Parameterized complexity has, so far, been largely confined to consideration of computational problems as decision or search problems. However, it is becoming evident that the parameterized point of view can lead to new insight into counting problems. The goal of this article is to introduce a formal framework in which one may consider parameterized counting problems.

The problem for many troubled youths seeking help within a Christian context is that their need for meaningful connections and spiritual growth is attached to relationships with their significant others. When needs of attachment are not adequately met due to the effect of an insecure attachment working model in a relationship with God, the teen may end up leaving the faith community seeking a new caregiver or regress into spiritual struggles, depression, anxiety, self-doubt and other negative emotions. This paper responds (...) to the issues associated with youth attachment behaviour towards God using a caregiving theology that draws on the 'power of two' through incarnational creativity and pneumatological ecclesiology. This proposed theology first supplements the work of the pastoral counsellor to create a transformative container through which young people, already within a redemptive Christian community, can grow spiritually and deepen their relationship with God. Secondly, pastoral juxtaposition targeting the spiritual needs of hurting youths serves to create a magnet space within the church community that models incarnational love, pastoral care and support for young people by entering their world order to reframe their personal stories of grief, abandonment and insecurity through creative means. Finally, we theologise that pastoral juxtaposition also integrates the power of the Holy Spirit, as the ultimate caregiver in times of conflict, into each youth's unique journey of faith and healing. Implications of this pastoral theology are discussed and applied to everyday life. (shrink)

In this paper we present a negative solution of counting problems for some classes slightly different from bounded arithmetic (▵ 0 sets). To get the results we study properties of chains of finite automata.

Gilbert Ryle is most famous for accusing the Cartesian dualist of committing a category mistake. Yet the nature of this accusation, and the idea of a category mistake more generally, remains woefully misunderstood. The aim of this paper is to rectify this misunderstanding. I show that Ryle does not conceive of category mistakes as mistakes of predication, as is so widely believed. Instead I show category mistakes are mistakes of conjunction and quantification. This thesis uniquely unifies and explains the wide (...) variety of Ryle’s remarks, judgments, and arguments. (shrink)

This paper is a critical response to Hylarie Kochiras’ “Gravity and Newton’s substance counting problem,” Studies in History and Philosophy of Science 40 267–280. First, the paper argues that Kochiras conflates substances and beings; it proceeds to show that Newton is a substance monist. The paper argues that on methodological grounds Newton has adequate resources to respond to the metaphysical problems diagnosed by Kochiras. Second, the paper argues against the claim that Newton is committed to two speculative doctrines (...) attributed to him by Kochiras and earlier Andrew Janiak: i) the passivity of matter and ii) the principle of local causation. Third, the paper argues that while Kochiras’ arguments about Newton’s metaphysical commitments are mistaken, it qualifies the characterization of Newton as an extreme empiricist as defended by Howard Stein and Rob DiSalle. In particular, the paper shows that Newton’s empiricism was an intellectual and developmental achievement that built on non trivial speculative commitments about the nature of matter and space.Keywords: Newton; Substance; Action at a distance; Space; Matter; Empiricism. (shrink)

A striking feature of Newton’s thought is the very broad reach of his empiricism, potentially extending even to immaterial substances, including God, minds, and should one exist, a non-perceiving immaterial medium. Yet Newton is also drawn to certain metaphysical principles—most notably the principle that matter cannot act where it is not—and this second, rationalist feature of his thought is most pronounced in his struggle to discover ‘gravity’s cause’. The causal problem remains vexing, for he neither invokes primary causation, nor accepts (...) action at a distance by locating active powers in matter. To the extent that he is drawn to metaphysical principles, then, the causal problem is that of discovering some non-perceiving immaterial medium. Yet Newton’s thought has a third striking feature, one with roots in the other two: he allows that substances of different kinds might simultaneously occupy the very same region of space. I elicit the implications of these three features. For Newton to insist upon all three would transform the causal question about gravity into an insoluble problem about apportioning active powers. More seriously, it would undermine his means of individuating substances, provoking what I call ‘Newton’s Substance Counting Problem’. (shrink)

The Standards' ecumenical implications are critically assessed in view of the risks which their cross-denominational or cross-faith cooperation implications on the one hand, and, on the other hand, their secular commitments to mutual learning, non-proselytizing, professionalism, and efficiency assessment might carry for chaplains' properly spiritual orientation. The problem posed by the ambiguity of language is raised as a warning that concepts like human dignity have a profoundly different meaning in secular and Christian contexts. Invoking such concepts can be seriously misleading.

