Bermúdez argues for rational framing effects in the form of quasi-cyclical preferences. This is supposed to refute the extensionality principle in standard decision theory. In response, I argue that it is better to analyze seemingly quasi-cyclical preferences as ceteris paribus preferences. Furthermore, if frames are included as objects of choice, we can acknowledge rational framing effects without rejecting extensionality.

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)

I focus on three mereological principles: the Extensionality of Parthood (EP), the Uniqueness of Composition (UC), and the Extensionality of Composition (EC). These principles are not equivalent. Nonetheless, they are closely related (and often equated) as they all reflect the basic nominalistic dictum, No difference without a difference maker. And each one of them—individually or collectively—has been challenged on philosophical grounds. In the first part I argue that such challenges do not quite threaten EP insofar as they are (...) either self-defeating or unsupported. In the second part I argue that they hardly undermine the tenability of EC and UC as well. (shrink)

I examine the link between extensionality principles of classical mereology and the anti‐symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti‐symmetry. I examine the notions of proper parthood, weak supplementation and non‐well‐foundedness. By rejecting anti‐symmetry, the anti‐extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non‐extensional mereology in which anti‐symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non‐anti‐symmetric mereology recaptures all of (...) the structure of classical mereology. (shrink)

E.J. Lowe is one of the few philosophers who defend both the existence of spatially coincident entities and the Principle of Weak Extensionality that no two objects which have proper parts have exactly the same proper parts at the same time. Lowe maintains that when spatially coincident things like the statue and the lump of bronze are in a constitution relation, the constituted entity (the statue) has parts that the constituting entity (the lump) doesn’t, hence the compatibility with (...) Weak Extensionality. My contention is that his argument for why the statue has parts the lump of bronze lacks can also be used to show that the lump of bronze has parts the statue doesn’t. This will mean that there is no basis for saying the statue and the lump are in a constitution relation. I argue for accepting a modified account of constitution and abandoning the Principle of Weak Extensionality. (shrink)

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality. In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, (...) the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality. (shrink)

A proof is presented showing that there is no paraconsistent logics with a standard implication which have a three-valued characteristic matrix, and in which the replacement principle holds.

One of the more persistent debates in mereology is whether distinct wholes can have the same parts. Extensional mereologists hold that if there is no part that makes the difference, then there is nothing to distinguish the wholes, so sameness of parts implies identity. Non-extensionalists, however, do think there are cases where distinct wholes share all their parts. This paper argues that the kind of argument non-extensionalists employ can also be levelled against a widely accepted extensionality principle of (...) plural logic. Non-extensionalists thus face a dilemma: either give up the argument for non-extensional mereology, or deny both the extensionality principle of mereology and the analogous principle for plural logic. (shrink)

In [17], we introduced an extensional variant of generic realizability [22], where realizers act extensionally on realizers, and showed that this form of realizability provides inner models of $\mathsf {CZF}$ (constructive Zermelo–Fraenkel set theory) and $\mathsf {IZF}$ (intuitionistic Zermelo–Fraenkel set theory), that further validate $\mathsf {AC}_{\mathsf {FT}}$ (the axiom of choice in all finite types). In this paper, we show that extensional generic realizability validates several choice principles for dependent types, all exceeding $\mathsf {AC}_{\mathsf {FT}}$. We then show that adding (...) such choice principles does not change the arithmetic part of either $\mathsf {CZF}$ or $\mathsf {IZF}$. (shrink)

The present paper has three closely related aims. We first argue that Agazzi’s scientific realism about Quantum Mechanics is in line with Selleri’s and Tarozzi’s proposal of Quantum Waves. We then go on to formulate rigorously different metaphysical principles such as property compositional determinateness and mereological extensionalism. We argue that, contrary to widespread agreement, realism about Quantum Mechanics actually refutes only the former. Indeed we even formulate a new quantum mechanical argument in favor of extensionalism. We conclude by noting that, (...) given the results of the work, Agazzi’s particular attitude towards Quantum Mechanics is still one of the most promising theoretical perspectives. (shrink)

Two distinct and apparently "dual" traditions of non-classical logic, three-valued logic and paraconsistent logic, are considered here and a unified presentation of "easy-to-handle" versions of these logics is given, in which full naive set theory, i.e. Frege's comprehension principle + extensionality, is not absurd.

