In the history of mathematics and philosophy, the connections and interactions between the two disciplines were clearer than they are today. For example, Descartes is today a well-respected figure in both philosophy and mathematics. Edmund Husserl was also a philosopher and a mathematician: he is best known to be a founder of phenomenology, but he earned his Ph.D. in Mathematics and worked as an assistant to Karl Weierstrass, known as the ‘father of modern analysis’. In my dissertation, I develop Husserlian phenomenological methods for studying contemporary philosophy of mathematics.

Recent literature in philosophy of mathematics often advocates the use of non-philosophical methods, turning towards the methods of empirical or social sciences (e.g. Maddy, 2000). I suggest, challenging this view, that phenomenology offers philosophical methods for studying mathematical practice. Phenomenology can be described as an ‘explicatory science’, whose methods should be adopted, along with cognitive science, as the means to study human cognition and understanding, especially when it comes to mathematics. Importantly, this explicatory science takes the first-person perspective seriously when clarifying our mathematical cognition. Thus, I call this an ‘empathy-first approach’. An empathy-first approach in mathematics is important, especially when we consider that philosophy of mathematics should take a ‘mathematics-first’ as opposed to a ‘philosophy-first’ approach. That latter strategy often begins with certain philosophical first principles and applies those to mathematical issues. The former kind of approach aims to begin from mathematical practice and to consider philosophical questions arising from that practice. The empathy-first approach to philosophy of mathematics not only would begin from mathematical practice, but would also focus on understanding the mathematics as experienced by the mathematicians. In doing so, we are able to evaluate philosophical problems based on how important or relevant they are to mathematical practice.

To demonstrate the empathy-first approach, I begin applying the method to our ordinary perspective on numbers, rather than the mathematicians’ perspective. By looking at the number sequence, expressed by the sequence of numerals ‘1, 2, 3, ...’, I describe different acts of accessing the numbers expressed in ‘...’. In our ordinary experience, there are ways, other than counting, of accessing a larger number. The numbers accessed by such acts could be considered non-arithmetical numbers, as opposed to those that can be accessed in principle only by counting, the arithmetical numbers. The demarcation of non-arithmetical and arithmetical numbers by the empathy-first approach suggests a way of demarcating between mathematical concepts and non-mathematical concepts in other areas. But not only that, this demarcation can be supported by other empirical evidence (e.g. Relaford-Doyle & Núñez, 2017, 2018, 2021). This shows how phenomenology, as an explicatory science, can work with cognitive science, and be developed into an interdisciplinary researchprogramme.

I also show that Husserlian methods offer a way of studying group knowledge, which I consider mathematical knowledge to be. Beyond the general method of phenomenological analysis, Husserl also offers a method for studying group knowledge by analysing scientific practice as teleological. This method, known as Besinnung, involves standing in the ‘community of empathy’ with scientists and clarifying the aims and goals that drive their discipline. I argue that Husserl’s notion of community is different from other existing notions of groups/communities in that it is defined from a first-person perspective, and that it is defined based on certain properties/experiences shared between an individual and others in relation to a teleological group subjectivity.

When the method of Besinnung is applied to mathematical practice, it can help philosophers to evaluate whether a philosophical question is genuinely important to practising mathematicians. Once mathematicians’ goals and aims are clarified, we can then consider whether a given philosophical question needs a philosophical answer with respect to the goals and aims. This is called ‘radical Besinnung’. This feature makes the method superior to the methods found in other disciplines, which do not offer this meta-analysis.

I demonstrate this by applying Besinnung to a contemporary foundational theory in mathematics, called Homotopy Type Theory (HoTT). Philosophers of HoTT (e.g. Ladyman and Presnell (2015); P. Walsh (2017)) have argued that the definition of identity in HoTT (also known as path induction) needs a philosophical justification. Once we have clarified what path induction is from the empathised perspective of the mathematicians, the definition can be internally justified, without appealing to external philosophical assumptions. In this clarification, we can further identify the goals of the homotopy type theorists, as rigour and homotopical autonomy. These goals are to be found within the community of empathy, rather than presupposed when looking at the mathematical theory.