In his 'paratactic' analysis of indirect speech reports, Davidson took the occurrence of 'that' in 'Galileo said that the Earth moves' to be a demonstrative expression which refers to the reporter's subsequent utterance of 'the Earth moves'. Ian McFetridge used his 'counting problem' to argue that we get a better version of the paratactic theory if we take the demonstrative 'that' to refer to the proposition expressed by the reporter's utterance, rather than to the utterance itself. In this note, (...) I defend McFetridge's argument against an objection of Richard Holton's. (shrink)

In this paper I propose a solution to the qualitative version of David Miller's verisimilitude reversal argument. Miller (1974) shows that verisimilitude rankings are relative to language choice and hence, are not objective. My solution stems from a reply to an earlier solution proposed by Eric Barnes (1991). Barnes argues that the verisimilitude reversal problem can be solved by revealing an epistemic dimension. I show that Miller's problem cannot be solved by side-stepping foundational metaphysical claims as his epistemic solution suggests. (...) Rather, a substantive metaphysical basis grounds identity relations among properties. The problem of verisimilitude cannot be solved without embracing the fundamental metaphysical distinctions between basic and composite properties that ground the relationship of partial identity among properties. (shrink)

There is a defeasible constraint against double counting. When I count colours, for instance, I can’t freely count both a colour and its shades. Once we properly grasp this constraint, we can solve the problem of the many. Unlike other solutions, this solution requires us to reject neither our counting judgments, nor the metaphysical principles that seemingly conflict with them. The key is recognizing that the judgments and principles are compatible due to the targeted effects of the defeasible (...) constraint. (shrink)

With the recent death of Prof. H. Odera Oruka, founder of the ‘sage philosophy’ school of research based at the University of Nairobi, there is a need to look at some now-problematic issues. I suggest that the original impetus for starting the sage philosophy project-the defense against Euro-American skeptics who thought Africans incapable of philosophizing-has been outgrown. The present need for studies of African sages is to benefit from their wisdom, both in Africa and around the world. I also suggest (...) that the title ‘sage’ has to be problematized. While there were good reasons to focus earlier on rural elders as overlooked wise philosophers, the emphasis now should be on admiring philosophical thought wherever it may be found—in women, youth, and urban Africans as well. In such a way, philosophy will be further relevant to people’s lives, and further light will be shed and shared regarding the lived experience in Africa. (shrink)

This paper addresses the problem of sound individuation (SI) and its connection to sound ontology (SO). It is argued that the problems of SI, such as aspatiality, extreme individuation, indexical perplexity and duration puzzles are due to SO’s uncertainties. Besides, I describe the views in SO, including the wave view (WV), the property view (PV), and the event view (EV), as Casey O’Callaghan defends it. According to O’Callaghan, EV offers clear standards to individuate sounds. However, this claim is countered (...) by the consideration that any view could also defend the standards in SO, and thus, EV does not solve any of the problems mentioned above. As a way of showing the difficulties inherited by sound’s inner ontology, the problem of its linguistic representation is also addressed. The problem of SI can be developed within the frame of the philosophy of language and, specifically, regarding the discussion about mass vs count-­sortal terms. Is the term sound a mass or a count­-sortal? It is shown that, for reasons pertaining SO, the decision regarding the case of sound as a mass or count-­sortal term remains open. SI is, thus, covered from the SO to the philosophy of language. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory [math] of [E. Jeřábek, Approximate counting by hashing in bounded arithmetic, J. Symb. Log. 74(3) (2009) 829–860]. In particular, the Ramsey and weak pigeonhole search problems lie in the new class. We (...) give a purely computational characterization of this class and show that, relative to an oracle, it does not contain the problem CPLS, a strengthening of PLS. As CPLS is provably total in the theory [math], this shows that [math] does not prove every [math] sentence which is provable in bounded arithmetic. This answers the question posed in [S. Buss, L. A. Kołodziejczyk and N. Thapen, Fragments of approximate counting, J. Symb. Log. 79(2) (2014) 496–525] and represents some progress in the program of separating the levels of the bounded arithmetic hierarchy by low-complexity sentences. Our main technical tool is an extension of the “fixing lemma” from [P. Pudlák and N. Thapen, Random resolution refutations, Comput. Complexity, 28(2) (2019) 185–239], a form of switching lemma, which we use to show that a random partial oracle from a certain distribution will, with high probability, determine an entire computation of a [math] oracle machine. The introduction to the paper is intended to make the statements and context of the results accessible to someone unfamiliar with NP search problems or with bounded arithmetic. (shrink)

