Extensional scientific realism is the view that each believable scientific theory is supported by the unique first-order evidence for it and that if we want to believe that it is true, we should rely on its unique first-order evidence. In contrast, intensional scientific realism is the view that all believable scientific theories have a common feature and that we should rely on it to determine whether a theory is believable or not. Fitzpatrick argues that extensional realism (...) is immune, while intensional realism is not, to the pessimistic induction. I reply that if extensional realism overcomes the pessimistic induction at all, that is because it implicitly relies on the theoretical resource of intensional realism. I also argue that extensional realism, by nature, cannot embed a criterion for distinguishing between believable and unbelievable theories. (shrink)

Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an influential (...) line of argument from the "higher-order evidence" debate, which purports to show that it would be dogmatic, even for a cognitively infallible agent, to refuse to revise her beliefs about logical matters in response to evidence indicating that those beliefs are irrational. Second, I defend this "anti-dogmatism" argument against two responses put forth by Declan Smithies and David Christensen. Against Smithies’ response, I argue that it leads to irrational self-ascriptions of epistemic luck, and that it obscures the distinction between propositional and doxastic justification. Against Christensen’s response, I argue that it clashes with one of two attractive deontic principles, and that it is extensionally inadequate. Taken together, these criticisms will suggest that the connection between logic and rationality cannot be what it is standardly taken to be—ideal rationality does not require logical omniscience. (shrink)

The paper explores the status of the proposition "God exists" in late scholastic debates of the sixteenth and seventeenth centuries in some key authors of the era. A proposition is said to be self-evident if its truth is known solely from the meaning of the terms and is not inferred from other propositions. It does not appear to be immediately evident from the terms that God exists, for the concept expressed by "God" is based on the relation to creatures and (...) negation of imperfection and does not reach to the divine essence. Thomas Aquinas maintains that there are two types of self-evident propositions: those self-evident in themselves but not to us and those self-evident in themselves as well as to us. "God exists" is of the fi rst type. For Scotus a self-evident proposition is such that if its terms are conceived by any intellect, the truth of the proposition becomes known from the terms, non-inferentially. In his view there is no distinction between a self-evident proposition in itself and that in relation to us, because any proposition self-evident in itself is known to be such to any intellect, even though it might not be actually known; it would be known, provided that the terms are conceived. So for Scotus the sentence "God exists" expresses diff erent propositions for the blessed in heaven, the angels and God on the one hand and humans on the other. The former is self-evident, the latter is not. While later scholastics accept either the solution of Thomas or that of Scotus, according to which "God exists" is not self-evident for humans, Thomas de Argentina diff ers in that for him "God exists" is self-evident for humans too. The position of Thomas Aquinas was defended by Domingo Ban¯ez, Francisco Zumel and Gregorio de Valentia. In contrast, Johannes Poncius was a famous adherent of Scotus. There is a fair number of scholastics harmonizing the doctrine of Thomas and Scotus: Bernard Sannig, Luis de Molina, Gabriel Vázquez, Rodrigo de Arriaga and Jean Lalemandet. According to these authors, when Thomas says that "God exists" is self-evident in itself, he speaks about the extensional proposition, i.e. the state of affairs being conceptualized, which does not contradict Scotus’s teaching. © FILOSOFIA, 2013. (shrink)

Nurses in Ghana believe that training, practise, practitioner and policy reforms are required for total nursing profession reform to be effective. Their views for role reformation in the nursing profession, which is currently needed, are not only academic but also clinically relevant in the pursuit of health equity and quality nursing care. We explored and described nurses’ views on their roles in the profession using data collected from 24 professional nurses in three regional hospitals in Ghana. Using an inductive descriptive (...) qualitative design, data were gathered and analysed using a qualitative content analysis to describe the views of the nurses. Four major themes, namely practise reforms, practitioner reforms, training reforms and policy reforms have emerged in relation to role reformation in the nursing profession. Three strategic areas, practitioner attitudes, new training modalities and policy realignment, must be reviewed and remodelled for better positioning of the nursing profession before its entire role reformation. (shrink)

Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entitities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a misguided philosophical doctrine. First, I argue that intensional phenomena are not confined to the realm of language and thought. Rather, the ontology of (...) such phenomena is intimately entwined with the ontology of properties. After providing some evidence to the popularity of extensionalism in contemporary analytic philosophy, I investigate the motivating reasons behind it. Considering several explanations, I argue that the main motivating reason is rooted in the identification of matter with extension, an identification which is one of the hallmarks of the mechanistic conception of nature inherited from the founding fathers of our modern scientific outlook. I then argue that such a conception is not only at odds with a robust ontology of properties but is also at odds with our best contemporary physics. Rather than vindicating extensionalism contemporary science undermines the position, and the lesson to be drawn from this surprising fact is that extensionalism needs no longer be espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the ontological approach to intensional phenomena advocated throughout the paper also gains support from an examination of the historical context within which ‘intension’ was first introduced as a semantic notion. (shrink)

There are at least two different concepts that philosophers might target when analyzing causation: a pre-selective notion and a selective notion. This paper argues that these two distinct conceptions have been conflated to date, citing the puzzles of overdetermination, extensionality, and transitivity as evidence. The primary aim of the paper is to help reset the methodological scene concerning analyses of causation.

Given Quine's views on philosophical methodology, he should not have taken the axioms of classical mereology to be "self-evident", or "analytic"; but rather, he should have set out to justify them by what might be broadly called an "inference to the best explanation". He does very little to this end. In particular, he does little to examine alternative theories, to see if there might be anything they could explain better than classical mereology can. I argue that there is something important (...) that needs to be explained, namely, the way that properties "travel around in clusters" (eg. we often know that "when and where there is something with such-and-such property, there is also something with so-and-so other property", and so on). I argue that these clusterings of properties can be given various subtle (broadly "commonsense") explanations using a version of mereology that denies the classical axiom of "extensionality" (that is, denying that two distinct things must have distinct parts). I offer a challenge to the Quinean metaphysics: to show that these "non-extensional" explanations can be replaced by better explanations that use only classical, extensional mereology and set theory. (shrink)

It is generally assumed that humans are the only animals who can possess a concept of death. However, the ubiquity of death in nature and the evolutionary advantages that would come with an understanding of death provide two prima facie reasons for doubting this assumption. In this paper, my intention is not to defend that animals of this or that nonhuman species possess a concept of death, but rather to examine how we could go about empirically determining whether animals can (...) have a concept of death. In order to answer this question, I begin by sketching an account of concept possession that favours intensional classification rather than mere extensional discrimination. Further, I argue that the concept of death should be construed as neither binary nor universal. I then present a proposal for a set of minimal conditions that must be met to have a concept of death. I argue that having a minimal understanding of death entails first expecting a dead individual to be alive, and then grasping its non-functionality and irreversibility. Lastly, I lay out the sort of observational and experimental evidence that we should look for to determine whether animals have the capacity for a minimal comprehension of death. (shrink)

Aristotle's philosophically most explicit and sophisticated account of the concept of a (primary-)universal proof is found, not in "Analytica Posteriora" 1.4, where he introduces the notion, but in 1.5. In 1.4 Aristotle merely says that a universal proof must be of something arbitrary as well as of something primary and seems to explain primacy in extensional terms, as concerning the largest possible domain. In 1.5 Aristotle improves upon this account after considering three ways in which we may delude ourselves (...) into thinking we have a primary-universal proof. These three sources of delusion are shown to concern situations in which our arguments do establish the desired conclusion for the largest possible domain, but still fail to be real primary-universal proofs. Presupposing the concept of what may be called an immediate proof, in which something is proved of an arbitrary individual, Aristotle in response now demands that a proof be immediate of the primary thing itself and goes on to sketch a framework in which an intensional criterion for primacy can be formulated. For the most part this article is a comprehensive and detailed commentary on Aristotle's very concise exposition in 1.5. One important result is that the famous passage 74a17-25 referring to two ways of proving the alternation of proportions cannot be used as evidence for the development of pre-Euclidean mathematics. (shrink)

Robert Sinclair: Quine on Evidence: Quine's influential “Epistemology Naturalized” is typically read as arguing for the replacement of the “normative” project of traditional epistemology with a psychological description of the causal processes involved in belief acquisition. Recent commentators have rejected this view, arguing that rather than eliminate normative concerns, Quine's proposal seeks to locate them within his scientific conception of epistemology. This chapter examines this debate concerning the normative credentials of Quine's naturalized account of knowledge and its consequences for (...) understanding the role of justification and evidence within his epistemology. It explains how Quine's appeal to psychology should be seen as addressing normative concerns over the evidential connections between theory and observation and further indicates how he addresses issues involving evidence and justification. It concludes by considering some later changes in Quine's epistemology that may be seen as challenging his attempt to address the evidential support of science. (shrink)

