I begin by drawing a parallel between the intuitionistic understanding of quantification over all natural numbers and the generality relativist understanding of quantification over absolutely everything. I then argue that adoption of an intuitionistic reading of relativism not only provides an immediate reply to the absolutist's charge of incoherence but it also throws a new light on the debates surrounding absolute generality.

This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (a sequence which (...) includes one task done for each ordinal number—thus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible. (shrink)

An introduction to composition, persistence, and identity.

Orthodoxy says that the thesis that composition is identity (CAI) entails universalism: the claim that any collection of entities has a sum. If this is true it counts in favour of CAI, since a thesis about the nature of composition that settles the otherwise intractable special composition question (SCQ) is desirable. But I argue that it is false: CAI is compatible with the many forms of restricted composition, and SCQ is no easier to answer given CAI than otherwise. Furthermore, in (...) seeing why this is the case we reveal an objection to CAI: that it allows for the facts concerning what there is to be settled whilst leaving open the question about what is identical to what. (shrink)

This paper responds to John Burgess's ‘Mathematics and _Bleak House_’. While Burgess's rejection of hermeneutic fictionalism is accepted, it is argued that his two main attacks on revolutionary fictionalism fail to meet their target. Firstly, ‘philosophical modesty’ should not prevent philosophers from questioning the truth of claims made within successful practices, provided that the utility of those practices as they stand can be explained. Secondly, Carnapian scepticism concerning the meaningfulness of _metaphysical_ existence claims has no force against a _naturalized_ version (...) of fictionalism, according to which our ordinary standards of scientific evidence may show that we have no reason to believe the mathematical existence claims made within the context of our mathematical and scientific theories. (shrink)

Are there any things that are such that any things whatsoever are among them. I argue that there are not. My thesis follows from these three premises: (1) There are two or more things; (2) for any things, there is a unique thing that corresponds to those things; (3) for any two or more things, there are fewer of them than there are pluralities of them.

Some have it that wholes are, somehow, identical to their parts. This doctrine is as alluring as it is puzzling. But in this paper, I show that the doctrine is inconsistent with two widely accepted theses. Something has to go.

In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.

In this paper, I develop a theory on which each of a thing’s abundant properties is immanent in that thing. On the version of the theory I will propose, universals are abundant, each instantiated universal is immanent, and each uninstantiated universal is such that it could have been instantiated, in which case it would have been immanent. After setting out the theory, I will defend it from David Lewis’s argument that such a combination of immanence and abundance is absurd. I (...) will then advocate the theory on the grounds that it accomplishes all of Lewis’s “new work” while providing a gain in parsimony and a new account of fine-grained content. I will close with a discussion of how the theory also affords a new reply to two objections to uninstantiated universals: Armstrong’s charge that they are inconsistent with naturalism, and a Benacerraf-Field-style objection about epistemic access. (shrink)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Alessandro Torza argues that Ted Sider’s Lewisian argument against vague existence is insufficient to rule out the possibility of what he calls ‘super-vague existence’, that is the idea that existence is higher-order vague, for all orders. In this chapter it is argued that the possibility of super-vague existence is ineffective against the conclusion of Sider’s argument since super-vague existence cannot be consistently claimed to be a kind of linguistic vagueness. Torza’s idea of super-vague existence seems to be better suited to (...) model vague existence under the assumption that vague existence is instead a form of ontic indeterminacy, contra what Ted Sider and David Lewis assume. (shrink)

Universalism (the thesis that distinct objects always compose a further object) has come under much scrutiny in recent years. What has been largely ignored is its role in the metaphysics of classes. Not only does universalism provide ways to deal with classes in a metaphysically pleasing fashion, its success on these grounds has been offered as a motivation for believing it. This paper argues that such treatments of classes can be achieved without universalism, examining theories from Goodman and Quine, Armstrong (...) and Lewis. In the case of each theory, universalism is drafted in to ensure that there are enough material objects to play a particular role. I argue that, for each theory, there's a better theory that ditches universalism and instead uses an alternative principle of composition demanding that the unrestricted composition of entities other than material objects (respectively: regions, states of affairs and singletons) play that role instead. I conclude that (1) non-universalists can consider accepting such theories of classes and (2) we should ignore any alleged motivation for universalism on the basis of dealing with classes. (shrink)

