Philosophers in general, and metaphysicians in particular, are largely concerned with metaphysical modality, that is, with what is possible and necessary, in the broadest sense, and with what makes propositions about metaphysical modality true. Metaphysicians are also concerned with ontology, that is, with what exists and the nature of what exists. Ontology covers such questions as 'do numbers exist?' and 'do universals exist?' and, if numbers and universals do exist, 'what are they like?' and 'how do they exist?'. The laws of nature, such as the law of universal gravitation, Coulomb's law and the Schrödinger equation, for example, raise interesting philosophical questions at the intersection of metaphysics and the philosophy of science, such as 'what is the relationship between laws of nature and scientific explanation?' and 'in what sense, if any, are we free to break the laws?'. Questions about modality, ontology and laws of nature connect in interesting ways. The kinds of things - propositions, universals, possible worlds, etc. - that one is willing to countenance will impact what one can say about the metaphysics of modality and natural laws. The point is illustrated nicely via consideration of Humean constraints on respectable ontology popularized by David Lewis and the ensuing metaphysics of laws and modality that Lewis defends. What distinguishes lawful from non-lawful regularities, according to Lewis, is the fact that the former, but not the latter, are axioms of the description of all property instances throughout the Humean mosaic, which maximizes the virtues of informativeness and simplicity. This is the crux of Lewis's best system analysis of natural laws (BSA) (see, e.g., Lewis 1983, 1994, 2001; Earman 1984; Loewer 1996). Natural laws are thus accounted for in a manner that the Humean finds metaphysically innocuous because no appeal is made to any mysterious governing forces or necessary connections between distinct existences. The Humean is primarily concerned with defending (the tenability of) an ontology, which then informs and places restrictions on what can be said about laws and modality. However, one's primary concern might just as well be with analysing the laws and, dissatisfied with regularity accounts, such as the BSA, one might be motivated to develop an alternative account of laws with its own distinctive ontological implications. My concern in this thesis is with exploring the interactions between a cluster of specific views about ontology, modality and the laws of nature. The particular ontology I am interested in is unHumean in the sense that it admits necessary connections between properties and the behaviours that they confer because properties have non-trivial essences which ground certain behaviours. The account of laws is metaphysically thin for it conceives of the laws as merely descriptive, à la the BSA. And the metaphysics of modality that I am interested in roots modality firmly in the actual world.

This thesis develops a teleological theory of mental representation to naturalise intentionality. Teleosemantics explains mental representation in terms of biological functions. The thesis addresses a number of foundational problems that threats the viability of teleosemantics. The first chapter, “The metaphysics of mental representation”, develops a basic conception of mental representation that is designed to satisfy certain intuitive requirements (misrepresentation and original intentionality) and methodological requirements (explanatory power and ontological parsimony). The second chapter, “Naturalising intentionality”, defends the thesis that mental representation is naturalistically reducible and in particular that it should be explained teleosemantically. After that, it addresses some of Tyler Burge’s objections to reductionist naturalism in general and teleosemantics in particular. The third chapter, “The minimal conditions for intentionality: the problem of demarcation”, considers the problem of demarcating the limits of intentionality and the objection that teleosemantics and other naturalist theories are too liberal. It adopts the method of reflective equilibrium to develop minimal conditions for intentionality based on mutual adjustments between intuitive and explanatory constraints. Finally, it rejects alternative proposals for demarcating intentionality in terms of causal independence or constancy mechanisms. The fourth chapter, “The minimal conditions for intentionality: the dual proposal”, develops a specific solution to the problem of demarcation – the dual proposal for the minimal conditions for intentionality. The fifth chapter, “The content problem: in defence of producer-based teleosemantics”, defends a producer-based version of teleosemantics and proposes solutions for functional indeterminacy problems facing teleosemantics.