In this paper, I defend an epistemic requirement on fitting hopes and worries: it is fitting to hope or to worry that p only if one’s epistemic position makes it rational to suspend judgment as to whether p. This view, unlike prominent alternatives, is ecumenical; it retains its plausibility against a variety of different background views of epistemology. It also has other important theoretical virtues: it is illuminating, elegant, and extensionally adequate. Fallibilists about knowledge have special reason to be friendly (...) to my view; it can help them explain why it can be unfitting to hold on to hope and worry in the face of overwhelming evidence, and it can also help them explain the sense in which knowledge that p and hope that –p are in tension with one another. (shrink)

How does the critical Kant view ontology? There is no shared scholarly answer to this question. Norbert Hinske sees in the Critique of Pure Reason a “farewell to ontology,” albeit one that took Kant long to bid (Hinske 2009). Karl Ameriks has found evidence in Kant’s metaphysics lectures from the critical period that he “was unwilling to break away fully from traditional ontology” (Ameriks 1992: 272). Gualtiero Lorini argues that a decisive break with the tradition of ontology is essential (...) to Kant’s critical reform of metaphysics, as is reflected in his shift from “ontology” to “transcendental philosophy,” two notions that Lorini takes to be related by mere “analogy” (Lorini 2015). I agree with Lorini that a thorough reform of ontology is a pivotal part of Kant’s critical plan for metaphysics and that ontology somehow “survives within the critical philosophy” (Lorini 2015: 76). To make this case, however, I deem it important to identify “ontology” and “transcendental philosophy” in the sense of extensional equivalence. While we can detect this identification in Kant’s writings, only from his metaphysics lectures can we get a full sense of its historical and philosophical significance. In this chapter I focus on how it represents a definitive turn from as well as notable continuity with traditional treatments of ontology, particularly the Wolffian one. (shrink)

How do modal expressions determine which possibilities they range over? According to the Modal Anchor Hypothesis (Kratzer in _The language-cognition interface: Actes du 19_ _e_ _congrès international des linguistes_, Libraire Droz, Genève, 179–199, 2013 ), modal expressions determine their domain of quantification from particulars (events, situations, or individuals). This paper presents novel evidence for this hypothesis, focusing on a class of Spanish relative clauses that host verbs inflected in the subjunctive. Subjunctive in Romance is standardly taken to be licensed (...) only in a subset of intensional contexts. However, in our relative clauses, subjunctive is exceptionally licensed in extensional contexts. At the same time, the interpretation of these relative clauses still involves modality, a type of modality that targets the goals of the agent of the main event. We argue that the pattern displayed by these relative clauses follows straightforwardly if subjunctive is associated with a modal operator that, like modal indefinites (Alonso-Ovalle and Menéndez-Benito in _Journal of Semantics_ 35(1):1–41, 2017 ), can project its domain from a volitional event. Overall, our proposal supports the event-based analysis of mood (Kratzer in Evidential mood in attitude and speech reports. Talk delivered at the 1st Syncart Workshop, Siena, July 13, 2016 ; Portner and Rubinstein in _Natural Language Semantics_ 28:343–393, 2020 ) and extends its application beyond attitudinal and modal complements. (shrink)

Framing effects occur when people respond differently to the same information, just because it is conveyed in different words. For example, in the classic ‘Disease Problem’ introduced by Amos Tversky and Daniel Kahneman, people’s choices between alternative interventions depend on whether these are described positively, in terms of the number of people who will be saved, or negatively in terms of the corresponding number who will die. In this paper, I discuss an account of framing effects based on ‘fuzzy-trace theory’. (...) The central claim of this account is that people represent the numbers in framing problems in a ‘gist-like’ way, as ‘some’; and that this creates a categorical contrast between ‘some’ people being saved (or dying) and ‘no’ people being saved (or dying). I argue that fuzzy-trace theory’s gist-like representation, ‘some’, must have the semantics of ‘some and possibly all’, not ‘some but not all’. I show how this commits fuzzy-trace theory to a modest version of a rival ‘lower bounding hypothesis’, according to which lower-bounded interpretations of quantities contribute to framing effects by rendering the alternative descriptions extensionally inequivalent. As a result, fuzzy-trace theory is incoherent as it stands. Making sense of it requires dropping, or refining, the claim that decision-makers perceive alternatively framed options as extensionally equivalent; and the related claim that framing effects are irrational. I end by suggesting that, whereas the modest lower bounding hypothesis is well supported, there is currently less evidence for the core element of the fuzzy trace account. (shrink)

