In a series of recent papers, Jane Friedman has argued that attitudes like wondering, enquiring, and suspending judgement are question-directed and have the function of moving someone from a position of ignorance to one of knowledge. Call such attitudes interrogative attitudes. Friedman insists that all IAs are governed by the following Ignorance Norm: Necessarily, if one knows Q at t, then one ought not have an IA towards Q at t. However, I argue that key premisses in Friedman’s argument actually (...) point towards an opposing conclusion; namely, that IAs are not governed by the Ignorance Norm, and IAs have functions other than moving someone from a position of ignorance to one of knowledge. I conclude that the Ignorance Norm should be rejected. (shrink)

I argue that the concept of direction of fit is best seen as picking out a certain inferential property of a psychological attitude. The property in question is one that believing shares with assuming and fantasizing and fails to share with desire. Unfortunately, the standard analysis of DOF obscures this fact because it conflates two very different properties of an attitude: that in virtue of which it displays a certain DOF, and that in virtue of which it displays certain revision (...) conditions. I claim that the latter corresponds with the aim of an attitude, not its DOF. In order to remedy this failure of the standard analysis, I offer an alternative account of DOF, which I refer to as the two-content analysis. (shrink)

According to the Strong Belief Thesis (SBT), intending to X entails the belief that one will X. John Brunero has attempted to impugn SBT by arguing that there are cases in which an agent intends to X but is unsure that she will X. Moreover, he claims that the standard reply to such putative counterexamples to SBT – namely, to claim that the unsure agent merely has an intention to try – comes at a high price. Specifically, it prevents SBT (...) from playing the kind of explanatory role the cognitivist requires. This article meets Brunero's challenge to SBT by offering an account of trying and intending to try that not only saves SBT from Brunero's criticism, but does so in a way that preserves the explanatory significance that cognitivists typically take SBT to have. (shrink)

The second essay of Nietzsche's Genealogy of Morality (GM) offers a naturalistic and developmental account of the emergence of conscience, a faculty uniquely responsive to remembering and honoring obligations. This article attempts to solve an interpretive puzzle that is invited by the second essay's explanation of nonmoral obligation, prior to the capacity to feel guilt. Ostensibly, Nietzsche argues that the conscience and our concept of obligation originated within contractual (“creditor-debtor”) relations, when creditors punished delinquent debtors (GM II:5). However, this interpretation, (...) which I call the contractualist reading, is incoherent and subject to an insoluble bootstrapping problem. I argue instead that Nietzsche provides two accounts of nonmoral obligation in the second essay, and that the conscience originated in the morality of custom to track rule prohibitions (“I will nots” [GM II:3]), which Nietzsche conceives of as involuntary or reciprocal obligations that, unlike contractual debts, do not require the making of promises. (shrink)

The purpose of this study is to develop a system of corporate ethics based on an understanding and interpretation of the ethical demand of human beings who are in relation with each other according to Emmanuel Levinas' teachings and the responsibility the human being has to and for herself and others whom she encounters based on Paul Ricoeur's teachings on human action, text and hermeneutics. While the philosophies to which we will be referring may not overtly present a normative ethic, (...) we shall convey them in such a way that is reasonably germane to the development of our system of corporate ethics that would, indeed, demonstrate why (and, perhaps, how in some instances) the human being must act in response to the demand of the other whom she encounters. -/- We must not abandon the discussion as it relates to the economy but rather include it in a broader and more comprehensive dialogue about working to promote, support and protect the human dignity of all people using the advancements of technology to improve the human condition. The broader discussion must include but not be limited to developing a working definition of corporate ethics. To engage in discussions about the economy as an indicator for human success, we must speak openly and honestly about all stakeholders that participate and are affected by the economy. Without forsaking other stakeholders, we find the corporation - the entity whose actions have the farthest reaching and, in some cases, longer lasting impact on the human condition - to be an appropriate point of departure for this endeavor. (shrink)

Richard Holton has argued that the traditional account of intentions—which only posits the existence of all-out intentions—is inadequate because it fails to accommodate dual-plan cases; ones in which it is rationally permissible for an agent to adopt two competing plans to bring about the same end. Since the consistency norms governing all-out intentions prohibit the adoption of competing intentions, we can only preserve the idea that the agent in a dual-plan case is not being irrational if we attribute to them (...) a pair of partial intentions. I argue that, contrary to initial appearances, (i) Holton has yet to offer us an actual account of partial intentions, and (ii) that the traditional account of intentions already has the resources necessary to accommodate dual-plan cases. (shrink)

