Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological (...) challenge. The purpose of this paper is to determine what Benacerraf’s challenge could be such that this view is warranted. I argue that it could not be any of the challenges with which it has been traditionally identified by its advocates, like of Benacerraf and Field. Not only are none of the challenges easier for the pluralist to meet. None satisfies a key constraint that has been placed on Benacerraf’s challenge. However, I argue that Benacerraf’s challenge could be the challenge to show that our set-theoretic beliefs are safe – i.e., to show that we could not have easily had false ones. Whether the pluralist is, in fact, better positioned to show that our set-theoretic beliefs are safe turns on a broadly empirical conjecture which is outstanding. If this conjecture proves to be false, then it is unclear what the epistemological argument for set-theoretic pluralism is supposed to be. (shrink)

Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.

Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at (...) most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that (...) fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

Pluralism about truth is the view that there are many properties, not just one, in virtue of which things are true. Pluralists hope to dodge the objections that face traditional monistic substantive views of truth, as well as those facing deflationary theories of truth. More specifically, pluralists hope to advance an explanatorily potent understanding of truth that can capture the subtleties of various realist and anti-realist domains of discourse, all while avoiding the scope problem. I offer a new objection (...) to pluralism that challenges its fundamental commitment to there being a set of alethic properties in virtue of which claims are true. In its place I offer an alternative view that merges standard truthmaker theory with a primitivist conception of truth. This combination of views satisfies the theoretical desires that pluralists claim for themselves, but without taking on pluralism's host of challenges and problems. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that (...) fruitfully interrelates a ‘structural’ perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I (...) argue that pluralist accounts of mathematics render fundamental mathematical disagreements compatible with mathematical realism in a way in which moral disagreements and moral realism are not. 11. (shrink)

When talking about truth, we ordinarily take ourselves to be talking about one-and-the-same thing. Alethic monists suggest that theorizing about truth ought to begin with this default or pre-reflective stance, and, subsequently, parlay it into a set of theoretical principles that are aptly summarized by the thesis that truth is one. Foremost among them is the invariance principle.

Despite the common use of the concept of emergence, no uncontroversial theoretical framework has been yet formulated in this regard. In this paper, I examine what this circumstance suggests about the significance and usefulness of this concept. I first trace a brief history of the notion of emergence from its first formulation among the British Emergentists to its contemporary uses. Then, I outline its most common features and examine three examples of emergent phenomena, namely particle decay, free will, and division (...) of labour in ant colonies. These three cases of emergence exhibit different features and imply criteria which only partially overlap. I then suggest that the multiplicity of features and criteria recognised as defining emergence, rather than being a threat to the tenability of the concept, should encourage the assumption of a pluralist attitude that is consistent with both the employment of this idea in different sciences and the recognition of emergent phenomena across different levels of organisation. Finally, I propose that emergence can be approached in a similar way to how Richard Boyd approached the problem of natural kinds, namely by identifying an open cluster of properties, rather than a set of necessary and sufficient conditions. (shrink)

Most theories of slurs fall into one of two families: those which understand slurring terms to involve special descriptive/informational content (however conveyed), and those which understand them to encode special emotive/expressive content. Our view is that both offer essential insights, but that part of what sets slurs apart is use-theoretic content. In particular, we urge that slurring words belong at the intersection of a number of categories in a sociolinguistic register taxonomy, one that usually includes [+slang] and [+vulgar] and (...) always includes [-polite] and [+derogatory]. Thus, e.g., what distinguishes ‘Chinese’ from ‘chink’ is neither a peculiar sort of descriptive nor emotional content, but rather the fact that ‘chink’ is lexically marked as belonging to different registers than ‘Chinese’. It is, moreover, partly such facts which makes slurring ethically unacceptable. (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- (...) class='Hi'>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)

In this paper, I argue that one of the arguments usually put forward in defence of universism is in tension with current set theoretic practice. According to universism, there is only one set theoretic universe, V, and when applying the method of forcing we are not producing new universes, but only simulating them inside V. Since the usual interpretation of set generic forcing is used to produce a “simulation” of an extension of V from a countable set inside (...) V itself, the above argument is credited to be a strong defence of universism. However, I claim, such an argument does not take into account current mathematical practice. Indeed, it is possible to find theorems that are available to the multiversists but that the advocate of universism cannot prove. For example, it is possible to prove results on infinite games in non-well-founded set-theories plus the axiom of determinacy (such as ZF + AFA + PD) that are not available in ZFC + PD. These results, I contend, are philosophically problematic on a strict universist approach to forcing. I suggest that the best way to avoid the difficulty is to adopt a pluralist conception of set theory and embrace a set theoretic multiverse. Consequently, the current practice of set generic forcing better supports a multiverse conception of set theory. (shrink)