While many animals — pigeons, for example — have analogue magnitude states , it has recently been argued that certain discriminatory tasks provide evidence for the claim that these states are non-conceptual . These states are taken to be nonconceptual in that they cannot meet a test for concept possession such as Evans’s Generality Constraint. I argue that while such animals probably do not have numerical concepts, the evidence suggests that they could have numerical-ish concepts. On what I call ‘the (...) diffuse’ account of numerical-ish concepts, animals could have analogue magnitude states which represent amount and these states could meet the Generality Constraint . This account also avoids the problems faced by a ‘centred’ account of numerical-ish concepts which cannot meet the Generality Constraint. (shrink)

This paper considers Newton’s position on gravity’s cause, both conceptually and historically. With respect to the historical question, I argue that while Newton entertained various hypotheses about gravity’s cause, he never endorsed any of them, and in particular, his lack of confidence in the hypothesis of robust and unmediated distant action by matter is explained by an inclination toward certain metaphysical principles. The conceptual problem about gravity’s cause, which I identified earlier along with a deeper problem about individuating substances, is (...) that a decisive conclusion is impossible unless certain speculative aspects of his empiricism are abandoned. In this paper, I situate those conceptual problems in Newton’s natural philosophy. They arise from ideas that push empiricism to potentially self-defeating limits, revealing the danger of allowing immaterial spirits any place in natural philosophy, especially spatially extended spirits supposed capable of co-occupying place with material bodies. Yet because their source ideas are speculative, Newton’s method ensures that these problems pose no threat to his rational mechanics or the profitable core of his empiricism. They are easily avoided by avoiding their source ideas, and when science emerges from natural philosophy, it does so with an ontology unencumbered by immaterial spirits. (shrink)

In “How Should We Aggregate Competing Claims?” Alex Voorhoeve develops a theory—Aggregate Relevant Claims (ARC)—which aims to reconcile intuitive judgments for and against aggregating claims in different situations. I argue that ARC does not justify these intuitions but instead ultimately relies on them. We ought not to trust the intuition in favor of nonaggregation, so we ought not to trust ARC. I then show that the nonaggregative part of ARC has a number of unacceptable implications. These problems afflict all (...) nonaggregative theories. Finally, I present a positive argument for full-blooded aggregation. The numbers always count. (shrink)

For most early Medieval and Scholastic philosophers working in the Aristotelian tradition, knowledge of any specific subject is knowledge of its causes and principles. Knowledge of individuals was no exception. As Jorge Gracia has written "To know individuality [for early Medieval and Scholastic philosophers] is to be able to determine the causes and principles that are responsible for it."1 The achievement of such ability is also known as the problem of individuation. This paper will be concerned with the solution to (...) the problem suggested by Leibniz’s writings and how it relates to the contemporary metaphysical debate. In the first section I introduce the problem of individuation along with the solution Leibniz proposed during the latter part of his life. The second section analyzes Leibniz’s solution in a contemporary perspective. I argue that, unlike during the Medieval and early Modern periods, today the epistemic side of the problem of individuation plays a major role in the debate. In this light, Leibniz’s proposal that humans cannot grasp what the individuality of an individual consists in seems problematic. I show, however, that Leibniz’s proposal can stand on its feet also nowadays, provided we are willing to give up the pretenses that there is a definitive count of individuals and that re-identifying individuals across time and space is part of the problem of individuation. (shrink)

In Jacques Derrida's formalisation of the problem of the gift in Donner le temps (1991), where Derrida offers a joint reading of Marcel Mauss’’ The Gift and Baudelaire's La Fausse monnaie, there is an apparent rejection of rational calculation (and of economism) in a narrow sense. This exclusion is only one of the steps in the deconstruction of the metaphysics of the gift, and of other motifs such as, for example, invention, forgiveness, and hospitality. In another step, calculation and economy (...) are the terms of logico-formal paradoxes, and engages us to think of the incompatible demands of calculability and incalculability between which reason is torn, and which Derrida has discussed, for example, in ‘‘The ““World”” of the Enlightenment to Come (Exception, Calculation and Sovereignty)’’ (2003). In this paper, I argue that in his evaluation of Mauss’’ moderate view of economy and exchange, Derrida has limited Mauss’’ notions of economy and rationality to reason as calculation. This evaluation jars with Derrida's deconstruction of calculation in his reading of Hegel and Rousseau among others, as I begin to show, Hegel, for whom ‘‘counting was a bad procedure’’. (shrink)

