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This thesis argues that a theological articulation of panpsychism, within the bounds of a broadly conceived Christian orthodoxy, would be of benefit to the doctrine of creation. Panpsychism is a family of theories within philosophy of mind, which seek to explain the existence of consciousness in the human person by positing mentality ("psyche") as fundamental and ubiquitous to the natural world ("pan"). In recent decades, emergence theory has become a popular via media between eliminative physicalism and substance dualism. However, in lieu of the inability (or refusal) of emergence theorists to provide an account of how matter gives rise to the mind, a significant group of contemporary analytic philosophers are returning to the historical concept of panpsychism as a more satisfactory alternative. Should this revival of panpsychism continue, what will the implications be for Christian theologians engaged in constructive and interdisciplinary articulations of the doctrine of creation? This is the driving question that this thesis sets out to answer. In addition to various scientific and philosophical ambiguities, theologies built upon the theory of emergence contain unrecognised tensions. As such, theologians should investigate alternative ontologies, which may serve Christianity better. The recent revival of panpsychism within contemporary philosophy of mind needs to be evaluated both for its coherence and conduciveness to theistic beliefs. To counteract any appearance that this project is merely chasing the winds of fashion, a brief historical interlude considering the panpsychism of Gottfried Wilhelm von Leibniz is given to exhibit the historical pedigree of employing panpsychism for theological ends. Philosophical rigour and historical pedigree, although important, are not enough to justify favouring one ontology above all others within the doctrine of creation. An ontology must also 'earn its keep', so to speak, through interaction and integration with other theological commitments. Panpsychism is so tested in the context of contemporary debates surrounding divine action and eco-theological ethics. These chapters reveal the possibility that panpsychism may not only be resourced from without but may also arise from within the Christian community's Scriptural and liturgical reflection. Panpsychism facilitates a robust and realistic account of God's active presence within creation and the response of all created beings in praise. If nothing more, the revival of panpsychism within analytic philosophy of mind should be welcomed and may be partnered with by theologians in the coming years.

G. W. Leibniz fue un lector frecuente de la obra filosófica de Suárez, lectura que dejó una huella profunda en su metafísica. En concreto, el uso que Leibniz hace de los principios se puede ver como una aplicación práctica del tratamiento que hace Suárez de los principios en las Disputaciones metafísicas.

In this dissertation, I analyze the distinction between different types of infinity that Leibniz identifies throughout his philosophical and mathematical works. By attending to these differences, I show how Leibniz’s rejection of infinite number as a contradictory notion does not entail the impossibility of infinitely small lines. Chapter 1 explains the differences between three grades of infinity that Leibniz identifies in a 1676 taxonomy on the infinite and how this taxonomy was an attempt to avoid paradoxes of the infinite. It also contains a description of a separate taxonomy of the infinite that Leibniz gave in 1706, in which Leibniz explicitly bans any type of infinity that is a whole composed of infinity many distinct parts. Chapter 2 treats five places where infinity lines arise in Leibniz’s mathematics: infinite number, the composition of the continuum, infinite series, infinitesimals and their bounded infinite counterparts, and unbounded infinite lines. Looking at the different ways Leibniz evaluates each of these concepts, we see that infinitesimals and bounded infinite lines stand on firmer conceptual footing then the others from Leibniz’s point of view. Chapter 3 argues that Leibniz’s claims that infinitesimals are “fictions” or “impossible,” this is in reference to a specific type of impossibility that he calls the impossible per accidens. Unlike the absolutely impossible, this type of impossibility is not rooted in contradiction, but conflict with metaphysical principles that bar their existence in the order of created things. Hence, Leibniz’s stance towards infinitesimals allows them to be perfectly coherent entities for the purposes of geometric reasoning, despite his ban on their existence within the physical world.