ABSTRACTI present a new objection to Bundle Theory. The objection rests on the repeatability of universals, and targets every version of Bundle Theory that assumes that concrete particulars constituted by the same universals are numerically identical. The only way that bundle theorists can elude this objection is to admit the possibility of distinct bundles constituted by the same universals. If even this view is untenable, then Bundle Theory as such is hopeless. Finally, I show how the present inquiry reshapes the (...) dialectical relationship between Bundle Theory and the principle of Identity of Indiscernibles. (shrink)

Jaegwon Kim’s principle of Explanatory Exclusion says there can be no more than a single complete and independent explanation of any one event. Accordingly, if we have a complete neurological explanation for some piece of human behavior, the mental explanation must either be excluded, or it must not be distinct from the neurological explanation. Jaegwon Kim argues that mental explanations are not distinct from neurological explanations on account of the fact that they refer to the same objective causal relation (...) between events. A number of critics have argued that this extensional model of explanatory individuation allows for too many descriptions to state the same explanation. In this paper I consider, and ultimately reject, a possible response to these critics called the Constitutive Property Reply. (shrink)

There are two main ways in which the notion of mereological fusion is usually defined in the current literature in mereology which have been labelled ‘Leśniewski fusion’ and ‘Goodman fusion’. It is well-known that, with Minimal Mereology as the background theory, every Leśniewski fusion also qualifies as a Goodman fusion. However, the converse does not hold unless stronger mereological principles are assumed. In this paper I will discuss how the gap between the two notions can be filled, focussing in particular (...) on two specific sets of principles that appear to be of particular philosophical interest. The first way to make the two notions equivalent can be used to shed some interesting light on the kind of intuition both notions seem to articulate. The second shows the importance of a little-known mereological principle which I will call ‘Mild Supplementation’. As I will show, the mereology obtained by adding Mild Supplementation to Minimal Mereology occupies an interesting position in the landscape of theories that are stronger than Minimal Mereology but weaker than what Achille Varzi and Roberto Casati have labelled ‘Extensional Mereology’. (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)

En este articulo quiero discutir algunos temas centrales deI tratamiento fregeano de los contextos no extensionales. Limitaré mi discusión al análisis de oraciones de creencia y de la oratio obliqua. En la primera parte, voy a describir dos tipos de teoría dentro deI marco de la semántica de Frege. En particular, compararé y evaluaré los análisis de oraciones no extensionales de primer y segundo nivel que se pueden llevar a cabo en las teorías de ambos tipos. En la segunda parte, (...) examinaré en que medida se puede establecer una jerarquía infinita de sentidos indirectos. En la tercera parte, voy a examinar el principio fregeano de sustitutividad de expresiones coreferenciales salva veritate. Además, haré algunas observaciones críticas sobre artículos de Tyler Burge y Jaakko Hintikka relacionados con esta temática.In this article, I discuss some important aspects of Frege’s treatment of nonextensional contexts. I focus on the analysis of belief sentences and of oratio obliqua. In the first part, I deseribe two types of theory within Fregean semantics and assess the analyses of non-extensional sentences of first and of second level whieh can be carried out in the theories of both types. In the seeond part, I examine to what extent one can establish an infinite hierarehy of indirect senses. In the third and final part, I examine Frege’s principle of substitutivity salva veritate of coreferential terms. I conelude with critieal observationson articles of Tyler Burge and Jaakko Hintikka which deal with this principle. (shrink)

Part is not a univocal term. Uses of parthood and composition that do not obey any supplementation principle have a long philosophical tradition and strong support from contemporary physics. We call such uses potential parts. This paper first shows why potential parts are important and incompatible with supplementation, then provides a formal mereology for such parts inspired by the path-integral approach to quantum electrodynamics.