Presentists have typically argued that the Block View is incapable of explaining our experience of time. In this paper I argue that the phenomenology of our experience of time is, on the contrary, against presentism. My argument is based on a dilemma: presentists must either assume that the metaphysical present has no temporal extension, or that it is temporally extended. The former horn leads to phenomenological problems. The latter renders presentism metaphysically incoherent, unless one posits a discrete present that, however, (...) suffers from the same difficulties that the instantaneous present is prone to. After introducing the main phenomenological models of our experience of time that are discussed in the literature, I show that none of them favors presentism. I conclude by arguing that if even the phenomenology of time sides against presentism, the latter metaphysical theory has no scientific evidence in its favor and ought to be dropped. (shrink)

The Mohist School's logical study focuses mainly on the following inference rule: suppose that N and M are coextensive terms, or N a subset of M; it follows that if a verb can appear in front of N, it can also appear in front of M. That is, if 'VM' then 'VN', where V is some extensional verb. Such an approach to logical inference necessitates the study of logical relations among nouns, verbs, and the relations between these two types (...) of words. Evidence is offered here that the Mohists clearly distinguished extensional verbs from intensional verbs, and that this insight enabled them to say, among other things, that VN does not follow from VM, even in cases where N is M or contained in M, as long as the V in question is an intensional verb. (shrink)

Interpreters have found it exceedingly difficult to understand how Hume could be right in claiming that his two definitions of ‘cause’ are essentially the same. As J. A. Robinson points out, the definitions do not even seem to be extensionally equivalent. Don Garrett offers an influential solution to this interpretative problem, one that attributes to Hume the reliance on an ideal observer. I argue that the theoretical need for an ideal observer stems from an idealized concept of definition, which many (...) interpreters, including Garrett, attribute to Hume. I argue that this idealized concept of definition indeed demands an unlimited or infinite ideal observer. But there is substantial textual evidence indicating that Hume disallows the employment of idealizations in general in the sciences. Thus Hume would reject the idealized concept of definition and its corresponding ideal observer. I then put forward an expert-relative reading of Hume’s definitions of ‘cause’, which also renders both definitions extensionally equivalent. On the expert-relative reading, the meaning of ‘cause’ changes with better observations and experiments, but it also allows Humean definitions to play important roles within our normative practices. Finally, I consider and reject Henry Allison’s argument that idealized definitions and their corresponding infinite minds are necessary for expert reflection on the limitations of current science. (shrink)

Semantic internalism is the view that linguistic meaning amounts to forms of conceptual instructions, and that the process of forming linguistic representations does not involve reference to extra-mental entities. Contemporary philosophy of language remains predominantly externalist in focus, having developed systems of extensional reference which depart from classical rationalist assumptions. Semantic internalism is defended here using a broad range of case studies. Particular focus is be placed on exemplar cases such as natural kind and artifactual terms. Typical natural kind (...) terms are shown to have their meaning constructed via a range of cognitive faculties (considerations of material basis being only one of them), and consulting basic properties of language processing and parsing can explain our intuitions about common word use, a major goal of the internalist enterprise. Copredication via inherent polysemy is used as a strong source of evidence for internalism, countering the received view of the externalist character of meaning. Semantic internalism is comprehensively defended against its critics, pushing the exploration of linguistic content and meaning “back into the head”. (shrink)

At Prior Analytics II 22.68a16–21, Aristotle argues that if A is predicated of all B and C and nothing else, and B is predicated of all C, then A and B convert. In justifying his argument, however, he appears to claim that B is not predicated of all A. This claim has long been a cause of puzzlement to commentators. A widespread view is that the kind of conversion discussed in the passage at issue should be explained in both (...) class='Hi'>extensional and intensional terms. After providing some textual evidence that Aristotle only apparently claims that B is not predicated of all A, I give a purely extensional account of Aristotle’s argument. This account is plausible, conservative and simpler than any of the intensional accounts that have been proposed so far. (shrink)

This chapter contains sections titled: Analyticity and the a priori Knowledge and the realm of the cognitive Evidence The relation of evidence to knowledge: observation sentences Naturalized epistemology and normativity Realism Metaphysics and regimentation: logic and extensionality Ontology and its relativity Conclusion.