El analysis situs es un proyecto geométrico desarrollado por Leibniz durante sus años en París. El objetivo del presente artículo es perfi lar la noción de “estructura situacional” a partir de las ideas presentes en el analysis situs. Esta noción permitirá establecer vínculos claros entre esta disciplina geométrica y el cálculo infinitesimal, la metafísica y la dinámica leibniziana. Un mejor entendimiento de estos vínculos posibilitará una comprensión más profunda de nociones leibnizianas como la de infinitesimal, impetus y conatus.

La investigación sobre el concepto metafísico de necesidad en la filosofía de Leibniz toma como punto de partida la consideración de los diferentes modos de ser -posibilidad, existencia, contingencia y necesidad- y las relaciones que se establecen entre ellos. De este modo, la noción de necesidad aparece como fundamento último de lo posible y lo existente, así como de la contingencia, conjunción de ambos. En esta investigación surgen diferentes problemas nucleares de la filosofía leibniziana, como es la cuestión del necesitarismo, el laberinto de la libertad o la creación. Todos estos interrogantes han de encontrar su solución última en la necesidad, que aparece así como la síntesis última de la realidad. En este sentido, pueden descubrirse dos modos de darse esta síntesis: por un lado, se puede ver la necesidad como tatalidad de la posibilidad. Por otro, esta síntesis se puede hacer viendo en lo necesario el origen de la existencia. En el plano de lo contingente, sin embargo, se hace imprescindible la articulación de la necesidad en diferentes tipos que den razón, precisamente, de los problemas anteriormente señalados: así, Leibniz distingue entre necesidad hipotética, absoluta, metafísica y moral. De la combinación de estos tipos de necesidad, mediante el empleo de la armonía preestablecida, surge la elección y constitución del mejor de los mundos posibles: el que actualmente existe. El aspecto más problemático, sin embargo, surge en la consideración de la necesidad per se, en la que la consideración del vínculo entre su esencia y su existencia no queda resuelta.

Through the analysis of idealistic arguments and evidence from physics, it will be demonstrated that monistic idealism has a great deal of explanatory power as a metaphysical system for the reality that one experiences. Some of the arguments that support this claim include the inadequateness of Cartesian matter, the seemingly infinite divisibility of atoms, matter being reducible to sensations, the unnecessary aspect of matter, and simplicity. Evidence from quantum physics includes such factors as the necessary role of an observer in the collapse of a quantum wave function and the element of nonlocality. Psychological experiments including nonlocal communication, the power of mental force, and the placebo effect further justify the case for monistic idealism.

Leibniz analyzes contingency in terms of a range of different notions: hypothetical necessity, per se contingency, infinite analysis, possible free decrees of God, and moral necessity. These have been interpreted as attempts to retreat from the neccesitarian view he adopts in his early work, but I defend the view that Leibniz’s commitment to necessitarianism—the claim that all truths are necessary—is an important and unwavering feature of his system. The core of Leibniz’s modal theory is the thesis that the denial of a necessary truth is contradictory. Leibniz thinks that if we take all necessary truths into account, including the nature of God, God’s understanding of essences, and his will to do what is best, then all things considered all truths are necessarily true. All truths are necessarily true because the denial of any truth contradicts some necessary feature of God. Instead of understanding Leibniz’s subsequent theories of contingency as abandoning necessitarianism, I treat them as attempts to account for distinctions his interlocutors draw. Rather than eschew all talk of contingency, Leibniz offers and liberally invokes proxies for this notion. I trace the development of Leibniz’s various accounts of contingency from his early to mature work in order to illustrate that they are best understood in a necessitarian framework. I develop versions of his various accounts of contingency, including per se contingency and hypothetical necessity (Chapter 1), infinite analysis and possible free decrees of God (Chapter 2), and moral necessity (Chapter 3). The outcome of my project is a systematic treatment of Leibniz’s surrogate or proxy theories of contingency within his necessitarian framework. It also establishes the character of Leibnizian possible worlds, which are key for the grounding of contingent truths in the goodness of God’s will. Instead of representing all logical space, possible worlds represent alternative plans for God’s world creation, and are thus constrained by metaphysical principles informed by God’s nature.