In this paper I propose and formalize a theory of the mass-count distinction in which the denotations of count nouns are built from non-overlapping generators, while the denotations of mass nouns are built from overlapping generators. Counting is counting of generators, and it will follow that counting is only correct on count denotations.I will show that the theory allows two kinds of mass nouns: mess mass nouns with denotations built from overlapping minimal generators, and neat mass nouns (...) with denotations built from overlapping generators, where the overlap is not located in the minimal generators. Prototypical mass nouns like meat and mud are of the first kind. I will argue that mass nouns like furniture and kitchenware are of the second type.I will discuss several phenomena—all involving one way or the other explicitly or implicitly individual classifiers like stuks in Dutch—that show that both distinctions mass/count and mess/neat are linguistically robust. I will show in particular that nouns like kitchenware pattern in various ways like count nouns, and not like mess mass nouns, and that these ways naturally involve the neat structure of their denotation. I will also show that they are real mass nouns: they can involve measures in the way mess mass nouns can and count nouns cannot.I will discuss grinding interpretations of count nouns, here rebaptized fission interpretations, and argue that these interpretations differ in crucial ways from the interpretations of lexical mass nouns. The paper will end with a foundational problem raised by fission interpretations, and in the course of this, atomless interpretation domains will re-enter the scene through the back door. (shrink)

Somatic cell count is a diagnostic test of milk for mastitis in cows. Its specificity and sensitivity are less than 1.0, making test results uncertain. I discuss epistemological problems of the test such as underdetermination, undercalibration and underdiscrimination, in the solution of which biomedical and economic factors may play a role. Diagnostics of the SCC should be considered as an epistemological network, functioning in a network in which farmers, veterinarians, epidemiologists and milk industry shift their position following biomedical, technological (...) and economic changes, which is described as an actor-network to understand how human and non-human agents in mastitis may be associated. (shrink)

For each $p \geq 2$ there exists a model ${\bf M}^{*}$ of $I\Delta_{0}(\alpha)$ which satisfies the Count( $p$ ) principle. Furthermore, if $p$ contains all prime factors of $q$ there exist $n,r \in {\bf M}^{*}$ and a bijective map $f \in {\rm dom}({\bf M}^{*})$ mapping $\{1,2,\ldots,n\}$ onto $\{1,2,\ldo ts,n+q^{r}\}$ . A corollary is a complete classification of the Count( $q$ ) versus Count( $p$ ) problem. Another corollary shows that the pigeon-hole principle for injective maps does not follow from any (...) of the Count( $q$ ) principles. This solves an open question [Ajtai 94]. (shrink)

ArgumentAimé Civiale's attempt at a complete photographic coverage of the High Alps seems to be a peculiar project at first sight. Carried out between 1859 and 1868, this was the earliest systematic attempt to introduce photography as a medium for studying the earth sciences. But as precise and determined as Civiale's approach appears, it was still quite unclear at the time how exactly photography could be useful in geology. This paper asks where the great confidence in the new medium in (...) regard to mountain representations came from. The answer is not an easy one, as sources on Civiale's project are scarce. To make things even more difficult, the confidence in photography in the earth sciences during that time seems to have been based more on hope than on actual results. It is difficult to extract hope from written sources, let alone from images. I argue that this confidence was not so much based on photography's classic attributes of exactness or objectivity, but on its promise to produce unexpected results. Therefore this argument will inevitably have speculative elements. Thus, this paper can also be understood as an attempt to deal with a specific historiographical problem that regularly occurs when writing about images. (shrink)

I argue that using a traditional biological account of parenthood causes problems for determining who counts as a parent for the purposes of filial obligations in alternative family structures. I then argue that a better way to understand parenthood is as a role. People who fill the role of parents are parents, regardless of their biological ties to a child. Next, I argue that children can have more than two parents and so can have filial obligations to more than (...) two people. I then demonstrate that understanding parenthood as a role allows us to correctly account for who should be a parent in cases of adoption, surrogacy, and extended families. In the final section I discuss three related worries about allowing a child to have more than two parents. (shrink)

We study the long-standing open problem of giving$\forall {\rm{\Sigma }}_1^b$separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the$\forall {\rm{\Sigma }}_1^b$Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak (...) pigeonhole principle for FPNPfunctions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of$T_2^1$augmented with the surjective weak pigeonhole principle for polynomial time functions. (shrink)