In this paper, I argue that a naturalist approach in philosophy of mathematics justifies a pluralist conception of set theory. For the pluralist, there is not a Single Universe, but there is rather a Multiverse, composed by a plurality of universes generated by various set theories. In order to justify a pluralistic approach to sets, I apply the two naturalistic principles developed by Penelope Maddy (cfr. Maddy (1997)), UNIFY and MAXIMIZE, and analyze through them the potential of the set (...) class='Hi'>theoretic multiverse to be the best framework for mathematical practice. According to UNIFY, an adequate set theory should be foundational, in the sense that it should allow one to represent all the currently accepted mathematical theories. As for MAXIMIZE, this states that any adequate set theory should be as powerful as possible, allowing one to prove as many results and isomorphisms as possible. In a recent paper, Maddy (2017) has argued that this two principle justify ZFC as the best framework for mathematical practice. I argue that, pace Maddy, these two principles justify a multiverse conception of set theory, more precisely, the generic multiverse with a core (GMH). (shrink)

This chapter sets out a theory of how to weigh alethic and pragmatic (non-alethic) reasons for belief, or more precisely, to say how alethic and non-alethic considerations jointly determine what one ought to believe. It replaces my earlier (2008) weighing account. It is part of _The true and the good: a new theory of theoretical reason_, which develops a view, welfarist pluralism, which comprises central two theses. One is that there are both irreducibly alethic or epistemic reasons for belief (...) and irreducibly pragmatic (and non-alethic) reasons for belief. The other is that despite this, the source of all normativity is pragmatic in a particular way, i.e. that all reasons are reasons in virtue of their being conducive to wellbeing. The pluralist theory of reasons emerges from the irreducibly plural nature of the components of wellbeing, on of which is being in a positively-valenced epistemic state. This view also offers some insight into outstanding problems concerning the scope, chronicity, and normativity of the requirements of theoretical rationality as well. (Updated 10 May 2022). (shrink)

In this dissertation, I address the question of how to construct scientific theories of emotions that are both conceptually sound and empirically fruitful. To do this, I offer an analysis of the main challenges scientific theories of emotions face, and I propose a meta-theoretical framework to construct scientific concepts of emotions as explications of folk emotion concepts. Part I discusses the main challenges theories of emotions in psychology and neuroscience encounter. The first states that a proper scientific theory of emotions (...) must explain all and only the phenomena under the vernacular term ‘emotion’ with a common set of conceptual resources and under an overarching generic concept of emotion. The second demands that each emotion category corresponds to well-coordinated sets of neural, physiological, and behavioral patterns of responses. I argue that none of the best contemporary theories of emotions in psychology and neuroscience overcomes these challenges. As a result, a new theory of emotions is required. In Part II, I develop the meta-theoretical framework to construct a theory of emotions that overcomes the challenges above. First, I propose a pluralistic account of scientific kinds based on different patterns of projection that various disciplines may take to justify inductive inferences. These are essentialist, historical, and social patterns. Each of these patterns provides a framework to construct different types of scientific concepts. I argue that among the frameworks for scientific kinds available, the one that is best suited to explicate emotion concepts is a functional framework. Consequently, I conclude by recommending scientists pursue functionalist theories of emotions over essentialist, historical, or social theories. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

Recent discussions of how axioms are extrinsically justified have appealed to abductive considerations: on such accounts, axioms are adopted on the basis that they constitute the best explanation of some mathematical data, or phenomena. In the first part of this paper, I set out a potential problem caused by the appeal made to the notion of mathematical explanation and suggest that it can be remedied once it is noted that all the justificatory work is done by appeal to the theoretical (...) virtues. In the second part of the paper, I appeal to the theoretical virtues account of axiom justification to provide an argument that judgements of theoretical virtuousness, and therefore of extrinsic justification, are subjective in a substantive sense. This tells against a recent claim by Penelope Maddy that such justification is “wholly objective”. (shrink)

A theistic science would have to represent the integration of all kinds of knowledge intent on explaining the whole of reality. These would include, at least, history, metaphysics, theology, formal logic, mathematics, and experimental sciences. However, what is the whole of reality that one wants to explain? :.

