Scientific inquiry has led to immense explanatory and technological successes, partly as a result of the pervasiveness of scientific theories. Relativity theory, evolutionary theory, and plate tectonics were, and continue to be, wildly successful families of theories within physics, biology, and geology. Other powerful theory clusters inhabit comparatively recent disciplines such as cognitive science, climate science, molecular biology, microeconomics, and Geographic Information Science (GIS). Effective scientific theories magnify understanding, help supply legitimate explanations, and assist in formulating predictions. Moving from their (...) knowledge-producing representational functions to their interventional roles (Hacking 1983), theories are integral to building technologies used within consumer, industrial, and scientific milieus. -/- This entry explores the structure of scientific theories from the perspective of the Syntactic, Semantic, and Pragmatic Views. Each of these views answers questions such as the following in unique ways. What is the best characterization of the composition and function of scientific theory? How is theory linked with world? Which philosophical tools can and should be employed in describing and reconstructing scientific theory? Is an understanding of practice and application necessary for a comprehension of the core structure of a scientific theory? How are these three views ultimately related? (shrink)

Functional reductionism characterises inter-theoretic reduction as the recovery of the upper-level behaviour described by the reduced theory in terms of the lower-level reducing theory. For instance, finding a statistical mechanical realiser that plays the functional role of thermodynamic entropy allows for establishing a reductive link between thermodynamics and statistical mechanics. This view constitutes a unique approach to reduction that enjoys a number of positive features, but has received limited attention in the philosophy of science. -/- This paper aims to clarify (...) the meaning of functional reductionism in science, with a focus on physics, to define both its place with respect to other approaches to reduction and its connection to ontology. To do so, we develop and explore two alternative frameworks for functional reduction, called Syntactic Functional Reductionism and Semantic Functional Reductionism. They represent two different possible stances on the view that expand and improve the basic functional reductionist approach along different lines, and make clear how the approach works in practice. The former elaborates on David Lewis’ account, is connected with the syntactic view of theories, is committed to a logical characterisation of functional roles, and is embedded within Nagelian reductionism. The latter adopts a semantic view of theories, spells out functional roles mainly in terms of mathematical roles within the models of theories, and is expressed in terms of the related structuralist approach to reduction. The development of these frameworks has the final goal of advancing functional reductionism, to make it a fully-fledged alternative account for reduction in science. (shrink)

In recent decades, the scientific study of consciousness has significantly increased our understanding of this elusive phenomenon. Yet, despite critical development in our understanding of the functional side of consciousness, we still lack a fundamental theory regarding its phenomenal aspect. There is an “explanatory gap” between our scientific knowledge of functional consciousness and its “subjective,” phenomenal aspects, referred to as the “hard problem” of consciousness. The phenomenal aspect of consciousness is the first-person answer to “what it’s like” question, and it (...) has thus far proved recalcitrant to direct scientific investigation. Naturalistic dualists argue that it is composed of a primitive, private, non-reductive element of reality that is independent from the functional and physical aspects of consciousness. Illusionists, on the other hand, argue that it is merely a cognitive illusion, and that all that exists are ultimately physical, non-phenomenal properties. We contend that both the dualist and illusionist positions are flawed because they tacitly assume consciousness to be an absolute property that doesn’t depend on the observer. We develop a conceptual and a mathematical argument for a relativistic theory of consciousness in which a system either has or doesn’t have phenomenal consciousness with respect to some observer. Phenomenal consciousness is neither private nor delusional, just relativistic. In the frame of reference of the cognitive system, it will be observable and in other frame of reference it will not. These two cognitive frames of reference are both correct, just as in the case of an observer that claims to be at rest while another will claim that the observer has constant velocity. Given that consciousness is a relativistic phenomenon, neither observer position can be privileged, as they both describe the same underlying reality. Based on relativistic phenomena in physics we developed a mathematical formalization for consciousness which bridges the explanatory gap and dissolves the hard problem. Given that the first-person cognitive frame of reference also offers legitimate observations on consciousness, we conclude by arguing that philosophers can usefully contribute to the science of consciousness by collaborating with neuroscientists to explore the neural basis of phenomenal structures. (shrink)