Although he does not know it, the man on the Clapham omnibus is a presentist. Or to put it more accurately, the man on the Clapham omnibus has ideas about time, which (at least) imply much of presentism. Or so I argue in this thesis. While some of our pre-theoretic ideas about time are no doubt under-determined in certain respects, the man on the bus might be alarmed to learn that the majority of philosophers claim that our intuitive views about time are naïve and wrong. This is a serious claim. And it requires a clear explanation; for it suggests that ordinary people are living under the illusion that temporal reality is a certain way, when in fact it is not. Starting from the assumption that presentism is the common-sense view of time, this thesis asks the following questions. Is presentism a viable theory? Are the metaphysical theories of time presented as the alternatives to presentism viable theories? And in what respects, if any, are these alternative theories superior to presentism, such that they require us to give up or amend our common-sense ideas about time? To answer these questions, I explain what each of these theories are, and what their commitments are. This is in order to clarify what the dispute between presentism and its rivals is really about. I then argue that despite facing a number of serious objections, there are versions of presentism that can meet these objections. I also argue that the alternatives to presentism have serious problems of their own. I therefore conclude that not only is the dispute between presentism and its rivals not settled, but also that there are good reasons to prefer presentism, as it allows us to keep many of our common-sense ideas about time.

This thesis brings together two concerns. The first is the nature of inference—what it is to infer—where inference is understood as a distinctive kind of conscious and self-conscious occurrence. The second concern is the possibility of doxastic agency. To be capable of doxastic agency is to be such that one is capable of directly exercising agency over one’s beliefs. It is to be capable of exercising agency over one’s beliefs in a way which does not amount to mere self-manipulation. Subjects who can exercise doxastic agency can settle questions for themselves. A challenge to the possibility of doxastic agency stems from the fact that we cannot believe or come to believe “at will”, where this in turn seems to be so because belief “aims at truth”. It must be explained how we are capable of doxastic agency despite that we cannot believe or come to believe at will. On the orthodox ‘causalist’ conception of inference for an inference to occur is for one act of acceptance to cause another in some specifiable “right way”. This conception of inference prevents its advocates from adequately seeing how reasoning could be a means to exercise doxastic agency, as it is natural to think it is. Suppose, for instance, that one reasons and concludes by inferring where one’s inference yields belief in what one infers. Such an inference cannot be performed at will. We cannot infer at will when inference yields belief any more than we can believe or come to believe at will. When it comes to understanding the extent to which one could be exercising agency in such a case the causalist conception of inference suggests that we must look to the causal history of one’s concluding act of acceptance, the nature of the act’s being determined by the way in which it is caused. What results is a picture on which such reasoning as a whole cannot be action. We are at best capable of actions of a kind which lead causally to belief fixation through “mental ballistics”. The causalist account of inference, I argue, is in fact either inadequate or unmotivated. It either fails to accommodate the self-consciousness of inference or is not best placed to play the very explanatory role which it is put forward to play. On the alternative I develop when one infers one’s inference is the conscious event which is one’s act of accepting that which one is inferring. The act’s being an inference is determined, not by the way it is caused, but by the self-knowledge which it constitutively involves. This corrected understanding of inference renders the move from the challenge to the possibility of doxastic agency to the above ballistics picture no longer tempting. It also yields an account of how we are capable of exercising doxastic agency by reasoning despite being unable to believe or come to believe at will. In order to see how such reasoning could amount to the exercise of doxastic agency it needs to be conceived of appropriately. I suggest that paradigm reasoning which potentially amounts the exercise of doxastic agency ought to be conceived of as primarily epistemic agency—agency the aim of which is knowledge. With inference conceived as suggested, I argue, it can be seen how to engage in such reasoning can just be to successfully exercise such agency.

