Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...) Replies5.1 Yablo’s likely response5.2 Charity6 Conclusion. (shrink)

Much recent discussion in the philosophy of mathematics has concerned the indispensability argument—an argument which aims to establish the existence of abstract mathematical objects through appealing to the role that mathematics plays in empirical science. The indispensability argument is standardly attributed to W. V. Quine and Hilary Putnam. In this paper, I show that this attribution is mistaken. Quine's argument for the existence of abstract mathematical objects differs from the argument which many philosophers of mathematics ascribe to him. Contrary to (...) appearances, Putnam did not argue for the existence of abstract mathematical objects at all. I close by suggesting that attention to Quine and Putnam's writings reveals some neglected arguments for platonism which may be superior to the indispensability argument. (shrink)

This paper discusses the significance of non-causal dependence for truthmaker theory. After introducing truthmaker theory (section 1), I discuss a challenge to it levelled by Benjamin Schnieder. I argue that Schnieder’s challenge can be met once we acknowledge the existence of non-causal dependence and of explanations which rely on it (sections 2 to 5). I then mount my own argument against truthmaker theory, based on the notion of non-causal dependence (sections 6 and 7).

Platonism in the philosophy of mathematics is the doctrine that there are mathematical objects such as numbers. John Burgess and Gideon Rosen have argued that that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either rely on a dubious epistemology, or resemble a dubious sceptical argument concerning perceptual knowledge. Against Burgess and Rosen, I show that an epistemological anti- platonist argument proposed by Hartry Field avoids both horns of their dilemma.

Truthmaker theory promises to do some useful philosophical work: equipping us to argue against phenomenalism and Rylean behaviourism, for instance, and helping us decide what exists (Lewis 1999, 207; Armstrong 1997, 113-119). But it has proved hard to formulate a truthmaker theory that is both useful and believable. I want to suggest that a neglected approach to truthmakers – that of Ian McFetridge – can surmount some of the problems that make other theories of truthmaking unattractive. To begin with, I’ll (...) outline some of the most prominent accounts of truthmaking in the current literature. Then the second part of the paper will explain McFetridge’s theory and argue for its superiority over these accounts. (shrink)

I defend Joseph Melia’s nominalist account of mathematics from an objection raised by Mark Colyvan.

Truthmaker theorists claim that for every truth, there is something in virtue of which it is true—or, more cautiously, that for every truth in some specified class of truths, there is something in virtue of which it is true. I argue that it is hard to see how the thought that truth is grounded in reality lends any support to truthmaker theory.

in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions between (...) different contexts of utterance. I present an alternative response which involves the negation of that claim, and argue that it is preferable to van Inwagen’s. (shrink)

The Brock-Rosen problem has been one of the most thoroughly discussed objections to the modal fictionalism bruited in Gideon Rosen’s ‘Modal Fictionalism’. But there is a more fundamental problem with modal fictionalism, at least as it is normally explained: the position does not resolve the tension that motivated it. I argue that if we pay attention to a neglected aspect of modal fictionalism, we will see how to resolve this tension—and we will also find a persuasive reply to the Brock-Rosen (...) objection. Finally, I discuss an alternative reading of Rosen, and argue that this position is also able to fend off the Brock-Rosen objection. (shrink)

Many philosophers of mathematics are attracted by nominalism – the doctrine that there are no sets, numbers, functions, or other mathematical objects. John Burgess and Gideon Rosen have put forward an intriguing argument against nominalism, based on the thought that philosophy cannot overrule internal mathematical and scientific standards of acceptability. I argue that Burgess and Rosen’s argument fails because it relies on a mistaken view of what the standards of mathematics require.

Many contemporary philosophers rate error theories poorly. We identify the arguments these philosophers invoke, and expose their deficiencies. We thereby show that the prospects for error theory have been systematically underestimated. By undermining general arguments against all error theories, we leave it open whether any more particular arguments against particular error theories are more successful. The merits of error theories need to be settled on a case-by-case basis: there is no good general argument against error theories.