Roughly, the problem of the Trinity is the problem of how God can be one and yet be the Father, the Son, and the Holy Spirit, which are three, not one. That one thing is identical with three distinct things seems to violate traditional laws of identity. I propose a solution to this problem according to which it is just an ordinary claim of one-many identity. For example, one pair of shoes is identical with two shoes; and my one body (...) is identical with its six limbs of arms, legs, head, and torso. The pair of shoes is not identical with each one of the two shoes, nor is my body identical with each one of its six limbs, but rather identical with all of them taken together, or collectively. I argue that the problem of the Trinity should be understood accordingly: God is identical with the Father, the Son, and the Holy Spirit collectively, but not with each one of them distributively. According to the way I develop this proposal, no traditional laws of identity are violated, but merely generalized in an intuitive way. I argue that this is compatible with Christian Orthodoxy as given by the Athanasian Creed. I end by responding to some anticipated objections. (shrink)

This article focuses on the main methods used in analytic metaphysics. It first considers five important sources of constraints on metaphysical theorizing: linguistic and conceptual analysis, consulting intuitions, employing the findings of science, respecting folk opinion, and applying theoretical virtues in metaphysical theory choice such as preferring simpler theories, or preferring more explanatory theories. It then examines the role of formal methods in metaphysics as well as the role of metaphysical communities, traditions, and the place of the history of metaphysics (...) in contemporary work. It also discusses the issue of whether metaphysics should be seen as an enterprise that will yield knowledge of metaphysical matters or whether it should have more modest epistemic goals. Finally, it explores the question of how much of metaphysics is a priori. (shrink)

The details of St. Thomas Aquinas’s anthropological view are subject to debate. Some philosophers believe he held that human persons survive their deaths. Other philosophers think he held that human persons cease to exist at their death, but come back into being at the general resurrection. In this paper, I defend the latter view against one of the most significant objections it faces, namely, that it entails that God punishes and rewards separated souls for the sins or merits of something (...) else: the (non-existent) persons to whom those souls once belonged. The objector takes this entailment to be problematic. I argue that it fits in well with St. Thomas’s views about punishment and about persons. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

In a series of publications, Eli Hirsch has presented a sustained defense of common-sense ontology. Hirsch's argument relies crucially on a meta-ontological position sometimes known as ‘superficialism’. Hirsch's argument from superficialism to common-sense ontology is typically resisted on the grounds that superficialism is implausible. In this paper, I present an alternative argument for common-sense ontology, one that relies on (what I argue is) a much more plausible meta-ontological position, which I call ‘constructivism’. Note well: I will not quite argue that (...) constructivism is true; merely that it is significantly more plausible than superficialism, and consequently affords a safer route to common-sense ontology. Thus my main goal in the paper is not quite to establish common-sense ontology, nor for that matter to refute Hirsch's argument for it. My goal is, in a way, more expressive than argumentative: I wish to articulate a novel meta-ontological position, one that I take to be in no way obviously less plausible than already familiar positions, and to point out that the position probably leads to common-sense ontology. I open, in section 1, with a discussion of Hirsch's argument and the main objection to it. I then develop, in section 2, a sketch of the alternative meta-ontology I have in mind. I close, in section 3, with the argument that this alternative meta-ontology, too, leads to common-sense ontology. (shrink)

Van Inwagen proposes that besides simples only living organisms exist as composite objects. This paper suggests expanding van Inwagen’s ontology by also accepting composite objects in the case that physical bonding occurs (plus some extra conditions). Such objects are not living organ-isms but rather physical bodies. They include (approximately) the complete realm of inanimate ordinary objects, like rocks and tables, as well as inanimate scientific objects, like atoms and mol-ecules, the latter filling the ontological gap between simples and organisms in (...) van Inwagen’s origi-nal picture. We thus propose a compositional pluralism claiming that composition arises if and on-ly if bonding or life occurs. (shrink)

It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' principle of compossibility (...) can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted. (shrink)