The dissertation is a compilation of three papers in the philosophy of mind. The common theme running through the dissertation concerns the relationship between two components of the mind that, during the 20th–century, were normally kept distinct– the phenomenal, and the intentional. It was a common assumption during this time that one could give a proper account of intentionality without having to account for, or discuss, phenomenality. And similarly for giving an account of the phenomenal. Recently, however, there has been interest in the idea that phenomenality and intentionality are intimately related, and so these earlier assumptions may have been misguided.

Roughly, the proposed relation between phenomenality and intentionality is this: What an intentional state is about, i.e., its intentionality, is grounded in phenomenal, or qualitative, aspects of experience. This is the notion of phenomenal intentionality. In Chapter 1 I develop an account of this kind, and argue that phenomenality is the source of intentionality. Because my main test cases in this chapter are sensory, more needs to be said about how my account applies to non-sensory intentional states. In Chapter 2 I seek to expand the scope of my account by arguing that there is such a thing as cognitive phenomenology. This is the thesis that cognitive episodes, and their contents, have a proprietary phenomenal character, one not based in sense experience. By establishing this thesis I show that phenomenality grounds the intentionality of at least one kind of non-sensory state. Thus, in two central intentional domains, phenomenality plays a crucial role in grounding intentionality. Finally, in Chapter 3, I develop an account of empathy– the phenomenon by which we understand others– and apply the results of the previous two chapters to this account. The account of empathy I develop holds that empathy is a species of intentionality. What makes an experience one of empathy is that the formal intentional structure is modified in certain ways. As I show, phenomenality is an essential part of this experience. Thus, we have reason to think that phenomenality plays an important role in how we understand others.

The present study concerns the general topic of life’s meaning or the meaning of life. There are three facets which I examine under this broad heading: meaning in life, meaningfulness/a meaningful life, and the meaning of life (understood in a more expansive cosmic sense). Regarding meaning in life, I mostly take a close look at what meaning in life amounts to as a concept, and I try to provide some specific content to the notion. Concerning a meaningful life, I see this as an individual human life with much meaning in it. Most of the space dedicated to this idea is spent considering standards for evaluating and formulating approaches to meaningfulness. In these sections, I also posit my own theory, the valuative account, for living a meaningful life. Lastly, I address the often-ignored idea of the meaning of life. My claim is that the question, “What is the meaning of life?” is sensible, and there is a clear way of understanding inquiry into the meaning of all of life.

Chapter 1 concerns issues in the construction of formal models of intensional notions. Intensional notions may be treated as modal operators or as predicates. Halbach and Welch (2009) have proposed a new formal technique to reduce the necessity predicate to an operator, demonstrating that the two methods are ultimately compatible. I show that the monotonicity constraint in the Halbach-Welch technique fails for almost all possible-worlds theories of knowledge. Since the monotonicity constraint is an important element of the proof of the Halbach-Welch rapprochement strategy in the case of necessity, the present results show that the most obvious way of emulating this strategy in the epistemic setting fail.

In Chapter 2, I reconstruct and reconsider Hintikka’s (1969) innovative operator approach to the logic of perception. I use a modal operator and a method of many-sorted substitutional quantification to formalize the notion of perceptual reference. I assimilate Hintikka’s logic to present-day norms of formal logic and I explore Hintikka’s treatment of quantification in the context of his overarching thesis that the possible-worlds theory of intensionality eo ipso provides a theory of mental intentionality. My reconstruction makes us well-posed to consider what is true about Hintikka’s philosophical claims, but also to see some of their decisive limitations.

In Chapter 3, I construct a framework for an adverbialist theory of phenomenal intentionality. I first pose the question: what is the logic of adverbial modification in the setting of phenomenal consciousness? I argue from tools in formal semantics that the logic is one of events, rather than a logic of intensionality. I then argue that the event adverbialist can offer elegant regimentations of crucial distinctions that give the event adverbialist purchase on phenomenal intentionality. This chapter is understood as the other side of the coin from chapter 2 above. There, I reconstruct an account of intentional reference; here, I give a novel account of a structure that determines the ways in which acts are directed toward their (putative) reference.