There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...) can be swiftly and decisively dispatched by appeal to disciplines other than philosophy. In this paper we will argue that such an attitude of uncritical deference to any non-philosophical discipline is badly misguided. With reference to the work of John Burgess and David Lewis, we consider deference to mathematics. We show that deference to mathematics is implausible and that main arguments for it fail. With reference to the work of Michael Blome-Tillmann, we consider deference to linguistics. We show that his arguments appealing to deference to linguistics are unsuccessful. We then show that naturalism does not entail deferentialism and that naturalistic considerations even motivate some anti-deferentialist views. Finally, we set out deferentialism’s failings and present our own anti-deferentialist approach to philosophical inquiry. (shrink)

Do numbers exist? Do properties? Do possible worlds? Do fictional characters? Many metaphysicians spend time and effort trying to answer these and other questions about the existence of various entities. These inquiries have recently encountered opposition: a group of philosophers, drawing inspiration from Aristotle, have argued that many or all of the existence questions debated by metaphysicians can be answered trivially, and so are not worth debating. Our task is to defend existence questions from the neo-Aristotelians' attacks.

Animalism is the theory that we are animals: in other words, that each of us is numerically identical to an animal. An alternative theory maintains that we are not animals but that each of us is constituted by an animal. Call this alternative theory neo-Lockean constitutionalism or Lockeanism for short. Stephan Blatti (2012) offers to advance the debate between animalism and Lockeanism by providing a new argument for animalism. In this note, we present our own objection to Blatti's argument, and (...) argue that Carl Gillett's earlier reply misses the fundamental problem. We also use Blatti's argument to illustrate a common methodological error, namely, uncritical deference to best theories from other disciplines. (shrink)

Some philosophers deny the existence of composite material objects. Other philosophers hold that whenever there are some things, they compose something. The purpose of this paper is to scrutinize an objection to these revisionary views: the objection that nihilism and universalism are both unacceptably uncharitable because each of them implies that a great deal of what we ordinarily believe is false. Our main business is to show how nihilism and universalism can be defended against the objection. A secondary point is (...) that universalism is harder to defend than nihilism. (shrink)

The zetetic turn in epistemology raises three questions about epistemic and zetetic norms. First, there is the relationship question: what is the relationship between epistemic and zetetic norms? Are some epistemic norms zetetic norms, or are epistemic and zetetic norms distinct? Second, there is the tension question: are traditional epistemic norms in tension with plausible zetetic norms? Third, there is the reaction question: how should theorists react to a tension between epistemic and zetetic norms? Drawing on an analogy to practical (...) philosophy, I develop a focal point view to resolve these motivating questions. On the focal point view, traditional epistemic norms and zetetic norms answer different types of normative questions. There is nevertheless a familiar type of evaluative tension between traditional epistemic norms and zetetic norms, but this tension is an unavoidable feature of the normative landscape and not a sign that traditional epistemic norms need revision. But if traditional epistemic norms are not zetetic norms, then in what sense is zetetic epistemology a project for epistemologists? I conclude by articulating a sense in which some nontraditional epistemic norms are zetetic norms, and in which zetetic epistemology is an important part of the study of theoretical rationality. (shrink)

We start by presenting three different views that jointly imply that every person has many conscious beings in their immediate vicinity, and that the number greatly varies from person to person. We then present and assess an argument to the conclusion that how confident someone should be in these views should sensitively depend on how massive they happen to be. According to the argument, sometimes irreducibly de se observations can be powerful evidence for or against believing in metaphysical theories.

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.

In different papers, David Liggins and Chris Daly tell philosophers what they should not do. There is no sign of them withdrawing any of these prohibitions, but I show that they fail to be consistent when asserting them. The inconsistency concerns when a philosopher should defer to the empirical findings of science.

Our aim in this entry is to articulate the state of the art in the moral psychology of personal identity. We begin by discussing the major philosophical theories of personal identity, including their shortcomings. We then turn to recent psychological work on personal identity and the self, investigations that often illuminate our person-related normative concerns. We conclude by discussing the implications of this psychological work for some contemporary philosophical theories and suggesting fruitful areas for future work on personal identity.