Introduction: Interdisciplinary, transdisciplinary and action research of a city in lockdown. As we write this chapter, most cities across the world are subject to a similar set of measures due to the spread of COVID-19 coronavirus, which is now a global pandemic. Independent of city size, location, or history, an observer would note that almost all cities have now ground to a halt, with their citizens being confined to their private dwellings, social and public gatherings being almost entirely forbidden, and (...) commercial areas being nearly devoid of visitors. Striking as these apparent similarities are, closer scrutiny would reveal important differences between cities and within cities – differences that can be highly relevant to consider when scholars are assessing the responses of cities to this pandemic or trying to predict the consequences of those responses. For example, the public health systems in some cities are better prepared than in others for coping with the increasing number of patients in life threatening conditions. Multigenerational households, which are associated with a greater risk for elderly members, are not equally common in all cities. Tourist destinations have taken a more severe economic hit from the lockdown than those cities which are economically less dependent upon this particular source of income. Communal celebrations in one city will result in a higher number of contagions and perhaps even deaths in this situation, whereas that same social fabric generally does contribute to a population’s health. The pandemic has also had unprecedented effects on differences and inequalities within cities. In cities in the United States, neighborhoods primarily inhabited by African Americans have been disproportionately affected by COVID-19 due to living and health conditions, yet also due to the fact they disproportionately perform vital jobs. Parks and green spaces are crowded, while city centers like Amsterdam’s Red Light District have suddenly lost the bustle of tourism, providing opportunities for citizens to reoccupy scarce public spaces and reclaim ownership. Clearly, such differences between cities are in many cases only discernible to the eye of an expert, possessing the necessary background knowledge to interpret the perceptible local changes caused by the global pandemic. Typically, drawing upon his or her disciplinary training, the expert also knows how to further probe the impact of the pandemic in an appropriate way. However, compared to the usual application of expertise, this crisis situation might, in an unusual way, test even experts. For the pandemic has created a unique situation, imposing unfamiliar constraints on the health, economic, social, and other conditions of cities, constraints that interact in sometimes unexpected ways with each other. Such interactions in turn force experts to collaborate across the boundaries commonly associated with disciplines, their concepts, theories, methods, and assumptions (Klein, 1996). These brief observations of how a virus pandemic can have differential impacts upon various cities, and what this exceptional situation might mean for the application of city methods, allow us to draw a few consequences for the current context of this chapter on interdisciplinary and transdisciplinary research. First, whenever we are investigating a complex and dynamic phenomenon it is by no means easy to determine which disciplinary perspectives are required to do justice to it. Indeed, the choice of useful disciplines can only be made after an initial overview of the situation and a preliminary selection of what appear to be the most important features of the situation. Relevance is key in guiding this selection process and scholars must remain open to the possibility that they may need to revise their earlier assessments of what is relevant and what is not. Second, if scholars from different disciplines were to study different features of a city in isolation, their ‘multidisciplinary’ account would miss important dynamic and complex interactions, such as those between a city’s demographics and geographical situation, its governance and economy. In other words, it is the integration of the perspectives of different disciplines that is crucial, as only then are such interactions taken into account. Indeed, this integration between disciplinary perspectives is what distinguishes an interdisciplinary from a multidisciplinary account. Thirdly, in addition to checking the relevance of disciplines and aiming for their integration, the outcome of interdisciplinary and transdisciplinary research has typically limited generalizability. Since a city is sensitive to a multitude of internal and external dynamical factors, in ways that partly rest upon its socio-cultural history, its investigation will often have the nature of a case study rather than be capable of leading to law-like insights (Krohn, 2010; Menken & Keestra, 2016). As can be seen from these three characteristics of ascertaining the relevance of different disciplinary contributions, the challenge of their integration, and the limited generalizability of their results owing to the specificity of interdisciplinary (ID) and transdisciplinary (TD) research, such research into ‘real world problems’ is clearly distinct from most monodisciplinary research. A consequence of this distinction is the absence of a general ID/TD methodology that can guide specific case studies. By contrast, the collaboration implied in such research requires researchers – and stakeholders, if they are involved – to reflect upon their potential contribution and the implicit assumptions associated with that. We will elaborate on this in the next section. Next, we offer several typologies of integration that urban scholars could employ for their research projects, after which we will offer a few brief analyses of initial collaborations of urban research. Finally, we discuss in more detail the process of the interdisciplinary research project. This will include a brief reflection upon the decision-making process that is implied in such projects. In sum, we aim to provide some guidance in conducting an ID/TD project, albeit not in the form of a definite methodology. (shrink)