Any problem is a problem until a solution is designed and implemented. This paper reports on a workshop that highlights preliminary work done by the working group on Gamification in the scope of European Network for Academic Integrity, which aims to explore the possibility of developing and testing a gamified learning module on academic integrity values. In this paper, the group aims to look at proposing steps we are currently using to develop storyboards of scenarios for the first phase of (...) the project, which were presented at the 6th International Conference Plagiarism Across Europe and Beyond 2020 held virtually in Dubai as a workshop. The study also presents updated findings and scenarios drawn from the workshop conducted and audience feedback, in the following sections that pave the way for the future stages of the gamification process. This serves as a guide to academics and researchers in academic integrity who may wish to study gamification and apply it to develop their own modules for their learning modules. (shrink)

The paper develops two approaches to mass term and count noun substantivals. One treats them on the model of adjectives, Designating phases of a more basic substratum. The other treats them in a more commonsense way, As multiply designating individuals. The two accounts are tested against two problems originally raised by aristotle and heraclitus respectively. The comparison is aimed at bringing out certain central features of one-Place predication, Or more materially, Features of the notion of kind.

This note suggests that the exercise of measuring poverty in a society is greatly aided by clarity on precisely what one means by “the extent of poverty”. The latter concept may refer to the extent of poverty normalized for population size, or to the extent of poverty not so normalized. Absence of clarity on this distinction – which is both simple and non-trivial – could lead to rather straightforward problems of coherence and consistency in the measurement of poverty.

_ Source: _Page Count 19 In this paper, we tackle the contribution that history of science can make to the _problem of rule-choice_, i.e., the choice from among competing methodological rules. Taking our cue from Larry Laudan’s writings, we extensively discuss what we call _historicist naturalism_, i.e., the view that history of science plays a pivotal role in the justification of rules, since it is one source of the evidence required to settle methodological controversies. As we illustrate, there are cases (...) of rule-choice that depend on conceptual considerations alone, and in which history of science does not factor. Moreover, there are cases in which methodological change is prompted – and explained – by empirical information that is not historical in nature: as suggested by what we call _scientific naturalism_, the justification of methodological choices comes from our knowledge of the structure of the world, as expressed by our currently accepted scientific theories. As we argue, due to its backward-looking character, historicist naturalism does not satisfactorily deal with the case of newly introduced rules, for which no evidence concerning their past performance is available. In sum, we conclude, the contribution that history of science can make to rule-choice is more modest than Laudan suggests. (shrink)

The foundations of almost all Islamic sciences were laid in the first and second centuries of hijra. With the expansion of the Islamic world since the first century of hijra, the existence of a collective effort to transfer oral information into writing is notable. With the invitation of the prophet Muḥammad to Islam, an unprecedented increase in the culture of writing has been observed. Since the emergence of Islam, the world history scene has witnessed feverish writing activity. Especially in the (...) 2th/8th century, when the transition from oral culture to written culture accelerated, the founding texts of the science of language and religion, which were the carriers of these sciences related to aqāid-kalām, fiqh and uṣūl al-fiqh, tasawwuf, tafsir, and hadith, were compiled. Thanks to the founding texts containing the basic principles, the sciences have had the opportunity to develop by deepening. In this study, the contribution of Fiqh al-akbar, the founding text of the science of creed, to the science of kalam, which has made significant progress, will be discussed. In order for a text to be considered a founding and root, there must be a system that it establishes as the fruit of the tree. In this sense, Fiqh al-akbar established a moderate and defensible belief system. There is an organic link between the most concise faith texts and the most voluminous kalām books. While the creed texts, which consist of writing the goals at the end of the road, are the counting of the principles of faith, the texts of the kalām represent the walking of the road that leads to the goal of faith. Fiqh al-akbar, which marks the end of the road by finishing the roads to be walked, is the first and most important of the milestones of Islamic thought. In this study, the contribution of Fiqh al-akbar, the founding text of the science of aqāid, to the science of kalām will be discussed in the context of its belonging to its author. This text gave direction to Ahl al-Sunna theology, which would be written in the later stages of Islamic thought. In this study, the internal and external contexts of the founding text mentioned will be confirmed in terms of its relative acumen to Abū Ḥanīfa. In addition, the reason for the increase in the commentaries (Sharḥ) of Fiqh al-akbar during the Ottoman period will be shown. As a matter of fact, each annotation strengthens that it belongs to the author. In the annotations, there is no sentence stating that the text does not belong to Abū Ḥanīfa, on the contrary, the authenticity of the belonging is emphasized. Of course, not all the annotations of the relevant text will be included here, but mostly printed works will be emphasized. Theology, prophecy and the hereafter are discussed in Fiqh al-akbar. Here, how theological debates and problems related to the history of theological concepts are handled in the commentaries will be shown. In this article, within the framework of the method discussed as an example, a preparation will be made for further studies to evaluate the topics and concepts of prophecy and the hereafter in the context of commentaries. The point that should be emphasized here is that none of the scholars who commented on the text pointed out that the subject or concept was not discussed in the period of Abū Ḥanīfa. Moreover, from the early period until as late as the 7th/13th century, both theology and bibliography books did not have any doubts about the belonging of Fiqh al-akbar to Abū Ḥanīfa. Moreover, since the early period, both theological and bibliographical works did not have any doubts about Fiqh al-akbar’s belonging to Abū Ḥanīfa. (shrink)