According to the cognitivist strategy, the desire to bring about P provides reasons for intending to bring about P in a way analogous to how perceiving that P provides reasons for believing that P. However, while perceiving P provides reasons for believing P by representing P as true, desiring to bring about P provides reasons for intending to bring about P by representing P as good. This paper offers an argument against this view. My argument proceeds via an appeal to (...) what I call the non-substitutability of perception, the thesis that, given that there is no independent evidence for P, one cannot substitute something that fails to provide reasons with respect to P for the perceptual experience that P, without altering the rational permissibility of believing that P. By contrast, I argue that it is always possible to substitute something that fails to provide reasons for a desire without altering the rational permissibility of an intention based on said desire. I take this to show that a desire does not provide reasons in a way analogous to perceptual experience. (shrink)

Governments are increasingly making use of field experiments to evaluate policy interventions in the spheres of education, public health and welfare. However, the research ethics literature is largely focused on the clinical context, leaving investigators, institutional review boards and government agencies with few resources to draw on to address the ethical questions they face regarding such experiments. In this article, we aim to help address this problem, investigating the conditions under which informed consent is required for ethical policy research conducted (...) or authorized by government. We argue that investigators need not secure participants' informed consent when conducting government policy experiments if: the government institution conducting or authorizing the experiment possesses a right to rule over the spheres of policy targeted by the research; and data collection does not involve the violation of participants' autonomy rights. (shrink)

My dissertation addresses the question "do desires provide reasons?" I present two independent lines of argument in support of the conclusion that they do not. The first line of argument emerges from the way I circumscribe the concept of a desire. Complications aside, I conceive of a desire as a member of a family of attitudes that have imperative content, understood as content that displays doability-conditions rather than truth-conditions. Moreover, I hold that an attitude may provide reasons only if it (...) has truth-evaluable content. Insofar as desires lack truth-evaluable content, I hold that the content of a desire has the wrong kind of logical structure to provide reasons. My second line of argument claims that even if a desire did have truth-evaluable content, it would not follow that desires provide reasons. This is because a desire has no more rational significance than a guess or coin-flip. My argument relies on what I call the non-substitutability principle, the thesis that (all things being equal) one cannot substitute something that lacks rational significance, relative to some attitude, A, for something that has rational significance, relative to A, and leave the rational standing of A unchanged. For example, one cannot substitute the guess that P (i.e., something that lacks rational significance relative to the belief that P) for the perception that P (i.e., something that is rationally significant relative to the belief that P) without altering the rational standing of the belief. I argue that when the non-substitutability principle is applied to a desire that gives rise to an intention, it turns out that one can always substitute a guess or coin-flip (i.e., something that lacks rational significance relative to the intention) for the desire, without altering the rational standing of the intention. I take this to show that desires are not rationally significant relative to the intentions to which they give. (shrink)

In 2011, a 5,000-year-old “male” skeleton buried in a “female” way was discovered by an archaeological team just outside of modern-day Prague. This article queries the impulse to name such a discovery as evidence of transgender identity, and bodies, in an increasingly ancient past. To do so, it takes up the work of Denise Ferreira da Silva, Sylvia Wynter, and Hortense Spillers as a means to push back against the impetus to name such discoveries “transgender” in order to shore up (...) the legitimacy of contemporary trans identity. Each of these three thinkers offers a different vantage point for rethinking such naming practices that push the reader to consider how desires to name and place “transgender” in a distant past papers over the violence of plantation slavery, global imperialism, and the Enlightenment's shift toward scientific reason. This article argues not that such anthropological discoveries should not be considered transgender, but rather that the desire for them to be, or become, transgender does not legitimate contemporary transgender identity, and may instead treat certain iterations of transness as spatially and temporally universal. (shrink)

The fourteen essays in this volume, by leading scholars in the field, explore the relationship between teleology and politics in Kant’s corpus. Among the topics discussed are Kant’s normative political theory and legal philosophy; his cosmopolitanism and views on international relations; his theory of history; his theory of natural teleology; and the broader relationship between morality, history, nature, and politics. _Politics and Teleology in Kant_ will be of interest to a wide audience, including Kant scholars; scholars and students working in (...) moral and political philosophy, the philosophy of history, and political theory and political science; legal scholars; and international relations theorists. (shrink)