The numerous and diverse roles of theory reduction in science have been insufficiently explored in the philosophy literature on reduction. Part of the reason for this has been a lack of attention paid to reduction2 (successional reduction)—although I here argue that this sense of reduction is closer to reduction1 (explanatory reduction) than is commonly recognised, and I use an account of reduction that is neutral between the two. This paper draws attention to the utility—and incredible versatility—of theory reduction. A non-exhaustive (...) list of various applications of reduction in science is presented, some of which are drawn from a particular case-study, being the current search for a new theory of fundamental physics. This case-study is especially interesting because it employs both senses of reduction at once, and because of the huge weight being put on reduction by the different research groups involved; additionally, it presents some unique uses for reduction—revealing, I argue, the fact that reduction can be of specialised and unexpected service in particular scientific cases. The paper makes two other general findings: that the functions of reduction that are typically assumed to characterise the different forms of the relation may instead be understood as secondary consequences of some other roles; and that most of the roles that reduction plays in science can actually also be fulfilled by a weaker relation than (the typical understanding of) reduction. (shrink)

We do not all make choices, reason, interpret our experience, or respond to our environment in the same way. A recent surge of scientific interest has thrust these individual differences into the spotlight: researchers in cognitive psychology and neuroscience are now devoting increasing attention to cognitive variation. The philosophical dimensions of this research, however, have yet to be systematically explored. Here I make an initial foray by considering how cognitive variation is characterized. I present a central dilemma facing descriptions of (...) individual differences, discuss several distinctions used to categorize variation, and show that these distinctions require further elaboration. Finally, by canvassing several philosophical topics for which the characterization of cognitive variation may have significant implications, I argue that philosophers should take note of how and why our minds differ. (shrink)

The numerous and diverse roles of theory reduction in science have been insufficiently explored in the philosophy literature on reduction. Part of the reason for this has been a lack of attention paid to reduction2 (successional reduction)---although I here argue that this sense of reduction is closer to reduction1 (explanatory reduction) than is commonly recognised, and I use an account of reduction that is neutral between the two. This paper draws attention to the utility---and incredible versatility---of theory reduction. A non-exhaustive (...) list of various applications of reduction in science is presented, some of which are drawn from a particular case-study, being the current search for a new theory of fundamental physics. This case-study is especially interesting because it employs both senses of reduction at once, and because of the huge weight being put on reduction by the different research groups involved; additionally, it presents some unique uses for reduction---revealing, I argue, the fact that reduction can be of specialised and unexpected service in particular scientific cases. The paper makes two other general findings: that the functions of reduction that are typically assumed to characterise the different forms of the relation may instead be understood as secondary consequences of some other roles; and that most of the roles that reduction plays in science can actually also be fulfilled by a weaker relation than (the typical understanding of) reduction. (shrink)

Explanation is a perennially hot topic in philosophy of science. Yet philosophers have exhibited a curious blind spot to the questions of how explanatory projects develop over time, as well as what processes are involved in generating their developmental trajectories. This paper examines these questions using research into the end-Permian mass extinction as a case study. It takes as its jumping-off point the observation that explanations of historical events tend to grow more complex over time, but it goes beyond this (...) observation by scrutinizing the processes responsible for generating this pattern. Surveying several decades of research into the end-Permian extinction, I suggest that the principal “driver” of explanation in geohistory is non-explanatory work: work that is undertaken to increase our descriptive understanding of a phenomenon, not to test a particular explanatory claim. Non-explanatory work drives explanation by imposing or eliminating demands on explanation, and by furnishing new resources for constructing explanatory models. Explanations grow more complex because the demands on explanation tend to increase with ongoing characterization of the target phenomenon, and characterization tends grows the roster of explanatory resources. However, the fact that non-explanatory work sometimes eliminates demands on explanation means that this trend is not irreversible. I suggest that to achieve a more rounded view of the dynamics of explanation, philosophers should ask how research into complex phenomena is organized, as well as how explanatory progress depends upon the coordination of different kinds of material and epistemic resources. (shrink)