The Minimum Description Length principle is the modernformalisation of Occam's razor. It has been extensively and successfullyused in machine learning, especially for noisy and long sources ofdata. However, the MDL principle presents some paradoxes andinconveniences. After discussing all these, we address two of the mostrelevant: lack of explanation and lack of creativity. We present newalternatives to address these problems. The first one, intensionalcomplexity, avoids extensional parts in a description, so distributingcompression ratio in a more even way than the MDL (...) principle. The secondone, information gain, forces that the hypothesis is informative wrt. the evidence, so giving a formaldefinition of what is to discover. (shrink)

ABSTRACT One of the overarching problems of the world today is that too many people see themselves as dominating other groups of people, and dominating nature. That is a root problem. And thus part of a core solution builds from Kohlberg’s commitment to a universal moral orientation, though extended to include not only all people but the more-than-human world: animals, trees, plants, species, ecosystems, and the land itself. In this article, I make a case for this form of ethical extensionism, (...) and then present psychological evidence for it in both children and adults, including studies with inner-city Black youth and their parents. Then I build on Piaget’s, Kohlberg’s, and Turiel’s emphasis that interaction with the physical and social world is a critical mechanism for development. My corollary is this: that to reverse the incredibly fast human-caused destruction of nature—the wellsprings of human existence—we need to deepen and extend people’s interactions with nature, and with its relatively wild forms, even in urban environments. Toward this end, I discuss my current body of research and framework for urban design based on what are referred to as interaction patterns. (shrink)

Preview: Beyond Baumgarten, the modern field of aesthetics can be seen as an attempt to go beyond the limits of older philosophies of beauty, sublimity, and taste in order to engage a much wider domain of qualities and judgments relating to our pleasurable and meaningful experiences of art and nature. The defining strategy of Hegelian aesthetics is to take the essence of aesthetics beyond the limits of nonconceptual sensuous experience and to celebrate instead the idea of art as purveying the (...) very highest spiritual truths, albeit in a somewhat sensuous form. The progressive revolutions of artistic forms and styles that define twentieth-century art similarly reflect the same play of dynamic movement in which art and aesthetics advance by challenging and overcoming the determination of established boundaries posited by prior aesthetic theory and practice. The limit-defying trend in aesthetics is evident in the continuing unsuccessful attempts by analytic philosophy to provide a satisfactory definition of art that will perfectly define its extensional limits by either providing its core essence or some formula that will select all and only those objects that are genuine works of art. Like other Wittgensteinian and pragmatist-inspired philosophers, I have criticized such compartmentalizing definitions of art, not simply for their failures to provide perfect extensional coverage of all the diverse works of art, but also for these theories’ explanatory poverty in explaining art’s meanings, purposes, functions, and values. One of the problems with traditional definitions of art is that they attempt to define something that is not a natural kind but a historically constructed field composed of rather diverse practices. These diverse practices employ a variety of different media and issue in a variety of different works of art that appear to belong to different ontological categories. (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)

The paper addresses various questions about the logical and metaphysical relations between notions of parthood, location and persistence. In particular it argues that the conjunction of mereological extensionalism and multilocation, is highly problematic, if not utterly inconsistent. It thus provides an alternate route to reject multilocation, one that does not rely on Barker and Dowe's well known argument, at least for those who endorse extensionality of parthood. It then argues that other major metaphysical theses such as three-dimensionalism turn out to (...) be at odds with extensionalism. (shrink)

A logic \ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an \-equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, there is exactly one self-extensional three-valued paraconsistent logic in the language of \ for which \ is a disjunction, and \ is a (...) conjunction. We also investigate the main properties of this logic, determine the expressive power of its language, and provide a cut-free Gentzen-type proof system for it. (shrink)

This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers :599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen, I assume that the universe consists of the union of alternatives to (...) the nominal and verbal predicates, where an alternative to a property ψ is one that shares a pragmatic presupposition with ψ, and a pragmatic presupposition is one that is selected by context from a set of potential presuppositions associated with the sentence. A many/few-quantified sentence is then true iff the proportion of the scope to the restrictor is greater/less than some threshold, n. In addition to explaining various problematic cases from the literature, the analysis shows how the readings of a many/few-quantified sentence can be derived from the same syntactico-semantic structure, it being unnecessary to claim lexical or structural ambiguity. The analysis also provides strong support for the idea that natural language quantification is always purely extensional. (shrink)