This thesis defends the notion of grounding — an explanatory connection of non-causal determination. I present four challenges to developing a systematic theory of grounding, and show that they can be met satisfactorily. The first challenge is that grounding is unintelligible or uninformative—or at any rate, that its work can be done by more familiar notions. If so, the notion of grounding is not even prima facie justified. I argue that grounding is at least as informative as—and, in some respects, more informative than—the more familiar notions it is supposed to supplant. It is necessary because we can express with it certain explanatory relation-ships which are just inexpressible with weaker notions of determination. My defence of grounding is preferable to extant defences since it is less concessive, requiring fewer assumptions about the nature of grounding. A key motivation for grounding is that it is an explanatory connection. The second challenge is that the sense in which grounding is a (distinctly) explanatory relation is unclear, wherefore the case for grounding is severely weakened. I motivate a theory of explanation and argue that it comports nicely with the sense in which grounding is explanatory. Moreover, I characterise a new explanatory notion I call philosophical ex-planation with grounding at its core. This notion illustrates the importance of grounding for philosophical methodology generally. The third challenge is to the internal coherence of grounding theory. A dilemma apparently show that grounding connections can be neither grounded nor ungrounded. Several treatments of this problem already exist, but none is satisfactory. Some imply implausible explanations. Others require new—dubious—posits. I present a new solu-tion, which o ̇ers satisfying explanations but requires no dubious posits. It explains, moreover, why some grounding connections appear to admit of explanation but others do not. The last challenge is to the usefulness of grounding. While it is an interesting meta-metaphysical posit, it o ̇ers little to the metaphysician working on first-order problems. I show how grounding can be fruitfully applied to breaking the deadlock in the debate about laws of nature.

How can we know ourselves? This thesis argues that Plato’s dialogue Phaedo replies to this difficult question. The dialogue suggests that we must discover our intellectual desire and governing function through the practice of philosophical investigation. Although this is an implicit suggestion, it is just as important as the explicit discussion of the soul’s immortality. Focusing on this topic, the thesis also argues that we should read the dialogue as a suggestion for the process of improving a human being; it does not intend to provide a complete definition of the soul’s nature. A philosopher will recognise his progress towards achieving his objective, the Forms, through the investigation itself. Moreover, this thesis argues that Phaedo asserts that a philosophical desire should be found explicitly in a process of discussion with Socrates. In the first main discussion of the dialogue, interlocutors of Socrates request him to defend the goodness of death (62c-63a). This goodness is based on a claim that death as the soul’s separation from the body provides them with wisdom. However, the defence will be meaningless to people who do not desire wisdom. When the interlocutors become clearly conscious of their desire for wisdom, Socrates’ arguments would succeed in the truest sense. The process of the philosophical investigation, though, is not simple. This thesis will argue that a philosopher must employ both objective discussion and subjective self-recognition of his desire, which contrasts with the view that focuses on the objective understanding of human psychology in Plato’s work. This thesis argues for a reading of Phaedo that focuses on the process of self-improvement, not the goal or the definition of the soul’s nature. Moreover, it also emphasizes self-discovery of intellectual desire in a philosopher, which cannot be reduced to an objective discussion.

This thesis is about two ways in which we use mathematics to understand the non-mathematical world: in particular, mathematical explanation and mathematical representation. In chapters 1 and 2, I motivate the project by suggesting that, in addition to shedding light on the nature of explanation and representation, it is necessary to develop accounts of these two world-oriented uses of mathematics in order to evaluate competing considerations in favour of, and against, mathematical realism. In chapters 3 and 4 I discuss extra-mathematical explanation. In chapter 3, I consider and reject four recent accounts of mathematical explanation. In chapter 4 I discuss and endorse what I call the modal account of extra-mathematical explanation. I argue, in line with Jansson and Saatsi and contra Baron, Colyvan and Ripley that such an account does not require countenancing counterpossibles, I discuss in virtue of what a mathematical fact can play this role and I address whether or not extra-mathematical explanations are causal. In chapters 5 and 6 I discuss mathematical representation. In chapter 5 I consider two fundamental challenges to developing an account of mathematical scientific representation: the first is Callender and Cohen’s claim that there are no special problems of scientific representation and the second is a set of influential objections owing to Frigg and Suárez that take aim at accounts of representation that appeal to the notion of structural similarity. In chapter 6 I argue that two recent accounts of mathematical representation are, in fact, complementary and, more generally, that mathematical representation is a special kind of epistemic representation. I draw on some work from epistemology to address, and argue against, Pincock’s claim that in order to understand a mathematical representation one must believe its mathematical content.