The mind–body problem is analyzed in a physicalist perspective. By combining the concepts of emergence and algorithmic information theory in a thought experiment, employing a basic nonlinear process, it is shown that epistemologically emergent properties may develop in a physical system. Turning to the significantly more complex neural network of the brain it is subsequently argued that consciousness is epistemologically emergent. Thus reductionist understanding of consciousness appears not possible; the mind–body problem does not have a reductionist solution. The ontologically emergent (...) character of consciousness is then identified from a combinatorial analysis relating to universal limits set by quantum mechanics, implying that consciousness is fundamentally irreducible to low-level phenomena. (shrink)

This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of (...) reduction and emergence. (shrink)

This paper does two things. Firstly, it clarifies the way that phenomenological data is meant to constrain cognitive science according to enactivist thinkers. Secondly, it points to inconsistencies in the ‘Radical Enactivist’ handling of this issue, so as to explicate the commitments that enactivists need to make in order to tackle the explanatory gap. I begin by sketching the basic features of enactivism in sections 1–2, focusing upon enactive accounts of perception. I suggest that enactivist ideas here rely heavily upon (...) the endorsement of a particular explanatory constraint that I call the structural resemblance constraint, according to which the structure of our phenomenology ought to be mirrored in our cognitive science. Sections 3–5 delineate the nature of, and commitment to, SRC amongst enactivists, showing SRC’s warrant and implications. The paper then turns to Hutto and Myin’s handling of SRC in sections 6–7, highlighting irregularities within their programme for Radical Enactivism on this issue. Despite seeming to favour SRC, I argue that Radical Enactivism’s purported compatibility with the narrow supervenience of perceptual experience is in fact inconsistent with SRC, given Hutto and Myin’s phenomenological commitments. I argue that enactivists more broadly ought to resist such a concessionary position if they wish to tackle the explanatory gap, for it is primarily the abidance to SRC that ensures progress is made here. Section 8 then concludes the paper with a series of open questions to enactivists, inviting further justification of the manner in which they apply SRC. (shrink)

Within physics there are two ways of establishing the relative fundamentality of one theory compared to another, via two senses of reduction: "inter-level" and "intra-level" (Crowther, 2018). The former is standardly recognised as roughly correlating with the chain of ontological dependence (i.e., the phenomena described by theories of macro-physics are typically supposed to be ontologically dependent on the entities/behaviour described by theories of micro-physics), and thus has been of interest to naturalised metaphysics. The latter, though, has not been considered interesting (...) for metaphysics, because it is not thought to correlate either with ontological dependence, nor causal or dynamical dependence. I argue, however, that this is a mistake, and that actually, the intra-level relation does reflect ontological dependence (in the same sense as the inter-level relation) and thus should not be neglected by metaphysics of physics. This argument further supports the assertion that the same notion of fundamentality underlies both the inter- and intra-level claims of fundamentality in physics, and that this notion of relative fundamentality in physics correlates with that of metaphysics. (shrink)

In their 2010 paper, Dizadji-Bahmani, Frigg, and Hartmann argue that the generalized version of the Nagel–Schaffner model that they have developed is the right one for intertheoretic reduction, i.e. the kind of reduction that involves theories with largely overlapping domains of application. Drawing on the GNS, DFH presented a Bayesian analysis of the confirmatory relation between the reducing theory and the reduced theory and argued that, post-reduction, evidence confirming the reducing theory also confirms the reduced theory and evidence confirming the (...) reduced theory also confirms the reducing theory, which meets the expectations one has about theories with largely overlapping domains. In this paper, I argue that the Bayesian analysis presented by DFH faces difficulties. In particular, I argue that the conditional probabilities that DFH introduce to model the bridge law entail consequences that run against the GNS. However, I also argue that, given slight modifications of the analysis that are in agreement with the GNS, one is able to account for these difficulties and, moreover, one is able to more rigorously analyse the confirmatory relation between the reducing and the reduced theory. (shrink)