Bounded rationality gets a bad rap in epistemology. It is argued that theories of bounded rationality are overly context‐sensitive; conventionalist; or dependent on ordinary language (Carr, 2022; Pasnau, 2013). In this paper, I have three aims. The first is to set out and motivate an approach to bounded rationality in epistemology inspired by traditional theories of bounded rationality in cognitive science. My second aim is to show how this approach can answer recent challenges raised for theories of bounded rationality. My (...) third aim is to clarify the role of rational ideals in bounded rationality. (shrink)

A familiar interpretation of quantum mechanics (one of a number of views sometimes labeled the "Copenhagen interpretation'"), takes its empirical apparatus at face value, holding that the quantum wave function evolves by the Schrödinger equation except on certain occasions of measurement, when it collapses into a new state according to the Born rule. This interpretation is widely rejected, primarily because it faces the measurement problem: "measurement" is too imprecise for use in a fundamental physical theory. We argue that this is (...) a weak objection, as there may be many ways of making "measurement" precise. However, measurement-collapse interpretations face a more serious objection: a dilemma tied to the quantum Zeno effect. Is measurement itself an observable that can enter superpositions? If yes, then the standard measurement-collapse dynamics is ill-defined. If no, then (at least if measurement is an observable), measurements can never start or finish. The best way out is to deny that measurement is an observable, but this leads to strong and revisionary consequences. This reinforces the view that there is no nonrevisionary interpretation of quantum mechanics. (shrink)

This paper explores an initially attractive principle connecting beliefs in general with beliefs about what beliefs are rational. The principle turns out to be violated by intuitively rational beliefs in some situations. The paper lays out some options for reacting to this fact.

Hylomorphists hold that substances are, in some sense, composites of matter and form. The form of a substance is typically taken to play a fundamental role in determining the unity or identity of the whole. Staunch hylomorphists think that this role is of a kind that precludes the ontological reduction of form to the physical and thus take their position to be inconsistent with physicalism. Forms, according to staunch hylomorphism, play a fundamental role in grounding their bearers’ proper parts and (...) that, it seems, rules out the physical grounding of form itself. I shall develop a physicalist version of hylomorphism that treats form as geometric structure and which, I shall argue, entails many of the central theses endorsed by staunch hylomorphists. Based on Shoemaker’s notion of conditional powers, I shall argue that the geometric structures of complex wholes are the conditions on at least some of the conditional powers of their bearers’ proper parts, transforming those powers into powers simpliciter. Thus, forms play a fundamental role in the dynamical evolution of the physical world, but without bestowing causal powers themselves and hence without violating the causal closure of the physical domain. If a substance’s proper parts are taken to be individuated by their powers simpliciter, then they derive their identities from their places in the substantial whole, which thus determines the identities of its proper parts without changing their intrinsic natures. (shrink)

Perceptualists say that having a pain in a body part consists in perceiving the part as instantiating some property. I argue that perceptualism makes better sense of the connections between pain location and the experiences undergone by people in pain than three alternative accounts that dispense with perception. Turning to fellow perceptualists, I also reject ways in which David Armstrong and Michael Tye understand and motivate perceptualism, and I propose an alternative interpretation, one that vitiates a pair of objections—due (...) to John Hyman—concerning the meaning of ‘Amy has a pain in her foot’ and the idea of bodily sensitivity. Perceptualism, I conclude, remains our best account of the location of pains. (shrink)