This paper addresses a set-theoretic completeness based on a relational semantics for fuzzy extensions of two versions Rt and R T of R (Relevance logic). To this end, two fuzzy logics FRt and FRT as extensions of Rt and R T, respectively, and the relational semantics, so called Routley-Meyer semantics, for them are first recalled. Next, on the semantics completeness results are provided for them using a set-theoretic way.

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic (...) formulas. It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)

Husserl holds that the theoretical sciences should be value-free, i.e., free from the values of extra-scientific practices and guided only by epistemic values such as coherence and truth. This view does not imply that to Husserl the sciences would be immune to all criticism of interests, goals, and values. On the contrary, the paper argues that Husserlian phenomenology necessarily embodies reflection on the epistemic values guiding the sciences. The argument clarifies Husserl’s position by comparing it with the pluralistic position developed (...) in feminist epistemology, according to which sciences may be guided by several competing sets of epistemic values. Further, the existence of alternative epistemic values suggests that choices among such values are social and historically conditioned. Indeed, this is how Husserl’s mature discussion in The Crisis can be understood: his examination of Galileo’s contribution in physics operates as a criticism of the unquestioned dominance of certain set of inherited epistemic values, including the values of accuracy and universal applicability. Indeed, his The Origin of Geometry endorses another set of epistemic values, most importantly that of ontological heterogeneity. Husserl’s analysis demonstrates that the choice of any set of epistemic values is influenced by historical and social factors. Moreover, Husserl argues that we can only avoid biases due to “spells of the time” by continued reflection – Besinnung, in his terms – on the role of values in science. (shrink)

Penelope Maddy’s Second Philosophy is one of the most well-known ap- proaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relations. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and (...) aims of the Second Philosopher’s investigation into set-theoretic methodology; pro- vides a platform to analyze the Second Philosopher’s methods themselves; and can be applied to further questions in the philosophy of set theory. (shrink)

The Riemann zeta function ζ(s) is a central object in number theory and complex analysis, defined for complex variables and intimately connected to the distribution of prime numbers through its zeros. The famous Riemann Hypothesis conjectures that all non-trivial zeros of the zeta function lie on the critical line Re(s) = 1 2 . In this paper, we explore the Riemann zeta function through the lens of set-theoretic and sweeping net methods, leveraging creative comparisons of specific sets to gain (...) deeper insight into the distribution of its zeros. By rewording and analyzing the Riemann Hypothesis using set-theoretic arguments, applying sweeping net techniques, and integrating modal logic interpretations, we aim to provide new perspectives and support for this profound conjecture. Our objectives are: • Define the zeta function and its properties relevant to the zeros. • Reword the Riemann Hypothesis using set-theoretic language and establish logical equivalence. • Introduce and compare specific sets related to the zeros of ζ(s). • Apply set-theoretic and sweeping net methods to analyze the distribution of zeros. • Provide rigorous proofs about the absence of zeros in certain regions, including mechanical justifi- cations with all steps. • Incorporate modal logic interpretations into the proof. • Discuss implications for the Riemann Hypothesis. (shrink)

Pure mathematical truths are commonly thought to be metaphysically necessary. Assuming the truth of pure mathematics as currently pursued, and presupposing that set theory serves as a foundation of pure mathematics, this article aims to provide a metaphysical explanation of why pure mathematics is metaphysically necessary.

Luck egalitarianism is a family of egalitarian theories of distributive justice that aim to counteract the distributive effects of luck. This article explains luck egalitarianism's main ideas, and the debates that have accompanied its rise to prominence. There are two main parts to the discussion. The first part sets out three key moves in the influential early statements of Dworkin, Arneson, and Cohen: the brute luck/option luck distinction, the specification of brute luck in everyday or theoretical terms and the specification (...) of advantage as resources, welfare, or some combination of these. The second part covers three later developments: the democratic egalitarian critique of luck egalitarianism, the luck egalitarian acceptance of pluralism, and luck egalitarian doubts about the significance of the brute luck/option luck distinction. (shrink)