After describing the disorder of psychopathy, I examine the theories and the evidence concerning the psychopaths’ deficient moral capacities. I first examine whether or not psychopaths can pass tests of moral knowledge. Most of the evidence suggests that they can. If there is a lack of moral understanding, then it has to be due to an incapacity that affects not their declarative knowledge of moral norms, but their deeper understanding of them. I then examine two suggestions: it is their deficient (...) practical reason or their stunted emotions that are at fault. The evidence supports both explanations. I conclude with an overview of the debate concerning whether they are morally or legally responsible for their actions. (shrink)

Non-naturalists claim that the nature of normativity precludes the possibility of normative naturalism. In particular, they think that normative reduction amounts to normative elimination. This is because it always leaves out the normative. In this paper, I examine the force that the normativity objection has against Humean reductionism. I argue that the normativity objection has no argumentative force against reductionism. When it is presented as a bare intuition, it begs the question against reduction. A more interesting reading of the argument (...) claims that the normative cannot be explained in terms of the natural because the natural is arbitrary. Yet, this version of the argument fails as well because the natural is not arbitrary in the relevant sense. The natural is contingent, so what has value is contingent. That is not an elimination of the normative though, because contingent reasons are still reasons. (shrink)

In this paper, I argue that explaining cognitive behavior can be achieved through what I call hybrid explanatory inferences: inferences that posit mechanisms, but also draw on observed regularities. Moreover, these inferences can be used to achieve unification, in the sense developed by Allen Newel in his work on cognitive architectures. Thus, it seems that explanatory pluralism and unification do not rule out each other in cognitive science, but rather that the former represents a way to achieve the latter.

Relationships of counterfactual dependence have played a major role in recent debates of explanation and understanding in the philosophy of science. Usually, counterfactual dependencies have been viewed as the explanantia of explanation, i.e., the things providing explanation and understanding. Sometimes, however, counterfactual dependencies are themselves the targets of explanations in science. These kinds of explanations are the focus of this paper. I argue that “micro-level model explanations” explain the particular form of the empirical regularity underlying a counterfactual dependency by representing (...) it as a physical necessity on the basis of postulated microscopic entities. By doing so, micro-level models rule out possible forms the regularity could have taken. Micro-model explanations, in other words, constrain empirical regularities and their associated counterfactual dependencies. I introduce and illustrate micro-level model explanations in detail, contrast them to other accounts of explanation, and consider potential problems. (shrink)

The present thesis explores some metaphysical issues concerning biochemical kinds and the relations between chemical and biological properties and phenomena. The main result of this thesis is that there is something sui generis about biochemical kinds. This result is motivated by two theoretical steps. The first is characterising biochemical functions as weakly emergent from the chemical structure [Chapter 3, Chapter 6]. The second is via an account for which biochemical kinds are natural categories [Chapter 4, Chapter 7]. The thesis comprises (...) four parts. Part I [Chapter 1, Chapter 2] aims to offer the methodological and conceptual tools that underpin this research. Chapter 1 presents the debate on the unity of science and the motivation of the research. Chapter 2 presents the account of natural kinds that will be used throughout the thesis. Part II [Chapter 3, Chapter 4] offers a detailed metaphysical analysis of the molecular gene. Chapter 3 argues that molecular genes are weakly emergent from nucleic acids. Chapter 4 argues that the category "molecular gene" can be deemed a natural kind, following the account presented in Chapter 2. Part III [Chapter 5, Chapter 6, Chapter 7] explores some of the themes related to biochemical kinds and generalises some of the results from Part II. Chapter 5 considers biochemical functions and how functional attribution should be interpreted for biochemical molecules. Chapter 6 considers the relation between biochemical functions and structure, spelt in terms of weak emergence and explores unity in biochemistry. Chapter 7 considers the topic of biochemical kinds per se and argues that biochemical kinds are natural categories. Part IV [Chapter 8] elucidates the main outcome and the implications that this research can have for future discussion in the philosophy and metaphysics of biochemistry and the unity of science. (shrink)