In this thesis I propose that Leibniz did not state Leibniz's Law, the logically and metaphysically robust principle that is typically understood as the following bi-conditional: ∀x ∀y [(x = y) ↔ ∀P (Px ↔ Py)]. To arrive at this conclusion, I examine the three principles that have become associated with Leibniz's Law: the Substitutivity Principle (salva veritate), the Indiscernibility of Identicals, and the Identity of Indiscernibles. I show that Leibniz intended salva veritate as a semantic principle, never explicitly stated the Indiscernibility of Identicals, and understood the Identity of Indiscernibles as a metaphysical principle. In the debate about Leibniz's Law, I focus on four commentators: (1) W. V. O. Quine's construal of salva veritate as the Indiscernibility of Identicals, (2) Nicholas Rescher's contention that both the Identity of Indiscernibles and salva veritate may be construed as Leibniz's Law, (3) Fred Feldman's argument that Leibniz did not state a law or definition of identity, but only a criterion of identity for concepts, and (4) Edwin Curley's response to Feldman, that Feldman's assumptions, along with passages in Leibniz, show Leibniz did state Leibniz's Law I argue that Feldman's position is not completely correct, but can be amended with insights from Quine, Rescher, and Curley, and by reference to Leibniz's Complete Concept Theory.

I propose a model of perception by which unconscious sensory input can become conscious in a way that is entirely mechanical and \'non-spooky\'. Based on the model of perception found G.W. Leibniz philosophy, primarily the New Essays on Human Understanding, the Leibnizian Aggregate Model (LAM) of perception may, when fully matured through future investigation, provide a way for contemporary philosophers of mind to evade certain anti-materialist objections without having to flatly deny the intuitions that underlie them.

A logic that utilizes higher-order quantification --quantifying over concepts (or relations), not just over the first-order level of individuals-- can be interpreted standardly or nonstandardly depending on whether one takes an intensional or extensional view of concepts. I argue that this decision is connected to how one understands the mathematical notion of function. A function is often understood as a rule that, when given an argument from a set of objects called a "domain," returns a value from a set of objects called a "codomain." Because a concept can be thought of as a two-valued function (that indicates whether or not a given object falls under the concept), having an extensional interpretation of higher-order variables --the standard interpretation-- requires that one adopt an extensional notion of function. Viewed extensionally, however, a function is understood not as a rule but rather as a correlation associating every element in a domain with an element in a codomain. When the domain is finite, the two understandings of function are equivalent (since one can define a rule for any finite correlation), but with an infinite domain, the latter understanding admits arbitrary functions, or correlations not definable by a finitely specifiable rule. Rejection of the standard interpretation is often motivated by the same reasons used to resist the extensional understanding of function. Such resistance is overt in the pronouncements of Leopold Kronecker, but is also implicit in the work of Gottlob Frege, who used an intensional notion of function in his logic. Looking at the problem historically, I argue that the extensional notion of function has been basic to mathematics since ancient times. Moreover, I claim that Gottfried Wilhelm Leibniz's combination of mathematical and metaphysical ideas helped inaugurate an extensional and ultimately model-theoretical approach to mathematical concepts that led to some of the most important applications of mathematics to science (e.g. the use of non-Euclidean geometry in the theory of general relativity). In logic, Frege's use of an intensional notion of function led to contradiction, while Richard Dedekind and Georg Cantor applied the extensional notion of function to develop mathematically revolutionary theories of the transfinite.