This thesis argues that the aesthetic character of some conceptual works of art can be determined by the possession of essential aesthetic properties. By discussing Peter Lamarque’s account of individual aesthetic essentialism one can suggest that conceptual works can be aesthetically investigated. Chapter I introduces the concept of the aesthetic and discusses Frank Sibley’s account of aesthetic concepts. Chapter II analyses in detail Sibley’s two fold relational character of aesthetic properties. Chapter III introduces Lamarque’s concept of aesthetic properties and it also insists on a distinction between artistic and aesthetic properties. Chapter IV introduces a general account of essentialism and then discusses Lamarque’s new object theory. Chapter V investigates Lamarque’s weaker version of individual aesthetic essentialism and analyses the distinction between essential and inessential aesthetic properties. Finally, Chapter VI considers the aesthetics of conceptual art and argues that some conceptual pieces have essential aesthetic properties. The philosophical discussions are supported by appeal to many different works of art, from traditional works to contemporary works. I conclude that all conceptual works have aesthetic properties but mostly there are inessential properties. My suggestion at the end of this thesis is more radical. A close analysis identified essential aesthetic properties in some conceptual works of art and this contribute to the aesthetic character and value of these works.

Two assumptions are often made about the nature of the cognitive attitudes that allow us to engage with fiction and in pretence: the uniformity and the non-doxastic assumptions. The uniformity assumption tells us that both of these activities involve the same cognitive attitudes. The non-doxastic assumption tells us that these cognitive attitudes are not beliefs, but belief-like states that we can call belief-like imaginings. I will challenge both of these assumptions in this thesis. In the case of the uniformity assumption, I will draw a distinction between voluntary and involuntary imaginative counterparts. I will argue that if a belief-like counterpart is involved in our engagement in pretence, it will be a voluntary counterpart, whereas an involuntary one will have to be associated with our engagement with fiction. Against the non-doxastic assumption, I will argue that we can explain our engagement with these activities by introducing beliefs with distinct contents. In the case of pretence, I will suggest that the relevant beliefs are of the form ‘[I believe] I PRETEND that “p”’. In the case of fiction, I will argue that the relevant beliefs are of the form ‘I believe p [in the fiction]’. This will lead to us challenging the non-doxastic assumption on the grounds that belief-like imaginings are unnecessary for explaining how we are able to engage with fiction and in pretence. I will also offer some arguments for why belief-like imaginings might be insufficient for explaining how we are able to engage with fiction and in pretence. In particular, I will argue that belief-like imaginings do not do enough to explain how we recognise when someone else is engaging in pretence, and that they struggle to make sense of why our representations related to fiction and pretence exhibit what Walton calls ‘clustering’.

My thesis concentrates on the distinction between pro tanto reasons and all-things-considered judgments, and their relation to normative justification. Negatively, it seeks to show that a prevailing kind of account of this relation should be rejected, namely that family of views which takes it that every reason has an associated weight, and the truth with respect to any issue is established by which set of reasons is weightiest. Through an examination of Ross’ doctrine of prima facie duties, this discussion also leads to a formulation of the central problem which any account of this relation must seek to solve. Positively, this thesis develops a new account of the relation between pro tanto reasons and all-things-considered judgements, based on the fundamental insight that a justification of normative propositions is identical to an explanation of their truth, were they to be true. I defend this identity claim, and seek to generate an account of justification from an account of explanation. Drawing on a deservedly popular ‘contrastive’ conception of explanation in the philosophy of science, I show how we can fruitfully think of justification as itself contrastive. Part of this is showing how the notion of a burden of explanation can shed light on the notion of a burden of justification, so a conception of justification emerges according to which a justification for a normative proposition consists in an solution to all those burdens of justification which it incurs. In turn, this feeds a conception of reasons, and their role in justification, alternative to that envisaged in a weighing model: pro tanto reasons determine the correct all-things-considered judgment insofar as they determine to what extent the truth of that judgement has an adequate explanation, such that the correct all-things-considered judgement is just that judgement whose truth would have a fully adequate explanation.