The purpose of this operation is to falsify one of the premises of the vagueness argument. Then, I discuss some examples and counter-examples to natural fusion. (shrink)