ArgumentWhen the New Deal administration attained power in the United States, it was confronted with two different problems that could be linked to one another. On the one hand, there was a huge problem of unemployment, affecting everybody including the white-collar workers. And, on the other hand, the administration suffered from a very serious lack of data to illuminate its politics. One idea that came out of this situation was to use the abundant unemployed white-collar workers as enumerators of (...) statistical studies. This paper describes this experiment, shows how it paradoxically affected the professionalization of statistics, and explains why it did not affect expert democracy despite its Deweysian participationist aspect. (shrink)

Many issues in medical ethics seem to turn on arguments about the moral status of some human beings. This essay criticizes attempts to make clear distinctions proposed by Engelhardt, Green/Wikler, Becker, and Brody. The author suggests that the theories discussed divert attention from more resolvable problems.

A problem of the many Fs arises in cases where intuitively there is precisely one F (in the region you are talking about), but when you look closely you find many candidates for being that F, each one apparently as well-qualified as the next. Imagine an apparently solitary cloud in an otherwise blue sky. Look closer, and you'll see lots of water vapor molecules, with no one collection of them more eligible than the others to count as the cloud. Many (...) things are like this when you look closely enough. The problem arises for mundane things like rocks, houses and coins. It also arises for entities that present special philosophical challenges, like persons and experiencers. In this essay, I present a new argument that the problem of the many experiencers is an especially hard problem of the many, and property dualism—the view that properties that there is something it is like to instantiate are irreducible—may be the best way to solve it. (shrink)

Baxter (Australas J Philos 79: 449-464, 2001) proposes an ingenious solution to the problem of instantiation based on his theory of cross-count identity. His idea is that where a particular instantiates a universal it shares an aspect with that universal. Both the particular and the universal are numerically identical with the shared aspect in different counts. Although Baxter does not say exactly what a count is, it appears that he takes ways of counting as mysterious primitives against which different (...) numerical identities are defined. In contrast, I defend the idea— suggested, though not quite endorsed, by Baxter himself—that counts are independent dimensions of numerical identity. Different ways of counting are explained by the existence of these different sorts of identity (i.e., counts). For the instantiation of a universal by a particular, I propose one dimension concerned with the individuation of particulars (the p-count) and another dimension concerned with the individuation of universals (the u-count). On that basis, I give a clear definition of cross-count identity that explains its asymmetrical nature (i.e., the fact that particulars instantiate universais, but not vice versa). I extend the theory to a third dimension—that of time, or the t-count—and thereby defend Baxter's ideas on change, and the contingency of instantiation. Baxter (Mind 97(388): 575-582, 1988; Australas J Philos 79: 449-464, 2001) proposes the related idea of composition as (cross-count) identity. Parts are individually cross-count identical with the wholes that they constitute, and they collectively share all aspects across counts with those wholes. I propose an innovation by which totality is shared distinctness across counts. The theory applies to both the totality of particulars that instantiate any given universal, and the totality of parts that constitute any given whole. I argue that this has several advantages over Armstrong's view, which is based on a dubious external totalling relation. I also argue that Armstrong's theory of numbers (or quantities) as internal relations ought to be rejected in favour of an account based on identity and distinctness. The paper concludes with a careful analysis of external relations in Baxter's framework. I argue that we must recognise one further dimension of identity in order to differentiate between, e.g., the aspects of Abelard insofar as he loves Heloise and Abelard insofar as he loves Isobel. Each of these aspects is identical with Abelard and identical with loving-by, yet they must be in some way distinct. I therefore propose the r-count, in which multiple distinct relational properties are the very same relation (-part). The existence of these four independent dimensions explains the fact that particulars, universals, relations, and times are fundamentally different sorts of things in the ontology. Each is individuated with respect to a different dimension of identity. (shrink)

I would like to attack a certain view: The view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. I introduce the Received View in Section 1. In Section 2 I explain what I mean by entity, and I argue (...) that supporters of the Received View should agree with my characterization of the corresponding notion of entity. I also explain what I mean by identity, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved. (shrink)