Recently, I’ve championed the doctrine that fundamentally different sorts of things exist in fundamentally different ways.1 On this view, what it is for an entity to be can differ across ontological categories.2 Although historically this doctrine was very popular, and several important challenges to this doctrine have been dealt with, I suspect that contemporary metaphysicians will continue to treat this view with suspicion until it is made clearer when one is warranted in positing different modes of existence.3 I address this (...) concern here. The question of when to posit ways of being is closely related to a more general question: when should one think that some philosophically interesting expression is analogous? Accordingly, my strategy here is as follows. First, I briefly explain my interpretation of ontological pluralism, the doctrine that there are ways of being.4 Second, I introduce the notion of an analogous term, and show how, on most ways of implementing ontological pluralism, “existence” is analogous. Third, I discuss two sufficient conditions for when one is warranted in claiming that a philosophically interesting term is analogous. Fourth, I present a series of ontological schemes, each of which satisfies at least one of the sufficient conditions. The upshot is this: if you are attracted to one of these ontologies, you have reason to believe in ways of being. The careful reader will have noted the apparent modesty of my conclusion. Unfortunately, I do not believe that one could ever be rationally required to believe in ways of being. Still, in general a metaphysic is a live option to the extent that it is shown to be rationally permissible to believe. Since the apparent consensus among contemporary analytic metaphysicians is that believing that things can exist in different ways is silly or confused, establishing the rational permissibility of belief in ways of being is a non-trivial task. Let us begin. (shrink)

Among theories of personal identity over time the simple view has not been popular among philosophers, but it nevertheless remains the default view among non philosophers. It may be construed either as the view that nothing grounds a claim of personal identity over time, or that something quite simple (a soul perhaps) is the ground. If the former construal is accepted, a conspicuous difficulty is that the condition of causal dependence between person-stages is absent. But this leaves such a view (...) open to an objection from the failure to provide a condition of individuation. If, on the other hand something like a soul is said to ground personal identity over time, such an account turns out to be more suited to a kind of continuity view. (shrink)

Let ‘monism’ be the view that there is only one basic object—the world. Monists face the question of whether there are also non-basic objects. This is in effect the question of whether the world decomposes into parts. Jonathan Schaffer maintains that it does, Terry Horgan and Matjaž Potrč that it does not. In this paper, I propose a compromise view, which I call ‘Kantian monism.’ According to Kantian monism, the world decomposes into parts insofar as an ideal subject under ideal (...) conditions would divide it into parts, but it does not decompose into parts in and of itself, that is, in an entirely mind-independent manner. After articulating Kantian monism more precisely (Section 1), I present a prima facie case for preferring it over more standard varieties of monism (Section 2). (shrink)

Abstract Theories are metaphysically equivalent just if there is no fact of the matter that could render one theory true and the other false. In this paper I argue that if we are judiciously to resolve disputes about whether theories are equivalent or not, we need to develop testable criteria that will give us epistemic access to the obtaining of the relation of metaphysical equivalence holding between those theories. I develop such ?diagnostic? criteria. I argue that correctly inter-translatable theories are (...) metaphysically equivalent, and what we need are ways of determining whether a putative translation is correct or not. To that end I develop a number of tools we can employ to discern whether a translation is a correct one. (shrink)

I address what I call the Number Issue, which is raised by our ordinary talk and beliefs about certain social groups and institutions, and I take the Hallé orchestra as my example. The Number Issue is that of whether the Hallé is one individual or several individuals. I observe that if one holds that it is one individual, one faces an accusation of metaphysical extravagance. The bulk of the paper examines the difficulty of reconciling the view that the Hallé is (...) several individuals with two prima facie plausible theses about the manner of its persistence through time. The paper is structured around some remarks made by Peter Simons about groups, and the Hallé in particular, in his 'Parts'. (shrink)

Dispositional monists believe that all properties are essentially causal. Recently, an overdetermination argument has been proposed by Trenton Merricks to support nihilism about ordinary objects. I argue that this argument can be extended to target both nihilism about ordinary objects and nihilism about physical particles when dispositional monism is assumed. It implies that a philosopher who both endorses dispositional monism and takes seriously the overdetermination argument should not believe in the existence of physical particles. I end up by discussing possible (...) objections. I suggest, then, that if we live in a world that is inhabited by causal properties but not by chairs and tables, then we also live in a world without electrons and quarks, a world of dispositional properties, that is, a world of causal fields. (shrink)