Modernity began in Leibniz s lifetime, arguably, and due to the efforts of a group of philosopher-scientists of which Leibniz was one of the most significant active contributors. Leibniz invented machines and developed the calculus. He was a force for peace, and industrial and cultural development through his work as a diplomat and correspondence with leaders across Europe, and in Russia and China. With Leibniz, science became a means for improving human living conditions. For Leibniz, science must begin with the God s eye view and begin with an understanding of how the Creator would have designed the universe. Accordingly, Leibniz advocated the a priori method of scientific discovery, including the use of intellectual constructions or artifices. He defended the usefulness and success of these methods against detractors. While cognizant of Baconian empiricism, Leibniz found that an unbalanced emphasis on experiment left the investigator short of conclusions on efficient causes. Leibniz worked outside, but complemented, the current of formal reasoning and empiricism which was developing in scientific circles during his lifetime. He supported the development of methods for calculation and demanded precise reasoning, while arguing that it was folly to omit the Neoplatonic orientation from science. Indeed, without Neoplatonism there would be no modernity. Leibniz s Neoplatonic course complemented his work with machines. Leibniz crystallised the Neoplatonic orientation as a pragmatic humanist agenda, and merged it with national imperatives for developing science. Leibniz s policy orientation is aligned with the Hermetic conception of Man as magus, who ultimately can control even the stars. The industrial-scientific age which followed Leibniz is a testament to the success of his life s work.

El presente trabajo aborda el problema del estatuto ontológico de las relaciones intermonádicas en la filosofía de Leibniz. Según argumentaré, dada (1) la concepción leibniziana de la sustancia como ser completo y (2) la caracterización que hace Leibniz de Dios como agente creador libre, las relaciones intersubstanciales no pueden ser entendidas como meros entes de razón fundados ab extra en la actividad de los sujetos cognoscentes, sino, antes bien, como genuinas propiedades (relacionales) fundadas en las configuración interna de las propias substancias individuales.

Abstract: Leibniz scholars have difficulty reconciling Leibniz’s metaphysical account of causation with his theological account, since the former claims that creatures are the source of their own actions, and the latter seemingly undercuts this claim by ascribing to God all that there is of positive reality in creaturely actions. If God is the sole source of positive reality in creaturely actions, then all that is left for the creature to contribute to the causal nexus with God is negative reality – limitations, but then the conclusion is close to hand that creatures are not causally efficacious. The present work avoids this conclusion by showing that, for Leibniz, the ontological status of limitation comes in degrees, and some limitations, for example those produced by free creaturely actions, though not positive realities proper, are not merely negative realities; creatures are causally efficacious insofar as they are responsible for limitations of this latter type.

I examine the methods of Georg Cantor and Kurt Gödel in order to understand how new symbolic innovations aided in mathematical discoveries during the early 20th Century by looking at the distinction between the lingua characterstica and the calculus ratiocinator in the work of Leibniz. I explore the dynamics of innovative symbolic systems and how arbitrary systems of signification reveal real relationships in possible worlds. Examining the historical articulation of the analytic/synthetic distinction, I argue that mathematics is synthetic in nature. I formulate a moderate version of mathematical realism called modal relationalism.

The principal goal of this dissertation is to develop and defend a criterion of intelligibility adequate to the task of explaining the variety of historical appeals to this notion in philosophy and, more importantly, science. The thesis I defend holds that any account capable of explaining the historical use of intelligibility in criticizing scientific explanations must begin with the fact that charges generally encapsulated concerns with theoretical terms and their associated representational contents. For individuals like Leibniz and Boyle as well as latter atomists and other nineteenth century scientists like Maxwell the pertinent question was whether the putative referents of the theoretical terms of explanations could be conceived of. “Conceiving of” for early modern thinkers had principally to do with associating terms with ideas that are either rationally grounded or derived from experience. Later theorists like Maxwell, while remaining faithful to the traditional use of intelligibility, implicitly extend the idea by associating theoretical abstractions with models that are accessible to the imagination. After establishing this core thesis I proceed to develop an alternative account of intelligibility that can accommodate the historical worries while at the same time addressing some potential philosophical challenges to the use of this notion in the assessment of scientific theories. The thesis defended in this regard is that terms are intelligible if and only if they can be associated with observationally based representations that figure in a broader network of such representations whose relations are suitably constrained by the theory.