This paper proposes a model for implementation of intrinsic natural language sentence meaning in a physical language understanding system, where 'intrinsic' is understood as 'independent of meaning ascription by system-external observers'. The proposal is that intrinsic meaning can be implemented as a point attractor in the state space of a nonlinear dynamical system with feedback which is generated by temporally sequenced inputs. It is motivated by John Searle's well known (Behavioral and Brain Sciences, 3: 417–57, 1980) critique of the then-standard (...) and currently still influential computational theory of mind (CTM), the essence of which was that CTM representations lack intrinsic meaning because that meaning is dependent on ascription by an observer_._ The proposed dynamical model comprises a collection of interacting artificial neural networks, and constitutes a radical simplification of the principle of compositional phrase structure which is at the heart of the current standard view of sentence semantics because it is computationally interpretable as a finite state machine. (shrink)

Psychoneural reduction has been debated extensively in the philosophy of neuroscience. In this article I will evaluate metascientific approaches that claim direct molecular and cellular explanations of cognitive functions. I will initially consider the issues involved in linking cellular properties to behaviour from the general perspective of neural circuits. These circuits that integrate the molecular and cellular components underlying cognition and behaviour, making consideration of circuit properties relevant to reductionist debates. I will then apply this general perspective to specific systems (...) where psychoneural reduction has been claimed, namely hippocampal long-term potentiation and the Aplysia gill-withdrawal reflex. (shrink)

In this paper, we reject commonly accepted views on fundamentality in science, either based on bottom-up construction or top-down reduction to isolate the alleged fundamental entities. We do not introduce any new scientific methodology, but rather describe the current scientific methodology and show how it entails an inherent search for foundations of science. This is achieved by phrasing metaphysical assumptions into falsifiable statements and define as fundamental those that survive empirical tests. The ones that are falsified are rejected, and the (...) corresponding philosophical concept is demolished as a prejudice. Furthermore, we show the application of this criterion in concrete examples of the search for fundamentality in quantum physics and biophysics. (shrink)

This thesis investigates the epistemological and metaphysical relations between chemistry and quantum mechanics. These relations are examined with respect to how chemistry and quantum mechanics each describe a single inert molecule. A review of how these relations are understood in the literature shows that there is a proliferation of positions which focus on how chemistry is separate from quantum mechanics. This proliferation is accompanied by a tendency within the philosophy of chemistry community to connect the legitimacy of the field with (...) the autonomy of chemistry. First, it is argued that this connection should not be made. Secondly, it is argued that chemistry and quantum mechanics are unified in accordance with Harold Kincaid’s model of non-reductive unity because the two theories exhibit particular epistemic and metaphysical interconnections. Thirdly, a metaphysical account is examined which is incompatible with Kincaid’s model of unity; namely strong emergence as understood by Robin Hendry. According to Hendry, the structure of a single inert molecule strongly emerges from its quantum mechanical entities in the sense that there is downward causation. However, Hendry’s defense of this account faces certain problems. Moreover, the putative empirical evidence for his understanding of strong emergence can be explained without invoking strong emergence. This is shown by considering how quantum mechanics assumes an idealized understanding of a molecule’s stability and structure. In the light of the philosophical literature on idealizations, this idealization can be interpreted in two different ways, both of which explain why quantum mechanics describes the structure of a single molecule the way it does, without assuming strong emergence in Hendry’s sense. Each interpretation has philosophical implications regarding the nature of chemical properties, and the relation of chemistry and quantum mechanics. These implications are consistent with Kincaid’s model of unity and thus further support chemistry’s unity with quantum mechanics (as per Kincaid). (shrink)

Two opposed movements of thought threaten philosophy as an autonomous practice from the inside: scientific naturalism and quietism. Naturalism (qua methodological thesis) threatens to turn philosophy into a mere ancilla of the sciences, quietism understood as the prescription to remain silent in philosophy would not countenance any more "positive" philosophy. This book reconstructs naturalism and quietism such that it becomes clear naturalism does have the potential to end philosophy as an autonomous practice and that quietism, correctly understood, does not. To (...) this end, this book provides arguments against the prevailing orthodox status of naturalism and a heterogenous reading of Wittgenstein's metaphilosophical quietism as the rejection of a certain kind of theories in philosophy, namely quasi-scientific theories. (shrink)