Is the world internally connected by a web of necessary connections or is everything loose and independent? Followers of David Hume accept the latter by upholding Hume’s Dictum, according to which there are no necessary connections between distinct existences. Roughly put, anything can coexist with anything else, and anything can fail to coexist with anything else. Hume put it like this: “There is no object which implies the existence of any other if we consider these objects in themselves.” Since Hume’s (...) day, Hume’s Dictum has played a major role in philosophy, especially in contemporary metaphysics. In ruling out necessary connections, Hume’s Dictum implies that causal relations and the laws of nature are contingent. It makes other demands on our metaphysics of science as well; for example, it places restrictions on our metaphysics of counterfactuals, dispositions, and explanation. The principle has applications in other areas too. Hume’s Dictum places constraints on our theories of abstract objects and moral properties. For example, Hume’s Dictum rules out the view that moral properties are distinct from, but necessarily connected to, non-moral properties. While Hume’s Dictum is a prominent principle in metaphysics, few Humeans have defended the principle at length. It is assumed more often than it is argued for. As a result, Hume’s Dictum no longer enjoys the reputation it once did. It’s common to hear complaints about the lack of arguments in support of Hume’s Dictum. Moreover, philosophers are increasingly willing to defend views that are at odds with Hume’s Dictum. A striking example of this is the recent explosion of interest in views that take causal relations and the laws of nature to be necessary. Humeans can no longer afford to be complacent. An extended defense of Hume’s Dictum is called for, and that’s what this dissertation aims to offer. This dissertation has three parts. In the first part, I lay out some preliminaries and offer a precise formulation of Hume’s Dictum. In the second part, I develop three arguments in favor of Hume’s Dictum. In the final part, I defend Hume’s Dictum against objections. (shrink)

John MacFarlane explores how we might make sense of the idea that truth is relative. He provides new, satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis, including what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do.

Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section (...) 6. (shrink)

Much of the debate about identity in recent decades has been about personal identity, and specifically about personal identity over time, but identity generally, and the identity of things of other kinds, have also attracted attention. Various interrelated problems have been at the centre of discussion, but it is fair to say that recent work has focussed particularly on the following areas: the notion of a criterion of identity; the correct analysis of identity over time, and, in particular, the disagreement (...) between advocates of perdurance and advocates of endurance as analyses of identity over time; the notion of identity across possible worlds and the question of its relevance to the correct analysis of de re modal discourse; the notion of contingent identity; the question of whether the identity relation is, or is similar to, the composition relation; and the notion of vague identity. A radical position, advocated by Peter Geach, is that these debates, as usually conducted, are void for lack of a subject matter: the notion of absolute identity they presuppose has no application; there is only relative identity. Another increasingly popular view is the one advocated by Lewis: although the debates make sense they cannot genuinely be debates about identity, since there are no philosophical problems about identity. Identity is an utterly unproblematic notion. What there are, are genuine problems which can be stated using the language of identity. But since these can be restated without the language of identity they are not problems about identity. (For example, it is a puzzle, an aspect of the so-called “problem of personal identity”, whether the same person can have different bodies at different times. But this is just the puzzle whether a person can have different bodies at different times. So since it can be stated without the language of personal “identity”, it is not a problem about identity, but about personhood.) This article provides an overview of the topics indicated above, some assessment of the debates and suggestions for further reading. (shrink)

When one takes an intersectional perspective on patterns of oppression and domination, it becomes clear that familiar forms of systemic injustice, such as misogyny and anti-Black racism, are inseparable. Some feminist theorists conclude, from this, that the systems behind these injustices cannot be individuated—for example, that there isn’t patriarchy and white supremacy, but instead only white supremacist patriarchy. This chapter offers a different perspective. Philosophers have long observed that a statue and a lump of clay can be individuated although inseparable, (...) and that statues and lumps of clay do different explanatory and predictive work for the same causal outcomes. This chapter suggests that the same is true of systems such as patriarchy and white supremacy. These systems, like the injustices they produce, are inseparable. But they can be individuated, and when they are individuated, they do different explanatory and predictive work. (shrink)

Grounding-theoretic account of the notion of transparency relevant to the explanatory gap between the mental and physical.