The Quality of Thought develops and defends the thesis that thinking is a kind of experience, characterized by a sui generis (“cognitive”) phenomenology, determinates of which are thought contents—what I call the phenomenal intentionality of thought thesis. It draws out the implications of this thesis for issues in philosophy of mind, philosophy of language and metaphysics. The view defended is radically internalist and intensionalist, and thus goes against received doctrines in philosophy of mind (externalism) and language (extensionalism). It also advocates (...) for a metaphysically neutral, non-naturalistic approach to the philosophical study of mind—what I call “Analytic Phenomenology”—in combination with agnosticism about the nature of the relationship between consciousness and physical reality. -/- The book identifies persistent problems with Dretske-inspired causal-informational-teleological theories of conceptual content, and diagnoses them as due to leaving out what it’s like to think a thought—to entertain or grasp a propositional (conceptual) content. It is thus a contribution to the increasingly influential Phenomenal Intentionality Research Program. It includes refutations of classic externalism (Putnam and Burge) and arguments that standard motivations for direct reference theories of names (Kripke), indexicals and demonstratives (Kaplan) are not inevitable, and alternative accounts of their (and their conceptual equivalents’) semantics. It also addresses outstanding challenges to the phenomenal intentionalist view of thought content, including the existence of unconscious thought, the elusiveness of conceptual phenomenology, the matching content problem, phenomenal compositionality, and the determination of conceptual reference. (shrink)

There is a difference between merely thinking that P and really grasping that P. For example, Jackson's (1982) black-and-white Mary cannot (before leaving her black-and-white room) fully grasp what it means to say that fire engines are red, but she can perfectly well entertain the thought that fire engines are red. The contrast between merely thinking and grasping is especially salient in the context of certain moral decisions. For example, an individual who grasps the plight of starving children thanks to (...) evocative images seems much more likely to donate for the children's benefit than someone who is merely told about their plight. This paper offers a phenomenal account of grasping according to which grasping a content (whether a proposition or concept) consists in one's thoughts about the content being constituted by phenomenal experiences of constituents of the content. This account improves on earlier phenomenal accounts of grasping (Bourget 2017a, 2018) by allowing for partial grasping and generalizing to concepts. The paper also addresses objections to phenomenal accounts of grasping, including the objection that recent developments in AI technology show that consciousness is irrelevant to grasping and understanding. (shrink)

Longtermists have recently argued that it is overwhelmingly important to do what we can to mitigate existential risks to humanity. I consider three mistakes that are often made in calculating the value of existential risk mitigation. I show how correcting these mistakes pushes the value of existential risk mitigation substantially below leading estimates, potentially low enough to threaten the normative case for existential risk mitigation. I use this discussion to draw four positive lessons for the study of existential risk. -/- (...) . (shrink)

According to intentionalism, the phenomenal character of experience is one and the same as the intentional content of experience. This view has a problem with moods (anxiety, depression, elation, irritation, gloominess, grumpiness, etc.). Mood experiences certainly have phenomenal character, but do not exhibit directedness, i.e., do not appear intentional. Standardly, intentionalists have re-described moods’ undirectedness in terms of directedness towards everything or the whole world (e.g., Crane, 1998; Seager, 1999). This move offers the intentionalist a way out, but is quite (...) unsatisfying. More recently, Angela Mendelovici (2013a, b) has suggested something that looks more interesting and promising: instead of re-describing moods’ phenomenology, she accepts its undirectedness at face value and tries to explain it in intentionalist terms. In this paper, I focus on and criticize Mendelovici’s proposal. As I will show, despite its prima facie virtues, the view is poorly motivated. For, contrary to what Mendelovici argues, introspection does not support her proposal—arguably, it provides some evidence against it. So, the problem that intentionalism has with moods is not solved, but is still there. (shrink)

Transdisciplinary research knits together knowledge from diverse epistemic communities in addressing social-environmental challenges, such as biodiversity loss, climate crises, food insecurity, and public health. This paper reflects on the roles of philosophy of science in transdisciplinary research while focusing on Indigenous and other subaltern forms of knowledge. We offer a critical assessment of demarcationist approaches in philosophy of science and outline a constructive alternative of transdisciplinary philosophy of science. While a demarcationist focus obscures the complex relations between epistemic communities, transdisciplinary (...) philosophy of science provides resources for meeting epistemic and political challenges of collaborative knowledge production. (shrink)