It is often maintained that co-referential terms can be substituted for one another whilst preserving truth-value in extensional contexts, and preserving grammaticality in all contexts. Crispin Wright calls this claim ‘The Reference Principle’ . Since Wright defines extensional contexts as those in which truth-value is determined only by reference, it is the assertion about substitution salva congruitate that is significant. Wright argues that RP is the key to understanding how Frege came to hold, paradoxically, that the concept horse is (...) not a concept, and to providing a resolution to the paradox .RP and Wright's application of it to Frege's Paradox have recently been criticized by Oliver . 1 Oliver argues that the syntax of natural languages is too complicated for the failure of two terms to fit into the same forms of speech to indicate a difference in semantic significance: RP is, he claims, an empirical falsehood.I shall argue that, although Oliver's arguments show that RP is false as it stands, a revised version of the principle, employing a more robust notion of substitution, is nevertheless correct. I shall end by outlining the implications of this revision for the appeal to RP and for Wright's resolution of Frege's Paradox.1. Referring terms and referential positionOliver's case against RP appeals to an impressive array of counter-examples. For our purposes it will be useful to regard these as being of three sorts. The first sort can be dealt with relatively swiftly: examples of the second and third sorts are more challenging.The first sort of counter-example involves referring terms that feature as parts of complex referring expressions. Oliver's examples include ‘William’ in the complex expression ‘William the Conqueror’ . The substitution of expressions co-referential with ‘William’ into sentences employing the complex referring expression often results in ungrammatical …. (shrink)

The theory of variable embodiments has been primarily formulated to model ordinary objects as things that change their parts over time. A variable embodiment /f/ is a sui generis whole constructed from a principle f, the principle of a variable embodiment, and it is manifested at different times by different things picked out by such a principle f. This principle is usually clarified as a function that picks out, at any given time the variable embodiment exists, (...) its corresponding manifestation at that time, and it fails to pick out anything at any other time. The first purpose of this article is to examine and refute three natural understandings of such a principle. Specifically, first, we argue against the view that it should be understood extensionally as either a partial function or total function. Next, we provide some motivations to reject the understanding of the principle as a function in intensional terms, where the notion of intension is analyzed in terms of a specific version of a possible world semantics. The second goal of the article is to make it plausible that the principle has an intensional character and, on the basis of the results achieved, to formulate some constraints that an account of such a principle should meet. (shrink)

In Prior Analytics 1.27–30, Aristotle develops a method for finding deductions. He claims that, given a complete collection of facts in a science, this method allows us to identify all demonstrations and indemonstrable principles in that science. This claim has been questioned by commentators. I argue that the claim is justified by the theory of natural predication presented in Posterior Analytics 1.19–22. According to this theory, natural predication is a non-extensional relation between universals that provides the metaphysical basis for demonstrative (...) science. (shrink)

We discuss several axiomatizations of set theory in first order predicate calculus with epsilon and a constant symbol W, starting with the simple system K(W) which has a strong equivalence with ZF without Foundation. The other systems correspond to various extensions of ZF by certain large cardinal hypotheses. These axiomatizations are unusually simple and uncluttered, and are highly suggestive of underlying philosophical principles that generate higher set theory.

In response to the paper by Cotnoir and Bacon published in RSL 2/2012, we would like to add some remarks regarding supplementation principles. It is known that in a classical mereology, the Strong Supplementation Principle (SSP) together with antisymmetry enforces the Weak Supplementation Principle (WSP). Instead, in the nonwellfounded mereology, the failure of extensionality causes the failure of antisymmetry (Cotnoir, 2010), hence the investigated model is also nonantisymmetric. Cotnoir supposes that the failure of antisymmetry implies the failure (...) of (WSP) when (PP1) is applied, however gives no explicit argument, which we would like to supply in this paper. Additionally, when (PP2) is applied, (SSP) implies (WSP), hence the failure of antisymmetry does not necessarily imply the failure of (WSP). (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in (...) the foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

The classical principle of double effect offers permissibility conditions for actions foreseen to lead to evil outcomes. I shall argue that certain kinds of closeness cases, as well as general heuristic considerations about the order of explanation, lead us to replace the intensional concept of intention with the extensional concept of accomplishment in double effect.