The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion of Tarski’s axiom (...) which implies the existence of inaccessible cardinals. See also related set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC# ∞# , based on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal with set theory NC# ∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens Rule. Nonconservative extensions of the canonical internal set theories IST and HST are proposed. (shrink)

Truth pluralists say that truth-bearers in different “discourses”, “domains”, “domains of discourse”, or “domains of inquiry” are apt to be true in different ways – for instance, that mathematical discourse or ethical discourse is apt to be true in a different way to ordinary descriptive or scientific discourse. Moreover, the notion of a “domain” is often explicitly employed in formulating pluralist theories of truth. Consequently, the notion of a “domain” is attracting increasing attention, both critical and constructive. I argue that (...) this is a red herring. First, I identify the theoretical role for which pluralists appeal to domains, which is to answer what I call the “Individuation Problem”: saying what determines the way in which a particular truth-bearer is apt to be true. Second, I argue that pluralists need not appeal to domains for this purpose. I thus conclude that, despite the usual way of glossing the view, there is no role for the notion of a “domain” to play in the pluralist’s theory of truth. I argue that this defuses the “Problem of Mixed Atomics” and allows the pluralist to sidestep potentially intractable disputes about the nature of domains. (shrink)

This paper introduces and defends an account of model-based science that I dub model pluralism. I argue that despite a growing awareness in the philosophy of science literature of the multiplicity, diversity, and richness of models and modeling practices, more radical conclusions follow from this recognition than have previously been inferred. Going against the tendency within the literature to generalize from single models, I explicate and defend the following two core theses: any successful analysis of models must target sets (...) of models, their multiplicity of functions within science, and their scientific context and history and for almost any aspect x of phenomenon y, scientists require multiple models to achieve scientific goal z. (shrink)

Grounding pluralism is the view that there are multiple kinds of grounding. In this essay, I motivate and defend an explanation-theoretic view of grounding pluralism. Specifically, I argue that there are two kinds of grounding: why-grounding—which tells us why things are the case—and how-grounding—which tells us how things are the case.

Social norms are commonly understood as rules that dictate which behaviors are appropriate, permissible, or obligatory in different situations for members of a given community. Many researchers have sought to explain the ubiquity of social norms in human life in terms of the psychological mechanisms underlying their acquisition, conformity, and enforcement. Existing theories of the psychology of social norms appeal to a variety of constructs, from prediction-error minimization, to reinforcement learning, to shared intentionality, to domain-specific adaptations for norm acquisition. In (...) this paper, we propose a novel methodological and conceptual framework for the cognitive science of social norms that we call normative pluralism. We begin with an analysis of the explanatory aims of the cognitive science of social norms. From this analysis, we derive a recommendation for a reformed conception of its explanandum: a minimally psychological construct that we call normative regularities. Our central empirical proposal is that the psychological underpinnings of social norms are most likely realized by a heterogeneous set of cognitive, motivational, and ecological mechanisms that vary between norms and between individuals, rather than by a single type of process or distinctive norm system. This pluralistic approach, we suggest, offers a methodologically sound point of departure for a fruitful and rigorous science of social norms. (shrink)

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

Evidential Pluralism maintains that in order to establish a causal claim one normally needs to establish the existence of an appropriate conditional correlation and the existence of an appropriate mechanism complex, so when assessing a causal claim one ought to consider both association studies and mechanistic studies. Hitherto, Evidential Pluralism has been applied to medicine, leading to the EBM+ programme, which recommends that evidence-based medicine should systematically evaluate mechanistic studies alongside clinical studies. This paper argues that Evidential (...) class='Hi'>Pluralism can also be fruitfully applied to the social sciences. In particular, Evidential Pluralism provides (i) a new approach to evidence-based policy; (ii) an account of the evidential relationships in more theoretical research; and (iii) new philosophical motivation for mixed methods research. The application of Evidential Pluralism to the social sciences is also defended against two objections. (shrink)