Ethical extensionism generally involves drawing one or more lines of moral standing. I argue for all living organisms, there is a non- zero probability of sentience and consciousness, and we cannot justify excluding beings from consideration on the basis of uncertainty of their sentience, etc., and rather we should incorporate this uncertainty into the strength of our moral responsibilities. This use of probabilities differs critically from multi-criteria theories of moral standing and those that assign benefit of the doubt, which involve (...) unjustified exclusions and dilutions of duties. From uncertainty rises certainty : we have duties to non-human organisms, although they may often be minor. This modification of extensionist ethics provides foundation for an environmental ethic that parallels interpersonal and animal welfare ethics, and it suggests that we owe much greater concern to 'lower' organisms than they are typically given. (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)

Ethical extensionism is a common argument pattern in environmental and animal ethics, which takes a morally valuable trait already recognized in us and argues that we should recognize that value in other entities such as nonhuman animals. I exposit ethical extensionism’s core argument, argue for its validity and soundness, and trace its history to 18th century progressivist calls to expand the moral community and legal franchise. However, ethical extensionism has its critics. The bulk of the paper responds to recent criticisms, (...) including (1) environmental ethicists’ objection against its austere conception of moral value (2), feminist ethicists’ claim that extensionism fails to account for the moral significance of difference, (3) disability theorists’ concern that ethical extensionist arguments are offensive, and (4) animal rights theorists’ lament that extensionism is a practical failure. While something is to be gained from each criticism, I argue that they ultimately fail and that extensionism remains compelling. (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.

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)

Mereology is the theory of the relation “being a part of”. The first exact formulation of mereology is due to the Polish logician Stanisław Leśniewski. But Leśniewski’s mereology is not first-order axiomatizable, for it requires every subset of the domain to have a fusion. In recent literature, a first-order theory named General Extensional Mereology can be thought of as a first-order approximation of Leśniewski’s theory, in the sense that GEM guarantees that every definable subset of the domain has a (...) fusion, and this has been achieved by positing an axiom schema which in effect defines infinitely many axioms. Intuitively, in order to range over every definable subset, such an axiom schema seems unavoidable. But this paper will show that GEM is finitely axiomatizable and that all we need are just finitely many instances of the said axiom schema. (shrink)

In this paper, we present an extensional system of mereology suitable to account for the intuitive distinction between heaplike and non-heaplike entities. Since the need to capture this distinction has been a key motivation for non-extensional mereologies, we first assess the main non-extensional systems advanced in the last years and highlight some mereological and metaphysical difficulties they involve. We then advance a novel program, according to which the distinction between heaplike and non-heaplike entities can be accounted for (...) by bringing together the parthood relation characterized by classical extensional mereology and an Aristotelian extensional notion of potential parthood. Thus, while rejecting the thesis of mereological monism, our proposal is consistent with the thesis of mereological extensionalism. We show that within this framework it is possible to characterize the above-mentioned distinction, to define the relation of material constitution, and to capture three fundamental standpoints in metaphysics. (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.

Philosophers of modern logic have cherished no project more dearly than that of extensional reduction. Despite occasional protests that this project was ill-conceived from the start, or that it fails to account for important areas of experience and thought, the extensionalist mills have been grinding away anyhow. Their grinding has brought with it a number of important technical successes, replete with philosophical claims that light has finally been shed on areas hitherto buried in incomprehensible darkness.

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)

We analyze some extensions of Martin-Löf 's constructive type theory by means of extensional set constructors and we show that often the most natural requirements over them lead to classical logic or even to inconsistency.

The charge that the limit-frequency theory of probability is inconsistent due to incompatibility between the required features of randomness and limit convergence is inapplicable when probability sequences are taken to be empirically (i.e., extensionally) generated, as they must be on a strictly empirical conception of probability. All past attempts to meet this charge by formulating constructive definitions of randomness that would still allow for a demonstrable limit-convergence have, in their exclusive concern with logically (i.e., intensionally) prescribed sequences, left the logic (...) of extensional classes essentially untouched. In the light of a strict differentiation between intensional and extensional classes a generalized approach is possible under which several closely connected senses of randomness, i.e., the formal, material, restricted and unrestricted senses may be easily distinguished and related to the notion of relevance. (shrink)

I argue that 'c' occurs extensionally in 'c caused e' and 'D' occurs extensionally in 'c caused e because c is D'. I claim that this has been insufficiently appreciated because the two contexts are often run together and because it has not been clear that the description D of c is among the referents of an explanatory argument. I argue as well that Hume's analysis of causation is consistent with taking causation to be a relation between single events, and (...) that even if events are eliminated as virtual entities, extensionality holds for all terms in the resulting context. (shrink)