Background: Interdisciplinarity is one of the current trends in the scientific world today, that began with the uneasiness about the loss of the unity of science. This trend also opens possibilities for explaining complex phenomena more comprehensively and creating more advanced applications and implementations of scientific theories. One of the biggest challenges to conducting interdisciplinary research is theoretical integration, how can we combine theories from various disciplines such that the combination is fruitful? Method: This dissertation attempts to answer this challenge (...) by analyzing the intertheoretical connections of some theories from various disciplines for some real interdisciplinary research. The structuralist metatheory of science is applied as the basic theory to model the intertheoretical connections formally. This research begins with modeling the scientific theories in question before modeling the intertheoretical connections and some modifications needed. This research focuses on some researches in cognitive science that involve psychology, neuroscience, and artificial intelligence. The first research is the research conducted by van Veen et al., who research the activity of neurons in a brain's field called dorsal Anterior Cingulate Cortex during a phase of dissonance between cognitions. This research serves as a context for the analysis of intertheoretical reduction between the Festinger theory of cognitive dissonance and the Hawkins-Kandel computational neuroscientific theory. The other research is the consonance model of simulation built by Shultz and Lepper, which implements the Hopfield network to build a simulation of the cognitive dissonance. The third research is the connectionist model of simulation built by van Overwalle and Jordens, which implements the two-layers feed-forward perceptron and the delta rule as its learning rule to build a simulation of forced compliance dissonance. Result: Through this research, the author concludes that the structuralist metatheory of science can be applied for modeling and analyzing intertheoretical connections in the same discipline and between disciplines in real scientific research. The structuralist metatheory of science enables us to model and analyze the structure of the theories and their intertheoretical connections with great detail and brings very fruitful results. This research delivers some results not only for the structuralist theory science itself but also for the philosophy of science in general and interdisciplinary researches, especially cognitive science. First, by analyzing the models, a revision of the definition of intertheoretical specialization, and specialization of the concept of theory-holon according to the structuralist theory of science, called the V-pattern and strategy for combining scientific theories, are proposed. These V-pattern and strategy can serve as a tool for combining scientific theories. Second, unlike other approaches on intertheoretical reduction such as the GNS model, the structuralist metatheory of science does not intend to formulate a generalized model of reduction nor focus only on intertheoretical reduction. It provides us powerful tools for modeling various intertheoretical relations, including intertheoretical reduction, case by case. Although the intertheoretical reduction in the structuralist model is more epistemological than ontological, the structuralist models show how the reduction has empirical claims and intended applications by applying the r* function that maps the T-theoretical level to T-non-theoretical level. Third, related to the notion of the unity of science, this dissertation still sees that the unity of science is still a plausible and essential agenda for the philosophy of science and the scientific world in general. This dissertation's idea of the unity of science proposed does not assume essentialism, reductionism, and epistemological monism. This dissertation sees that the unity of science is closely related to scientific practice. Fourth, for interdisciplinary research, primarily cognitive science, this dissertation proposes an approach to model and analyze intertheoretical connections for any scientific research or any philosophical school in philosophy of science related to the idea of intertheoretical relation. This dissertation is the first example of such modeling and analysis. (shrink)

This PhD thesis concerns introspective approaches to the study of the mind. Across three standalone papers, I examine the significance of introspective data and advise on appropriate kinds of training for the production of such data. An overview document first introduces major themes, methods and arguments of the thesis. Paper 1 then begins the argumentative work, interrogating the constraining function of introspection in cognitive science. Here, I evaluate “enactivist” claims about the significance of introspection, clarifying central enactivist suggestions to draw (...) out the broader importance of introspection in science and philosophy. Paper 2 then examines the proposed employment of Buddhist meditation practices in the production of rigorous introspective data. I defend such proposals against concerns that meditators yield ungeneralizable data, given the transformative character of these attention-training techniques. I argue that some meditation-trained transformations are actually epistemically-beneficial, undermining popular associations between transformation and “distortion”. Paper 3 then reviews difficulties involved in integrating meditative training into research. I emphasise the importance of specific contextual supports to meditation as critical ingredients of introspective proficiency, showing how difficulties replicating these threaten to limit the scope of meditation’s scientific benefits. I layout methodological responses to this that can maximise meditation’s positive impact going forwards. (shrink)

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)