This paper is an explication of Gadamer's idea of "application." I argue that the relation between the first and third persons in application contains a viable conception of the normativity of understanding. Application includes a measure for understanding. The thing that is to be understood must be allowed to address me, and such involvement responds to the text’s meaning. While this measure is not expressible in principled rules, application is normatively accountable both to the text’s third-person claim to meaning and (...) to my first-person involvement with the text. The participation of the interpreter with the item of her understanding forms a normative standard. (shrink)

In this paper, we discuss the inherent temporal orientation of fear, a matter on which philosophers seem to have contrasting opinions. According to some, fear is inherently present-oriented; others instead maintain that it is inherently future-oriented or that it has no inherent temporal orientation at all. Despite the differences, however, all these views seem to understand fear’s temporal orientation as one-dimensional—that is, as uniquely determined by the represented temporal location of the intentional object of fear. By contrast, we present a (...) view that introduces a two-dimensional account of fear’s temporal orientation. On such a view, we can say that fear is inherently future-oriented, independently of its being about something in the present or in the future. (shrink)

This paper is on the metaphysics and normativity of Jewish identity. It starts with a metaphysical question: “Can a Jewish person become non-Jewish?” This question and the related question “What is Jewishness?” are both ambiguous, because the word “Jewish” is ambiguous. The paper outlines five concepts of Jewishness: halachic, religious, ethnic, and cultural Jewishness, as well as being Jewish in the sense of belonging to the Jewish community. In some of these senses of “Jewish” a Jewish person is always Jewish. (...) In other senses a Jewish person can become non-Jewish. The paper closes with a normative question: Should a person who is Jewish, in the sense of belonging to the Jewish community, become non-Jewish? The paper explains reasons for and against staying in the Jewish community and in doing so highlights a tension, rather than telling anyone how they should identify. (shrink)

According to a traditional Cartesian epistemology of perception, perception does not provide one with direct knowledge of the external world. Instead, your immediate perceptual evidence is limited to facts about your own visual experience, from which conclusions about the external world must be inferred. Cartesianism faces well-known skeptical challenges. But this chapter argues that any anti-Cartesian view strong enough to avoid these challenges must license a way of updating one’s beliefs in response to anticipated experiences that seems diachronically irrational. To (...) avoid this result, the anti-Cartesian must either license an unacceptable epistemic chauvinism, or else claim that merely reflecting on one’s experiences defeats perceptual justification. This leaves us with a puzzle: Although Cartesianism faces problems, avoiding them brings a new set of problems. (shrink)

Corruptionism is the view that following physical death, the human being ceases to exist but their soul persists in the afterlife. Survivalism holds that both the human being and their soul persist in the afterlife, as distinct entities, with the soul constituting the human. Each position has its defenders, most of whom appeal both to metaphysical considerations and to the authority of St Thomas Aquinas. Corruptionists claim that survivalism violates a basic principle of any plausible mereology, while survivalists tend to (...) reject the principle, though without as much detail as one would like. In this paper I examine both the key exegetical issues and the mereological question, arguing that Aquinas cannot be shown to have supported the principle in question, and that the principle should be rejected on independent grounds. If correct, some key planks in support of survivalism are established, with others to await further examination. (shrink)

There is an apparent tension in Shepherd’s accounts of space and time. Firstly, Shepherd explicitly claims that we know that the space and time of the unperceived world exist because they cause our phenomenal experience of them. Secondly, Shepherd emphasizes that empty space and time do not have the power to effect any change in the world. My proposal is that for Shepherd time has exactly one causal power: to provide for the continued existence of self-same or changing objects. Because (...) Shepherd takes causation to be a relation whereby two objects combine to form a third, their effect, whenever we perceive a continually existing object, since time is a proper part of such objects, our perception of time is caused by time itself. Likewise, space’s causal power is to provide for the possibility of the motion or rest of objects, and so when we perceive objects with space as a proper part, we come into causal contact with space. (shrink)

David Liggins and Chris Daly have argued against a recent trend in which some philosophical debate or other is said to be settled by claims from a discipline other than philosophy, because claims from that discipline entail a position on the debate and any claims from that discipline have greater authority than any philosophical claims when the aim is to extend our knowledge. They label this trend deferentialism. This paper presents a dilemma for their argument.