Value pluralists see themselves as philosophical grown-ups. They profess to face reality as it is and accept resultant pessimism, while criticising their monist rivals for holding on to the naïve idea that the right, the good and the beautiful are ultimately harmonisable with each other. The aim of this essay is to challenge this self-image of value pluralists. Notwithstanding its usefulness as a means of subverting monist dominance, I argue that the self-image has the downside of obscuring various theoretical positions (...) that do not fall into either the pluralist or monist camp. Yet such positions do exist, as shown by my discussion of Albert Camus and Hannah Arendt. Near contemporaries of the pioneering value pluralist Isaiah Berlin, the pair, just like him, sought to be realistic about the lived experiences of political disasters and moral disorientation in the twentieth century. Moreover, they shared with Berlin a keen interest in real-world moral dilemmas, which seemed to them to have made traditional morality obsolete. But the three thinkers’ perspectives on ‘reality’ hardly converged, and neither Camus nor Arendt became a value pluralist as a result of their reflections on moral dilemmas. This, however, by no means indicates the pair’s immaturity. Rather, it shows that there is more than one way of observing fidelity to our actual experience and that value pluralists’ commitment to realism and resultant pessimism is not as uniquely mature as they would have us believe. (shrink)

This paper outlines a new pluralistic theory of normative reasons for belief, welfarist pluralism, which aims to explain how there can be basic alethic/epistemic reasons for belief and basic pragmatic/non-alethic reasons for belief that can combine to determine what one ought to believe. The paper shows how this non-derivative first-order pluralism arises from a purely welfarist account of the foundations of theoretical normativity, thereby combining foundational pragmatism with non-derivative pluralism about normative reasons for belief. In addition, this (...) paper outlines how welfarist pluralism provides a new and potentialy attractive account of the value of truth (or its indicators), namely that the value of truth (or its indicators) is its direct contribution to individuals' personal good or wellbeing. (shrink)

Explanatory pluralism holds that the sorts of comprehensive theoretical and ontological economies, which microreductionists and New Wave reductionists envision and which antireductionists fear, offer misleading views of both scientific practice and scientific progress. Both advocates and foes of employing reductionist strategies at the interface of psychology and neuroscience have overplayed the alleged economies that interlevel connections (including identities) justify while overlooking their fundamental role in promoting scientific research. A brief review of research on visual processing provides support for the (...) explanatory pluralist=s general model of cross-scientific relations and discloses the valuable heuristic role hypothetical identities play in cross-scientific research. That model also supplies grounds for hesitation about the correlation objection to the psycho-physical identity theory and complaints about an explanatory gap in physicalist accounts of consciousness. These takes on psycho-neural connections miss both the sorts of considerations that motivate hypothetical identities in science and their fundamental contribution to progressive research. Thus, their focus on the contributions of research at multiple levels of analysis does not bar explanatory pluralists from considering heuristic identity theory (HIT). Arguably, it encourages it. (shrink)

Pluralism is relevant to conceptual engineering in many ways. First of all, we face the issue of pluralism when trying to characterise the very object(s) of conceptual engineering. Is it just concepts? Could concepts be pluralistically conceived for the purposes of conceptual engineering? Or rather, is it concepts and other representational devices as well? Second, one may wonder whether concepts have only one function in our mental life (representation) or, rather, a plurality of functions (including non-representational ones). Third, (...) it is a contended question whether conceptual engineering projects should pursue only one set of values and goals (epistemic ones) or, rather, a variety of values and goals, including non-epistemic ones. Finally, the engineering of a concept may result in a form of “local” conceptual pluralism, which gives rise to its own ontological and semantic challenges. Having explored the various ways in which pluralism becomes important for conceptual engineers, this contribution presents and summarizes the articles published in this special issue. (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...) of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

Animal welfare has a long history of disregard. While in recent decades the study of animal welfare has become a scientific discipline of its own, the difficulty of measuring animal welfare can still be vastly underestimated. There are three primary theories, or perspectives, on animal welfare - biological functioning, natural living and affective state. These come with their own diverse methods of measurement, each providing a limited perspective on an aspect of welfare. This paper describes a perspectival pluralist account of (...) animal welfare, in which all three theoretical perspectives and their multiple measures are necessary to understand this complex phenomenon and provide a full picture of animal welfare. This in turn will offer us a better understanding of perspectivism and pluralism itself. (shrink)

This brief commentary has three goals. The first is to argue that ‘‘framework debate’’ in cognitive science is unresolvable. The idea that one theory or framework can singly account for the vast complexity and variety of cognitive processes seems unlikely if not impossible. The second goal is a consequence of this: We should consider how the various theories on offer work together in diverse contexts of investigation. A final goal is to supply a brief review for readers who are compelled (...) by these points to explore existing literature on the topic. Despite this literature, pluralism has garnered very little attention from broader cognitive science. We end by briefly considering what it might mean for theoretical cognitive science. (shrink)