Kant develops his political philosophy in the context of a teleological conception of both nature and human history. For Kant, political thought must be undertaken in the context of a progressive historical view of humanity’s place in nature. For this reason Kant would strongly agree with John Rawls’s claim that one of the key roles that political philosophy plays in a society’s political culture is that of ‘probing the limits of practicable political possibility. In this role, we view political philosophy (...) as realistically utopian’ (Rawls 2007, pp. 10-11). The fact that political philosophy has this public role helps to explain the close links that exist between politics and teleology in Kant’s work. Teleology is the study of ends and of the purposiveness of both nature and history. One of the key roles of political philosophy is, for Kant, to probe what politics and human societies more generally can, will and should become in the context of the historically developing and purposive natural systems of which humans are part. Politics must be understood in its natural and historical context, but nature (especially human nature) and history must in turn be understood from a progressive political perspective. For Kant, the historical outcome of this purposive natural system, the end of history, is the full development of humanity’s predispositions for the use of reason within a moral and just society. This volume explores these issues. (shrink)

There are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Nevertheless, some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is more “legitmate” in virtue of being “more basic” or “more fundamental”. This paper addresses two related issues. (...) First, we review some of these non-egalitarian arguments, lay out a laundry list of different, legitimate, notions of relative priority, and suggest that these arguments plausibly employ different such notions. Secondly, we argue that given a metaphysical-cum-epistemological gloss suggested by Frege’s foundationalist epistomology, the ordinals are plausibly more basic than the cardinals. This is just one orientation to relative priority one could take, however. Ultimately, we subscribe to an egalitarian attitude towards these formal characterizations: they are, in some sense, equally “legitimate”. (shrink)

The thesis of Weak Unrestricted Composition says that every pair of objects has a fusion. This thesis has been argued by Contessa and Smith to be compatible with the world being junky and hence to evade an argument against the necessity of Strong Unrestricted Composition proposed by Bohn. However, neither Weak Unrestricted Composition alone nor the different variants of it that have been proposed in the literature can provide us with a satisfying answer to the special composition question, or so (...) we will argue. We will then go on to explore an alternative family of purely mereological rules in the vicinity of Weak Unrestricted Composition, Cardinal Composition: A plurality of pairwise non-overlapping objects composes an object iff the objects in the plurality are of cardinality smaller than $$\kappa $$ κ. As we will show, all the instances for infinite $$\kappa $$ κ s determine fusion and are compatible with junk, and every instance for a $$\kappa > \aleph _0$$ κ > ℵ 0 is furthermore compatible with gunk and dense chains of parthood. (shrink)

Creationism about fictional entities requires a principle connecting what fictions say exist with which fictional entities really exist. The most natural way of spelling out such a principle yields inconsistent verdicts about how many fictional entities are generated by certain inconsistent fictions. Avoiding inconsistency without compromising the attractions of creationism will not be easy.

Permissivist metaontology proposes answering customary existence questions in the affirmative. Many of the existence questions addressed by ontologists concern the existence of theoretical entities which admit precise formal specification. This causes trouble for the permissivist, since individually consistent formal theories can make pairwise inconsistent demands on the cardinality of the universe. We deploy a result of Gabriel Uzquiano’s to show that this possibility is realised in the case of two prominent existence debates and propose rejecting permissivism in favour of substantive (...) ontology conducted on a cost–benefit basis. (shrink)

The cardinal role that notions of respect and self-respect play in Rawls’s A Theory of Justice has already been abundantly examined in the literature. In contrast, it has hardly been noticed that these notions are also central to Michael Walzer’s Spheres of Justice. Respect and self-respect are not only central topics of his chapter “Recognition”, but constitute a central aim of a “complex egalitarian society” and of Walzer’s theory of justice. This paper substantiates this thesis and elucidates Walzer’s criticism (...) of Rawls that we need to distinguish between “self-respect” and “self-esteem”. (shrink)

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large (...) class='Hi'>cardinal axioms are restrictive. I argue, however, that large cardinals are still important axioms of set theory and can play many of their usual foundational roles. (shrink)

The cardinal role that notions of respect and self-respect play in Rawls’s A Theory of Justice has already been abundantly examined in the literature. However, it has hardly been noticed that these notions are also central for Michael Walzer’s Spheres of Justice. Respect and self-respect are not only central topics of his chapter on “recognition”, but constitute a central aim of his whole theory of justice. This paper substantiates this thesis and elucidates Walzer’s criticism of Rawls’s that we need (...) to distinguish between “self-respect” and “self-esteem”. (shrink)

In this chapter, I argue that the films of Andrei Tarkovsky are particularly suitable for inducing feelings of the numinous. This suitability is a formal rather than semantic feature of his films, and is tied indelibly to what film scholars call ‘suture’. I with a summary of what film theorists mean by ‘suture’, before providing a principled defence of the Merleau-Pontian suture theory outlined by George Butte. Second, I will demonstrate that, in spite of the strength of Butte’s formulation, the (...) numinousness of Tarkovsky’s films pose an analytical challenge to his suture theory. Finally, I will then provide my own extension of Butte’s suture theory, arguing that, by virtue of the formal properties they possess, we encounter Tarkovsky’s films more like religious objects than ordinary films. The tenor of these encounters is why Tarkovsky’s films are appropriate loci for feelings of the numinous. (shrink)