Dark matter has never been detected, yet it is a key part of the dominant theory of cosmology. An alternative theory, MOND, is empirically equivalent and more successful at making predictions. But the fact that it has no place for the existence of dark matter is a problem for scientific realists who see science as building on past theories.

Since the 1990s the so-called transparency of experience has played a crucial role in core debates in philosophy of mind. However, recent developments in the literature have made transparency itself quite opaque. The very idea of transparent experience has become quite fuzzy, due to the articulation of many different notions of transparency and transparency theses. Absent a unified logical space where these notions and theses can be mapped and confronted, we are left with an overall impression of conceptual chaos. This (...) is a problem, given the constant and ubiquitous references to transparency in the literature and its prominent position in the contemporary philosophy of mind. My goal in this paper is to restore clarity through proper analysis of the mutual relations between the different transparency theses. This allows me to uncover a unitary multidimensional logical space where existing (as well as possible) views can be properly singled out and located. (shrink)

This chapter explores the relationship between ethical judgement writ large (as opposed to merely moral judgement) and motivation. We discuss arguments for and against views on which ethical judgement entails motivation, either alone or under conditions of rationality or normalcy, either at the individual or community level.

I argue that the debate concerning the nature of first-person moral judgment, namely, whether such moral judgments are inherently motivating or whether moral judgments can be made in the absence of motivation, may be founded on a faulty assumption: that moral judgments form a distinct kind that must have some shared, essential features in regards to motivation to act. I argue that there is little reason to suppose that first-person moral judgments form a homogenous class in this respect by considering (...) an ordinary case: student readers of Peter Singer’s “Famine, Affluence, and Morality”. Neither internalists nor externalists can provide a satisfying account as to why our students fail to act in this particular case, but are motivated to act by their moral judgments in most cases. I argue that the inability to provide a satisfying account is rooted in this shared assumption about the nature of moral judgments. Once we consider rejecting the notion that first-person moral decision- making forms a distinct kind in the way it is typically assumed, the internalist/externalist debate may be rendered moot. (shrink)

The chapter challenges hyperbolic claims about the centrality of appreciation of beauty to Buddhism. Within the texts, attitudes are more mixed, except for a form of 'inner beauty' - the beauty found in the expression of virtues or wisdom in forms of bodily comportment. Inner beauty is a stable presence throughout Buddhist history, practices, and art.

The thesis that nothing is true has long been thought to be a self-refuting position not worthy of serious philosophical consideration. Recently, however, the thesis of alethic nihilism—that nothing is true—has been explicitly defended (notably by David Liggins). Nihilism is also, I argue, a consequence of other views about truth that have recently been advocated, such as fictionalism about truth and the inconsistency account. After offering an account of alethic nihilism, and how it purports to avoid the self-refutation (...) problem, I argue that it avoids the problem at the expense of changing the subject. I then present other arguments against nihilism and responses to the considerations offered in defense of it. The only tenable position is that something is indeed true. (shrink)

Comments and replies from the 2021 Eastern APA book symposium on Jill North's Physics, Structure, and Reality.

Formally inclined epistemologists often theorize about ideally rational agents—agents who exemplify rational ideals, such as probabilistic coherence, that human beings could never fully realize. This approach can be defended against the well-known worry that abstracting from human cognitive imperfections deprives the approach of interest. But a different worry arises when we ask what an ideal agent should believe about her own cognitive perfection (even an agent who is in fact cognitively perfect might, it would seem, be uncertain of this fact). (...) Consideration of this question reveals an interesting feature of the structure of our epistemic ideals: for agents with limited information, our epistemic ideals turn out to conflict with one another. This suggests that we must revise the way we see ideal agents in epistemic theorizing. (shrink)

In virtue of what are later and an earlier group members of one and the numerically same tradition? Gallie was one of the few philosophers to have engaged with issues surrounding this question. My article is not a faithful exegesis of Gallie but develops a terminology in which to discuss issues surrounding the numerical identity of a tradition over time, based on some of his insights.