The shift from the logical to the empirical argument from evil against the existence of God has been seen as a victory by analytic philosophers of religion who now seek to establish that the existence of evil fails to make the existence of God improbable. I examine several arguments in an effort to establish the following: (i) Their victory is pyrrhic. They distort the historical, philosophical and religious nature of the problem of evil. (ii) In attempting to refute the empirical (...) argument they rely on disguised but well-worn strategies. (iii) A refusal to let evil count in any way against the probability of the existence of God indicates that their rejection is ideological and contrary to traditional theism. (iv) Aspects of their arguments are morally repugnant. (v) Their arguments are indicative of a lack of vitality, relevance and “seriousness” in Christian analytic philosophy of religion. (shrink)

In The Conservation of Races, Du Bois advocates that African Americans hold on to their distinctiveness as members of the black race because this enables them to participate in a cosmopolitan process of cultural exchange in which different races collectively advance human civilization by means of different contributions. Kwame Anthony Appiah and Tommie Shelby have criticized the position that Du Bois expresses in that essay as a problematic form of racial essentialism. This article investigates how Du Bois’ 1924 book The (...) Gift of Black Folk escapes or fails to escape that criticism. It is easy to worry that the diversity of what Du Bois in this book is willing to treat as a black contribution to the development of America pushes us from the problem of essentialism to the other extreme: a lack of any conceptual constraints whatsoever on what can count as a black gift. I will argue that recognizing the cultivation of historical memory as a form of cultural activity is key to understanding the concept's unity. (shrink)

In quantum mechanics it is usually assumed that mutually exclusives states of affairs must be represented by orthogonal vectors. Recent attempts to solve the measurement problem, most notably the GRW theory, require the relaxation of this assumption. It is shown that a consequence of relaxing this assumption is that arithmatic does not apply to ordinary macroscopic objects. It is argued that such a radical move is unwarranted given the current state of understanding of the foundations of quantum mechanics.

We consider scenarios with distributed decision processes, e.g., coupled majorities and personal union in parliament chambers, supranational decisions and supervisory boards. When computing the adoption rate for reaching a decision in these scenarios, multiple linear inequality restrictions in combinatorial countings are present. These rates cannot be computed in closed form. We introduce a general method for incorporating multiple inequality conditions in multiple majority decisions, which significantly reduces the number of involved summations and removes restrictions on the summation indices. Exact solutions (...) are provided through integral representations which can be evaluated numerically, and unrestricted, contracted sums over discrete events. Further, we provide methods to reduce the number of necessary summations by splitting or recurring the original problem to easier sub-problems. For five dedicated scenarios, full results are given which indeed require a single unrestricted summation only. (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)

How are we to understand the use of probability in Popper’s corroboration function? Popper says logically, but this raises a problem that becomes apparent when his views on logical probability are compared with those of Keynes. Specifically, Popper does not make it clear how we could have access to, or even calculate, probability values in a logical sense. For first, he would likely want to deny the Keynesian distinction between primary and secondary propositions, and the underlying notion of knowledge-by-acquaintance with (...) Neo-Platonic entities. Second, he would presumably reject not only the notion of non-numerical probabilities, but also the claim that the principle of indifference is aught other than a heuristic, given paradoxes such as Bertrand’s. An attempt might be made to solve this problem by appeal to semantic or possible world analyses over the relative truth-values of statements, but this seems to fail due to concerns relating to infinity: if the set of possible worlds in which p is true is infinite, and the set of possible worlds in which q is true is infinite, then no numerical value for P can be reasonably determined by a comparison between those worlds. As such, an all-too-familiar sort of criticism of Popper’s view of science seems to loom large: if the corroboration function only makes sense when the probabilities employed therein are subjective, then what counts as impressive evidence for a theory might seem to be a matter of convention, or even whim. However, we now have a new interpretation of probability at our disposal: the intersubjective interpretation, recently championed by Gillies, according to which probabilities can lie on a spectrum between the aleatory and the epistemic. Might we employ this to preserve the corroboration function, and deliver ourselves from Bayesianism, without succumbing to radical subjectivism? (shrink)

Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology (...) look counterintuitive to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)