David Hume’s thought has interrupted entire disciplines from dogmatic slumbers. Yet Hume’s influence is even more expansive and continuous than we might have thought. There are two significant areas of inquiry where Hume’s influence has not been adequately appreciated or articulated: analytic phenomenology and analytic process philosophy. My dissertation explores these traditions’ indebtedness to Hume by engaging with the work of Edmund Husserl and Alfred North Whitehead, who introduce consequential changes into their systems in direct response to what they see as Humean problems with their initial models.

Three major themes are of special interest. First, vis-à-vis “Unity of Mind,” each philosopher asks what accounts for the apparent unity of mind and experience, including what principles connect distinct experiences. Second, vis-à-vis “Temporal Awareness,” each philosopher inquires into what grounds temporality and the experience of temporal passage, including what principles connect distinct moments. Third, vis-à-vis “Personal Identity,” each philosopher investigates what constitutes the experience of continuity and unity over time, including personal continuity and unity qua “personal identity.”

A fourth concordance is methodological. In pursuing the aforementioned themes, each philosopher accords epistemic primacy to lived experience and what discloses itself therein. An overarching Humean problem for all, correlatively, is how continuity and unity arise from distinct items: perceptions, intentional experiences, and actual occasions, respectively. My dissertation attempts to explicate this and related systematic issues from a historical perspective informed by contemporary analytic metaphysics, philosophy of mind, and recent scholarship in Hume, Husserl, and Whitehead studies.

Chapter One argues that Hume’s infamous “Appendix problem” concerns reconciling the incontrovertible unity of mind with his unrenounceable epistemological principle that the mind never perceives real connections between distinct perceptions. Chapter Two traces Hume’s proto-phenomenological influence on Husserl’s theories (not theory) of temporal awareness. Chapter Three examines Hume’s proto-processual influence on Whitehead's theories (not theory) of personal identity.

Unfortunately, neither Husserl nor Whitehead read each other’s work. Nevertheless, both take Hume to be the one who knocks at, yet ultimately fails to walk through the doors that his explorations unveil. By so doing, they beg that we do the same with them.

Universal egoism runs rampant in Western ethics. Too many theories justify intrinsic moral value only in terms of some moral 'self' that is defined by a concrete set of identity conditions. Such theories have failed to justify the value of non-human natural phenomena such as landscapes, plants, and animals because these theories require a basic similarity, or shared identity that grants them moral status. Understanding and acting upon the value of others, especially radically different others becomes increasingly important in a time of melting polar ice, rising sea levels and increasingly polarized political discourse. Only if we supplement identity arguments with alterity arguments can we create an ethics that not only overcomes universal egoism but also offers insight into how we face new ecological consciousness and crisis. Alterity arguments differ from identity arguments because the characterization of the other need not be particular, epistemically closed or metaphysically secure. An ethics of alterity can be grounded in resources from the phenomenal-existential tradition. Relying on insights from classic phenomenology and West-coast phenomenology, alterity arguments can justify intrinsic moral value for non-human natural phenomena such as landscapes, plants, and animals. Indeed, when paired with identity arguments, we can justify action-guiding norms and principles as well. Using resources from the phenomenological-existential tradition also allows us to reconceptualize ethics in a way that addresses both the is/ought distinction and the relationship between metaethics, ethics, and applied ethics.

Introduction: Mild traumatic brain injury (mTBI) is a common cause for visits to the emergency department (ED). The actual time required for an ED workup of a patient with mTBI in the United States is not well known. National emergency medicine organizations have recommended reducing unnecessary testing, including head computed tomography (CT) for these patients.10

Methods: To examine this issue, we developed a care map that included each step of evaluation of mTBI (Glasgow Coma Scale Score 13-15) – from initial presentation to the ED to discharge. Time spent at each step was estimated by a panel of United States emergency physicians and nurses. We subsequently validated time estimates using retrospectively collected, real-time data at two EDs. Length of stay (LOS) time differences between admission and discharged patients were calculated for patients being evaluated for mTBI.

Results: Evaluation for mTBI was estimated at 401 minutes (6.6 hours) in EDs. Time related to head CT comprised about one-half of the total LOS. Real-time data from two sites corroborated the estimate of median time difference between ED admission and discharge, at 6.3 hours for mTBI.

Conclusion: Limiting use of head CT as part of the workup of mTBI to more serious cases may reduce time spent in the ED and potentially improve overall ED throughput.