We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes's contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes's doctrine with the major deviation from ordinalism that conceives of utility functions (...) as representing preference differences, while being non- etheless empirically related to choices. We highlight the originality, promises and limits of this choice-based cardinalism. (shrink)

As a representative of the papacy Bellarmine was an extremely moderate one. In fact Sixtus V in 1590 had the first volume of his Disputations placed on the Index because it contained so cautious a theory of papal power, denying the Pope temporal hegemony. Bellarmine did not represent all that Hobbes required of him either. On the contrary, he proved the argument of those who championed the temporal powers of the Pope faulty. As a Jesuit he tended to maintain the (...) relative autonomy of the state, denying the temporal powers ascribed by radical papalists and Augustinians. Their argument was generally framed as a syllogism: Christ, who possessed direct temporal power as both God and man, exercised it on earth; the Pope is the vicar of Christ; therefore the Pope possesses and may exercise direct temporal jurisdiction. Bellarmine simply denied that Christ had exercised the temporal power, which as God, it is true, he possessed. Moreover, he drew up and circulated a list of patristic passages collected under the title De Regno Christi quale sit, to prove to the Pope the orthodoxy of his position. (shrink)

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability of the atomist picture. The condition is: (...) logical space is a power of two. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss, which goes back to Carruthers. And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical (...) philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de (...) Lógica Matemática y Fundamentos de la Matemática (ver). También en la entrada "The Continuum Hypothesis" de la web de Enciclopedia de Filosofía de la Universidad de Stanford existe información importante y actualizada al respecto. En esta breve nota se comenta sobre el tema de una manera divulgativa. (shrink)

This paper presents a model-theoretic semantics for discourse "about" natural numbers, one that captures what I call "the mathematical-object picture", but avoids what I can "the mathematical-object theory".

An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.

There are long-standing doubts about whether data from subjective scales—for instance, self-reports of happiness—are cardinally comparable. It is unclear how to assess whether these doubts are justified without first addressing two unresolved theoretical questions: how do people interpret subjective scales? Which assumptions are required for cardinal comparability? This paper offers answers to both. It proposes an explanation for scale interpretation derived from philosophy of language and game theory. In short: conversation is a cooperative endeavour governed by various maxims (Grice (...) 1989); because subjective scales are vague and individuals want to make themselves understood, scale interpretation is a search for a focal point (Schelling 1960). A specific focal point it hypothesised; if this hypothesis is correct, subjective data will be cardinally comparable. Four individually necessary and jointly sufficient conditions for cardinal comparability are specified. The paper then argues this hypothesis can be empirically be tested, makes an initial attempt to do so using subjective well-being data, and concludes it is supported. Numerous areas for further research are identified including, at the end of the paper, how certain tests could be used to ‘correct’ subjective data if they are not cardinal. (shrink)

In this paper, I introduce an iterative method aimed at exploring numbers within the interval [0, 1]. Beginning with a foundational set, S0, a series of algorithms are employed to expand and refine this set. Each algorithm has its designated role, from incorporating irrational numbers to navigating non-deterministic properties. With each successive iteration, our set grows, and after infinite iterations, its cardinality is proposed to align with that of the real numbers. This work is an initial exploration into this approach, (...) and further investigation is encouraged to understand its full implications and potential. (shrink)

In this article, a possible generalization of the Löb’s theorem is considered. Main result is: let κ be an inaccessible cardinal, then ¬Con( ZFC +∃κ) .

An ancient argument attributed to the philosopher Carneades is presented that raises critical questions about the concept of an all-virtuous Divine being. The argument is based on the premises that virtue involves overcoming pains and dangers, and that only a being that can suffer or be destroyed is one for whom there are pains and dangers. The conclusion is that an all-virtuous Divine (perfect) being cannot exist. After presenting this argument, reconstructed from sources in Sextus Empiricus and Cicero, this paper (...) goes on to model it as a deductively valid sequence of reasoning. The paper also discusses whet her the premises are true. Questions about the possibility and value of proving and disproving the existence of God by logical reasoning are raised, as well as ethical questions about how the cardinal ethical virtues should be defined. (shrink)

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.