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.

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. (...) In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through.

According to the principle of compositionality, the meaning of a composed expression depends only on its logical form and the meaning of its descriptive sub-expressions. This dependence can be understood as the substitutivity of expressions that have the same meaning without changing the meaning of the composed expression. In this book the hidden complexity of Frege's and Quine's conceptions of extensionality is revealed. The insights gained by this analysis as well as two versions of the principle of (...) compositionality are used in a formal reconstruction of Gödel's and Quine's versions of the slingshot argument. (shrink)

It is well known that the extensional axiom of choice implies the law of excluded middle . We here prove that the converse holds as well if we have the intensional axiom of choice ACint, which is provable in Martin-Löf's type theory, and a weak extensionality principle , which is provable in Martin-Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory.

Bermúdez describes the extensionality principle as being “almost unquestioned.” This claim might come as a surprise to philosophers who work on agency and ethics. In Kantian deontological ethics and in Platonic or Aristotelian virtue ethics, our preferences for outcomes can be rationally affected by how those outcomes are framed in terms of maxims and character traits.

This volume presents a collection of refereed papers reflecting the state of the art in the area of over-constrained systems. Besides 11 revised full papers, selected from the 24 submissions to the OCS workshop held in conjunction with the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Marseilles in September 1995, the book includes three comprehensive background papers of central importance for the workshop papers and the whole field. Also included is an introduction by (...) one of the volume editors together with a bibliography listing 243 entries. All in all this is a very useful reference book relevant for all researchers and practitioners interested in hierarchical, partial, and over-constrained systems. (shrink)

The Univalent Foundations project constitutes what is arguably the most serious challenge to set-theoretic foundations of mathematics since intuitionism. Like intuitionism, it differs both in its philosophical motivations and its mathematical-logical apparatus. In this paper we will focus on one such difference: Univalent Foundations’ reliance on an intensional rather than extensional logic, through its use of intensional Martin-Löf type theory. To this, UF adds what may be regarded as certain extensionality principles, although it is not immediately clear how these (...) principles are to be interpreted philosophically. In fact, this framework gives an interesting example of a kind of border case between intensional and extensional mathematics. Our main purpose will be the philosophical investigation of this system, and the relation of the concepts of intensionality it satisfies to more traditional philosophical or logical concepts such as those of Carnap and Quine. (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)

A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that beefing up WST with moderate extensionality principles or quotient sets enables the derivation to go through.

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification problem in typed λ-calculi is much more complex than that for first-order terms, since it has to take the theory of αβη-equality (...) into account. As a consequence, the higher-order unification problem is undecidable and sets of solutions need not even always have most general elements that represent them. Thus the mentioned calculi for higher-order logic have take special measures to circumvent the problems posed by the theoretical complexity of higher-order unification. In this paper, we will exemplify the methods and proof- and model-theoretic tools needed for extending first-order automated theorem proving to higherorder logic. For the sake of simplicity take the tableau method as a basis (for a general introduction to first-order tableaux see part I.1) and discuss the higherorder tableau calculi HT and HTE first presented in [19]. The methods in this paper also apply to higher-order resolution calculi [1, 13, 6] or the higher-order matings method of Peter [3], which extend their first-order counterparts in much the same way. Since higher-order calculi cannot be complete for the standard semantics by Gödel’s incompleteness theorem [11], only the weaker notion of Henkin models [12] leads to a meaningful notion of completeness in higher-order logic. It turns out that the calculi in [1, 13, 3, 19] are not Henkin-complete, since they fail to capture the extensionality principles of higher-order logic. We will characterize the deductive power of our calculus HT (which is roughly equivalent to these calculi) by the semantics of functional Σ-models. To arrive at a calculus that is complete with respect to Henkin models, we build on ideas from [6] and augment HT with tableau construction rules that use the extensionality principles in a goal-oriented way.. (shrink)