The democratic boundary problem arises because it appears that the units within which democratic decision procedures will operate cannot themselves be constituted democratically. The study argues that setting the boundaries of democracy involves attending simultaneously to three variables: domain (where and to whom do decisions apply), constituency (who is entitled to be included in the deciding body) and scope (which issues should be on the decision agenda). Most of the existing literature has focussed narrowly on the constituency question, endorsing either (...) the All‐Affected Interests Principle or the All Subjected Principle, but neither is satisfactory as a general solution. In particular, the former fails to explain why having interests at stake in a decision necessarily gives you the right to participate in making it, and the latter, although more plausible on that count, assumes that the domain and scope issues have already been settled. To make progress, we need to bring democratic values to bear on the boundary problem. The units we favour should be those that are likely to promote political equality and solidarity among members of the demos. Although this approach will often justify existing territorial states as sites of democracy, it can also generate arguments for making boundary changes along one or other dimension. (shrink)

This paper addresses both semantic issues of countability in linguistics, and philosophical issues arising from the problem of the many. I argue (i) that the problem of the many is orthogonal to vagueness and we should look to the semantics of count nouns and numerals for its solution; (ii) that the problem of the many is a challenge for contemporary mereological analyses of count nouns in semantics; but (iii) that the count criterion in these theories can be weakened to avoid (...) the problem. Specifically, _weak quantization_ is proposed as the criterion: a sum, _x_, counts as _n_ _P_s if and only if _x_ has _n_ disjoint parts, each of which is in the extension of _P_, but where the sum of no two of them is also in the extension of _P_. I show how importing this idea into the semantics of numerals provides a semantic means of dissolving the paradox. (shrink)

Clarence Sloat, Ora Matushansky, and Delia Graff Fara advocate a Syntactic Rationale on behalf of predicativism, the view that names are predicates in all of their occurrences. Each argues that a set of surprising syntactic data compels us to recognize names as a special variety of count noun. This data set, they say, reveals that names’ interaction with the determiner system differs from that of common count nouns only with respect to the definite article ‘the’. They conclude that this special (...) distribution of names is best explained by the-predicativism, the view that posits the existence of the null-determiner ‘the’ preceding bare singular names. This essay argues that they have incorrectly discerned the syntactic facts: their critical data point concerning the ungrammaticality of sentences like “The Katherine wants coffee” is mistaken. Such sentences’ grammaticality undermines the Syntactic Rationale and presents serious auxiliary problems for predicativism. (shrink)

A topological constraint language is a formal language whose variables range over certain subsets of topological spaces, and whose nonlogical primitives are interpreted as topological relations and functions taking these subsets as arguments. Thus, topological constraint languages typically allow us to make assertions such as “region V1 touches the boundary of region V2”, “region V3 is connected” or “region V4 is a proper part of the closure of region V5”. A formula f in a topological constraint language is said to (...) be satisfiable if there exists an assignment to its variables of regions from some topological space under which φ is made true. This paper introduces a topological constraint language which, in addition to the usual mechanisms for expressing Boolean combinations of regions and their topological closures, includes primitives for bounding the number of components of a region. We call this language T CC, a rough acronym for “topological constraint language with component counting”. Our main result is that the problem of determining the satisfiability of a T CC-formula is NEXPTIME-complete. (shrink)

In recent years a principle for responsible risk-taking called "The Precautionarity Principle" (PP) has been put forward in several policy documents regarding risk-management of technological and environmental issues. PP involves two claims: 1. An ethical claim according to which it is irresponsible to, for example, use new technologies, regdless of how large benefits these are known to bring, unless it has been proven that they will not give rise to unacceptable long term risks. 2. An administrative/political claim according to which (...) the burden of supplying the proof spoken of in claim 1 is to be laid on the supplier of the new technology. This paper deals only with claim 1, which is the real "precautionarity claim". PP has produced much enthusiasm in different political circles, where it is often held out as a landmark for a new thinking in risk-management. However, while claim 2 is clear enough, it is rather obscure how the precautionarity claim is to be understood. In particular, it is not clear to what extent (if any) this claim implies anything new for risk-analysis. This is so since the precautionarity claim does not say anything about what is to be counted as a proof, or what constitutes an unacceptable risk. The paper explores different conlicting interpretations of the precautionarity claim and demonstrates how the choice between these actualise hard ethical issues. In particular, the issue of how much damage we are allowed to cause in order to pursue safety and certainty is discussed. This issue is actualized when new technologies with known beneficiary effects cannot be proven to be "safe enough" according to some interpretations of the precautionarity claim unless investigated for a rather long period of time, during which the technology is not allowed to be used to produce the beneficiary effects it can produce. This problem is structurally similar to a well known issue in medical ethics regarding the rsponsibility of continuing a controlled clinical trial of a drug known to cure when this means that half of the patients suffers extra agony and earlier death because they get a placebo instead of the new drug.. (shrink)