Pragmatism and the correspondence theory of truth are longtime foes. Nevertheless, there is an argument to be made that pragmatists must embrace truth as correspondence. I show that there is a distinctive pragmatic utility to taking truth to be correspondence, and I argue that it would be inconsistent for pragmatists to accept the utility of the belief that truth is correspondence while resisting the premise that this belief is correct. -/- In order to show how pragmatists can embrace truth as (...) correspondence, I develop a kind of alethic pluralism, which treats pragmatist truth as theoretically fundamental to truth as correspondence. This theoretical fundamentality of pragmatist truth allows the pragmatist to conditionally accept truth as correspondence for certain discourses without falling prey to the typical pragmatist objections to correspondence. This pluralist account of truth thus allows pragmatists to concede that, for certain domains of discourse, truth is correspondence, without thereby betraying their pragmatist principles. (shrink)

One of the most fascinating debates in the field of political theory has been the one about the relationship between value pluralism and liberalism. Based on their different conceptions and definitions, various theorists have often theorized a tension in the relationship between pluralism and liberalism. On the one hand, liberal authors who believe in the universality of liberal values that have to do with the safeguard of freedom (conceived at least to some extent as “negative freedom”), in the (...) expressions and the free choices that individuals within a society or group can make, tolerance, in their individuality, in the equality of opportunities for everyone, etc., and on the other hand, the pluralists, who emphasize that different values, beliefs and human goods (the diversity) in society are essentially incompatible with one another, and as such, also incommensurable. Against the positions of some various authors who theorize an inherent conflict between these two ideas, in this paper, we argue that in practice, but also theoretically justified, there is a connection and a mutual support relationship existing between pluralism and liberalism. Therefore, the main principles that pluralism protects, such as pluralism of value, incommensurability between multiple conceptions of the goods, etc., can find themselves best in the context of a liberal society. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of (...) categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

Truth pluralists say that the nature of truth varies between domains of discourse: while ordinary descriptive claims or those of the hard sciences might be true in virtue of corresponding to reality, those concerning ethics, mathematics, institutions might be true in some non-representational or “anti-realist” sense. Despite pluralism attracting increasing amounts of attention, the motivations for the view remain underdeveloped. This paper investigates whether pluralism is well-motivated on ontological grounds: that is, on the basis that different discourses are (...) concerned with different kinds of entities. Arguments that draw on six different ontological contrasts are examined: concrete versus abstract entities; mind-independent versus mind-dependent entities; sparse versus merely abundant properties; objective versus projected entities; natural versus non-natural entities; and ontological pluralism. I argue that the additional premises needed to move from such contrasts to truth pluralism are either implausible or unmotivated, often doing little more than to bifurcate the nature of truth when a more theoretically conservative option is available. If there is a compelling motivation for pluralism, I suggest, it’s likely to lie elsewhere. (shrink)

I defend a radical interpretation of biological populations—what I call population pluralism—which holds that there are many ways that a particular grouping of individuals can be related such that the grouping satisfies the conditions necessary for those individuals to evolve together. More constraining accounts of biological populations face empirical counter-examples and conceptual difficulties. One of the most intuitive and frequently employed conditions, causal connectivity—itself beset with numerous difficulties—is best construed by considering the relevant causal relations as ‘thick’ causal concepts. (...) I argue that the fine-grained causal relations that could constitute membership in a biological population are huge in number and many are manifested by degree, and thus we can construe population membership as being defined by massively multidimensional constructs, the differences between which are largely arbitrary. I end by showing that positions in two recent debates in theoretical biology depend on a view of biological populations at odds with the pluralism defended here. (shrink)

Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in (...) themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

There are a number of debates that are relevant to questions concerning objectivity in science. One of the eldest, and still one of the most intensely fought, is the debate over epistemic relativism. —All forms of epistemic relativism commit themselves to the view that it is impossible to show in a neutral, non-question-begging, way that one “epistemic system”, that is, one interconnected set of epistemic standards, is epistemically superior to others. I shall call this view “No-metajustification”. No-metajustification is commonly taken (...) to deny the objectivity of standards. In this paper I shall discuss two currently popular attempts to attack “No-metajustification”. The first attempt attacks no-metajustification by challenging a particular strategy of arguing in its defence: this strategy involves the ancient Pyrrhonian “Problem of the Criterion”. The second attempt to refute No-metajustification targets its metaphysical underpinning: to wit, the claim that there are, or could be, several fundamentally different and irreconcilable epistemic systems. I shall call this assumption “Pluralism”. I shall address three questions with respect to these attempts to refute epistemic relativism by attacking no-metajustification: Can the epistemic relativist rely on the Problem of the Criterion in support of No-metajustification? Is a combination of Chisholmian “particularism” and epistemic naturalism an effective weapon against No-metajustification? And is Pluralism a defensible assumption? (shrink)