In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Godel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionality principles and without reducibility (...) cannot recover mathematical induction. The finite cardinals are indefinable in it. This paper shows that while Gödel and Myhill are correct, Russell was not wrong. The 1925 system employs a different grammar than the original Principia. A new proof for *89.16 is given and induction is recovered. (shrink)

It is well known that the extensional axiom of choice implies the law of excluded middle. We here prove that the converse holds as well if we have the intensional axiom of choice ACint, which is provable in Martin-Löf's type theory, and a weak extensionality principle, which is provable in Martin-Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory.

Thus, despite the di culty of higher-order automated theorem proving, which has to deal with problems like the undecidability of higher-order uni - cation (HOU) and the need for primitive substitution, there are proof problems which lie beyond the capabilities of rst-order theorem provers, but instead can be solved easily by an higher-order theorem prover (HOATP) like Leo. This is due to the expressiveness of higher-order Logic and, in the special case of Leo, due to an appropriate handling of the (...) extensionality principles (functional extensionality and extensionality on truth values). (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)

The received view of framing has multiple interpretations. I flesh out an interpretation that is more open-minded about framing effects than the extensionality principle that Bermúdez formulates. My interpretation attends to the difference between preferences held all things considered and preferences held putting aside some considerations. It also makes room for decision principles that handle cases without a complete all-things-considered preference-ranking of options.

In this article the notions of local and global extensionality principle are defined; the problem of relations between extensionality of a language and theory of extension of a name and extension of a sentence is discussed.

How natural is natural deduction?– Gentzen's system of natural deduction intends to fit logical rules to the effective mathematical reasoning in order to overcome the artificiality of deductions in axiomatic systems (¶ 2). In spite of this reform some of Gentzen's rules for natural deduction are criticised by psychologists and natural language philosophers for remaining unnatural. The criticism focuses on the principle of extensionality and on formalism of logic (¶ 3). After sketching the criticism relatively to the main (...) rules, I argue that the criteria of economy, simplicity, pertinence etc., on which the objections are based, transcend the strict domain of logic and apply to arguments in general (¶ 4). (¶ 5) deals with Frege's critique of the concept of naturalness as regards logic. It is shown that this concept means a regression into psychologism and is exposed to the same difficulties as are: relativity, lack of precision, the error of arguing from `is' to `ought' (the naturalistic fallacy). Despite of these, the concept of naturalness plays the role of a diffuse ideal which favours the construction of alternative deductive systems in contrast to the platonic conception of logic (¶ 6). (shrink)

David Lewis famously endorsed Unrestricted Composition. His defense of such a controversial principle builds on the alleged innocence of mereology. This innocence defense has come under different attacks in the last decades. In this paper I pursue another line of defense, that stems from some early remarks by van Inwagen. I argue that Unrestricted Composition leads to a better metaphysics. In particular I provide new arguments for the following claims: Unrestricted Composition entails extensionality of composition, functionality of location (...) and four-dimensionalism in the metaphysics of persistence. Its endorsement yields an impressively coherent and powerful metaphysical picture. This picture shows a universe that might not be innocent but it is certainly elegant. (shrink)

The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...) categorial grammar, and also on the ground of its extension to the bi-level, intensional and extensional semantic-pragmatic theory ST for L. In T, according to the token-type distinction of Ch.S. Peirce, L is characterized first as a language of well-formed expression-tokens (wfe-tokens) - material, concrete objects - and then as a language of wfe-types - abstract objects, classes of wfe-tokens. In ST the semantic-pragmatic notions of meaning and interpretation for wfe-types of L of intensional semantics and the notion of denotation of extensional semanics for wfe-types and constituents of knowledge are formalized. These notions allow formulating a postulate (an axiom of categorial adequacy) from which follow all the most important conditions of the language adequacy, including the above, and a structural one connected with three principles of compositionality. (shrink)