This article reintroduces Fr. Zeferino González, OP (1831-1894) to scholars of Church history, philosophy, and cultural heritage. He was an alumnus of the University of Santo Tomás in Manila, a Cardinal, and a champion of the revival of Catholic Philosophy that led to the promulgation of Leo XIII’s encyclical Aeterni Patris. Specifically, this essay presents, firstly, the Cardinal’s biography in the context of his experience as a missionary in the Far East; secondly, the intellectual tradition in Santo Tomás (...) in Manila, which he carried with him until his death; and lastly, some reasons for his once-radiant memory to slip into an undeserved forgetfulness. (shrink)

The chemical characterization of the substance responsible for the phenomenon of “transformation” of pneumococci was presented in the now famous 1944 paper by Avery, MacLeod, and McCarty. Reception of this work was mixed. Although interpreting their results as evidence that deoxyribonucleic acid (DNA) is the molecule responsible for genetic changes was, at the time, controversial, this paper has been retrospectively celebrated as providing such evidence. The mixed and changing assessment of the evidence presented in the paper was due to (...) the work’s interpretive flexibility – the evidence was interpreted in various ways, and such interpretations were justified given the neophytic state of molecular biology and methodological limitations of Avery’s transformation studies. I argue that the changing context in which the evidence presented by Avery’s group was interpreted partly explains the vicissitudes of the assessments of the evidence. Two less compelling explanations of the reception are a myth-making account and an appeal to the wartime historical context of its publication. (shrink)

An analysis of Cardinal Joseph Ratzinger's statements regarding relativism in his 2005 homily to the conclave meeting to elect the new pope in the context of the charge of "relativism" in 20th-century philosophy. Parts of this essay are adapted from Barbara Herrnstein Smith,"Pre-Post-Modern Relativism," in *Scandalous Knowledge: Science, Truth and the Human* (Edinburgh: Edinburgh University Press, 2005; Durham, NC: Duke University Press, 2006), 18 – 45.

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and (...) that the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...) out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a consequence, relative (...) counting requires the relativization either of quantifiers, or of identity, or of the is one of relation. However, some of these relativizations do not deliver the expected results, and others rely on problematic assumptions. In another broad variety of relativization, cardinality ascriptions are about concepts or sets. The most promising development of this approach is prima facie connected with a violation of the so-called Coreferentiality Constraint, according to which an identity statement is true only if its terms have the same referent. Moreover - even provided that the problem with coreferentiality can be fixed - the resulting analysis of cardinality ascriptions meets several difficulties. (shrink)

I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the (...) cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark of (...) cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

We address Steel’s Programme to identify a ‘preferred’ universe of set theory and the best axioms extending ZFC by using his multiverse axioms MV and the ‘core hypothesis’. In the first part, we examine the evidential framework for MV, in particular the use of large cardinals and of ‘worlds’ obtained through forcing to ‘represent’ alternative extensions of ZFC. In the second part, we address the existence and the possible features of the core of MV_T (where T is ZFC+Large Cardinals). In (...) the last part, we discuss the hypothesis that the core is Ultimate-L, and examine whether and how, based on this fact, the Core Universist can justify V=Ultimate-L as the best (and ultimate) extension of ZFC. To this end, we take into account several strategies, and assess their prospects in the light of MV’s evidential framework. (shrink)

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic community---set-theoretic (...) practitioners with a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (shrink)

This paper explores the value of benevolence as a cardinal virtue by analyzing the evolving history of virtue ethics from ancient Greek tradition to emotivism and contemporary thoughts. First, I would like to start with a brief idea of virtue ethics. Greek virtue theorists recognize four qualities of moral character, namely, wisdom, temperance, courage, and justice. Christianity recognizes unconditional love as the essence of its theology. Here I will analyze the transition within the doctrine of virtue ethics in the (...) Christian era and afterward since the eighteenth-century thinkers are immensely inspired by this Christian notion of love consider universal benevolence as the cardinal virtue. Later, Hume introduces an emotivist turn by considering the moral worth of sympathetic emotions in his ethical doctrine. In this paper, I aim to discover the cardinality of the virtue of benevolence following the evolutionary history of virtue ethics. (shrink)

In this paper I present two new arguments against the possibility of an omniscient being. My new arguments invoke considerations of cardinality and resemble several arguments originally presented by Patrick Grim. Like Grim, I give reasons to believe that there must be more objects in the universe than there are beliefs. However, my arguments will rely on certain mereological claims, namely that Classical Extensional Mereology is necessarily true of the part-whole relation. My first argument is an instance of a problem (...) first noted by Gideon Rosen and requires an additional assumption about the mereological structure of certain beliefs. That assumption is that an omniscient being’s beliefs are mereological simples. However, this assumption is dropped when I present my second argument. Thus, I hope to show that if Classical Extensional Mereology is true of the part-whole relation, there cannot be an omniscient being. (shrink)