Background and Objectives: In this research article, the researcher addresses the issue of creating public understanding in a democratic society about the progress of science, with an emphasis on pluralism from philosophers of science. The idea that there is only one truth and that there are just natural laws awaiting discovery by scientists has historically made it difficult to explain scientific progress. This belief motivates science to develop theories that explain the unity of science, and it is thought that (...) diversity in the way different ideas presented by scientists is a problem that results in time being wasted in search of the most accurate theory. Some scientists perceive a benefit in having a range of scientific hypotheses, though. One benefit that is frequently cited is that scientific diversity as a whole contributes to the development of a democratic society that permits the expression of a range of viewpoints. The road to accountable scientific pluralism is fraught with difficulties, though. Therefore, it is crucial to take into account both pluralism's advantages and disadvantages. This research aims at: 1. analyzing in an epistemological way the interpretation of scientific theories and the progress of science from the perspectives of scientific pluralists; 2. analyzing the relationship between science and democracy in explaining scientific significance and progress; and 3. synthesizing new knowledge on epistemic dependentism and to argue that it plays a significant role in evaluating research issues related to scientific pluralism. Methodology: The research methodology involves the application of documentary investigation along with philosophical discourse. The method of philosophical argumentation involves analyzing the lines of arguments found in relevant academic publications in order to assess their validity and soundness. Main Results: One key argument of the pluralists is the use of the concept of theoretical pluralism, which suggests that scientific knowledge is created from a variety of perspectives according to the social and cultural context of knowledge creation. It is found that part of Longino's argument is based on the negation of rational/social dichotomy. Moreover, her theory is a departure from philosopher of science Philip Kitcher, who advocates the creation of scientific knowledge and the evaluation of scientific progress through the means of democratic society. He explains that these procedures will lead to "well-ordered science" in democratic society. Discussions: The researcher examines the underlying ideas accepted by these two philosophers of science and finds that although their opinions differ, they have common ground in the acceptance of consensus. However, the views of both philosophers still lack weight in explaining the knowledge itself. The researcher argues that the acceptance of pluralism as a way of understanding scientific progress necessarily lends itself to dependentism, which points to interdependence in comparisons of superiority/inferiority between scientific theories. It is undeniable that the situation has emerged all the time, even though the success of the scientific theories being compared to each other comes from different social and cultural grounds of thought. Conclusions: Some popular models of scientific pluralism in the philosophy of science still lack a compelling justification, particularly on the epistemic grounds. By elucidating the epistemic significance of the interdependence of these things, scientific pluralism can be strengthened by incorporating the notion of epistemic dependentism into the analysis of scientific progress. (shrink)

The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation (...) and semi-negations. (shrink)

The focus in this essay will be upon the paradoxes, and foremostly in set theory. A central result is that the librationist set theory £ extension \Pfund $\mathscr{HR}(\mathbf{D})$ of \pounds \ accounts for \textbf{Neumann-Bernays-Gödel} set theory with the \textbf{Axiom of Choice} and \textbf{Tarski's Axiom}. Moreover, \Pfund \ succeeds with defining an impredicative manifestation set $\mathbf{W}$, \emph{die Welt}, so that \Pfund$\mathscr{H}(\mathbf{W})$ %is a model accounts for Quine's \textbf{New Foundations}. Nevertheless, the points of view developed support the view that the truth-paradoxes and (...) the set-paradoxes have common origins, so that the librationist resolutions of the set theoretic paradoxes are at the same time resolutions of the truth theoretic paradoxes. Both the librationist resolutions of the set theoretic paradoxes and the truth theoretic paradoxes have non-trivial philosophical implications: librationist set theories have the consequence that there are no absolutely uncountable sets, and librationist truth theories allow the use of syntactical modalities in ways which circumvent limitations as those of \parencite{Montague1963}, and a truth predicate which is useful for more precise philosophical discourse. (shrink)