Traditionally, social entities (i.e., social properties, facts, kinds, groups, institutions, and structures) have not fallen within the purview of mainstream metaphysics. In this chapter, we consider whether the exclusion of social entities from mainstream metaphysics is philosophically warranted or if it instead rests on historical accident or bias. We examine three ways one might attempt to justify excluding social metaphysics from the domain of metaphysical inquiry and argue that each fails. Thus, we conclude that social entities are not justifiably excluded (...) from metaphysical inquiry. Finally, we ask how focusing on social entities could change the character of metaphysical inquiry. We suggest that starting from examples of social entities might lead metaphysicians to rethink the assumption that describing reality in terms of intrinsic, independent, and individualistic features is preferable to describing it in terms of relational, dependent, and non-individualistic features. (shrink)

On a view implicitly endorsed by many, a concept is epistemically better than another if and because it does a better job at ‘carving at the joints', or if the property corresponding to it is ‘more natural' than the one corresponding to another. This chapter offers an argument against this seemingly plausible thought, starting from three key observations about the way we use and evaluate concepts from en epistemic perspective: that we look for concepts that play a role in explanations (...) of things that cry out for explanation; that we evaluate not only ‘empirical' concepts, but also mathematical and perhaps moral concepts from an epistemic perspective; and that there is much more complexity to the concept/property relation than the natural thought seems to presuppose. These observations, it is argued, rule out giving a theory of conceptual evaluation that is a corollary of a metaphysical ranking of the relevant properties. -/- conceptual ethics, explanation, naturalness, epistemic value, concept/property, semantic internalism. (shrink)

Our aim in this paper is to bring to light two sources of tension for Christian theists who endorse the principle of unrestricted composition, that necessarily, for any objects, the xs, there exists an object, y, such that the xs compose y. In Value, we argue that a composite object made of wholly valuable parts is at least as valuable as its most valuable part, and so the mereological sum of God and a wholly valuable part would be at least (...) as valuable as God; but Christian theism arguably demands that no concrete object other than God can be as valuable as God. And in Creation, we argue that the conjunction of theism and unrestricted composition, together with the claim that every concrete entity that is numerically distinct from God is created by God, implies that God is created by God. We conclude by examining the prospects of restricting the thesis of unrestricted composition to the domain of material or spatiotemporal objects as a way to sidestep the above arguments against the conjunction of Christian theism and unrestricted composition. (shrink)

In this chapter, a generic definition of fundamentality as an ontological minimality thesis is sought and its applicability examined. Most discussions of fundamentality are focused on a mereological understanding of the hierarchical structure of reality, which may be combined with an atomistic, object-oriented metaphysics. But recent work in structuralism, for instance, calls for an alternative understanding and it is not immediately clear that the conception of fundamentality at work in structuralism is commensurable with the mereological conception. However, it is proposed (...) that once we understand fundamentality as an ontological minimality thesis, these two as well as further conceptions of fundamentality can all be treated on a par, including metaphysical infinitism of the ‘boring’ type, where the same structure repeats infinitely. (shrink)

Friends of states of affairs and structural universals appeal to a relation, structure-making, that is allegedly a kind of composition relation: structure-making ?builds? facts out of particulars and universals, and ?builds? structural universals out of unstructured universals. D. M. Armstrong, an eminent champion of structures, endorses two interesting theses concerning composition. First, that structure-making is a composition relation. Second, that it is not the only (fundamental) composition relation: Armstrong also believes in a mode of composition that he calls mereological, and (...) which he takes to be the only kind of composition recognized by his philosophical adversaries, such as David Lewis. Armstrong, accordingly, is a kind of pluralist about compositional relations: there is more than one way to make wholes from parts. In this paper, I critically evaluate Armstrong's compositional pluralism. (shrink)

In Plato's Parmenides , Socrates proposes a 'Day' analogy to express one possible model of part/whole relations. His analogy is swiftly rejected and replaced with another analogy, that of the 'Sail'. In this paper, it is argued that there is a profound difference between these two analogies and that the 'Day' represents a distinct way to think about part/whole relations. This way of thinking, I argue, is the standard way of thinking in East Asian Buddhism. Plato's 'Day' analogy can then (...) be used to illuminate the meaning of an opaque but very important concept in East Asian Buddhism: li , which in this paper is developed as a modal concept of 'Wholeness'. (shrink)

In my dissertation, I address a variety of issues in the metaphysics of space and related areas. I begin by discussing the popular thesis that regions of space are identical to sets of points in space. I present three arguments against this thesis and conclude that we should be skeptical of it. In its place, I propose an axiomatic theory of regions of space that is consistent with both reductive accounts of their nature and with accounts that treat them as (...) sui generis entities. -/- I next explore the consequences of the aforementioned considerations. In particular, I describe five different sorts of structure each of which is such that the claim that space could have that structure is consistent with the axiomatic theory previously proposed. I claim that this fact, together with the skepticism concerning reductive accounts argued for earlier, shows that we should take seriously the claim that space could have any of these structures. -/- Having argued that we should be skeptical of the thesis that regions of space are identical to sets of points in space and suggesting that space could have different sorts of structure, I discuss how best to analyze continuity. I present an analysis of continuity inspired by remarks of Richard Cartwright in his 1975 paper ‘Scattered Objects’. I argue that this Cartwrightian analysis should be rejected because it identifies regions of space with sets of points in space, and I present a modified version of the analysis that does not do so. I note, however, that there is an intuitive notion of continuity that is not captured by this modified Cartwrightian analysis. I present and defend an analysis of continuity that better captures this intuitive notion. -/- I then turn to the issue of how to analyze what it is for a region of space to be open and what it is for a region of space to be closed. Here I argue that Cartwright’s analyses of these notions are incorrect. I then present a series of alternative analyses, revising each in response to objections. This process culminates with my proposed analyses of what it is for a region of space to be open and what it is for a region of space to be closed. -/- Finally, I discuss the Maximally Continuous Account of Simples (MaxCon), originally formulated and defended by Ned Markosian in his 1998 paper ‘Simples’. I argue that Markosian’s version of MaxCon, which identifies regions of space with sets of points in space and relies on the Cartwrightian analysis of continuity, should be rejected. I then formulate a new version of MaxCon that builds on the views defended earlier in my dissertation and defend this new version of MaxCon from objections. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

Tracing the leading role of emotions in the evolution of the mind, a philosopher and a psychologist pair up to reveal how thought and culture owe less to our faculty for reason than to our capacity to feel. Many accounts of the human mind concentrate on the brain’s computational power. Yet, in evolutionary terms, rational cognition emerged only the day before yesterday. For nearly 200 million years before humans developed a capacity to reason, the emotional centers of the brain were (...) hard at work. If we want to properly understand the evolution of the mind, we must explore this more primal capability that we share with other animals: the power to feel. Emotions saturate every thought and perception with the weight of feelings. The Emotional Mind reveals that many of the distinctive behaviors and social structures of our species are best discerned through the lens of emotions. Even the roots of so much that makes us uniquely human—art, mythology, religion—can be traced to feelings of caring, longing, fear, loneliness, awe, rage, lust, playfulness, and more. From prehistoric cave art to the songs of Hank Williams, Stephen T. Asma and Rami Gabriel explore how the evolution of the emotional mind stimulated our species’ cultural expression in all its rich variety. Bringing together insights and data from philosophy, biology, anthropology, neuroscience, and psychology, The Emotional Mind offers a new paradigm for understanding what it is that makes us so unique. (shrink)

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda (...) ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Kim. (shrink)

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of denying (...) each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive. (shrink)

This paper focuses on the concept of collective essence: that some truths are essential to many items taken together. For example, that it is essential to conjunction and negation that they are truth-functionally complete. The concept of collective essence is one of the main innovations of recent work on the theory of essence. In a sense, this innovation is natural, since we make all sorts of plural predications. It stands to reason that there should be a distinction between essential and (...) accidental plural predications if there is a distinction among singular predications. In this paper I defend the view that the concept of collective essence is governed by the principle of Monotonicity: that something is essential to some items only if it is essential to any items to which they belong. (shrink)

In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the (...) regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages. (shrink)