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The Early Modern Debate on the Problem of Matter's Divisibility: a Neo- Aristotelian Solution

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The Early Modern Debate on the Problem of Matter's Divisibility: a Neo- Aristotelian Solution The Early Modern Debate on the Problem of Matter's Divisibility: A Neo- Aristotelian Solution Author: Colin Edward Connors Persistent link: http://hdl.handle.net/2345/bc-ir:103593 This work is posted on eScholarship@BC, Boston College University Libraries. Boston College Electronic Thesis or Dissertation, 2014 Copyright is held by the author. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (http:// creativecommons.org/licenses/by-nc-nd/4.0). Boston College The Graduate School of Arts and Sciences Department of Philosophy THE EARLY MODERN DEBATE ON THE PROBLEM OF MATTER’S DIVISIBILITY: A NEO-ARISTOTELIAN SOLUTION A dissertation by COLIN EDWARD CONNORS submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy December 2014 © copyright by COLIN EDWARD CONNORS 2014 The Early Modern Debate on the Problem of Matter’s Divisibility: A Neo-Aristotelian Solution Colin Connors Dissertation Director: Professor Jean-Luc Solere Abstract My dissertation focuses on the problem of matter’s divisibility in the 17th-18th centuries. The problem of material divisibility is a focal point at which the metaphysical principle of simplicity and the mathematical principle of space’s infinite divisibility conflict. The principle of simplicity is the metaphysical requirement that there must be a simple or indivisible being that is the constitutive foundation of all composite things in nature. Without simple beings, there cannot be composite beings. The mathematical principle of space’s infinite divisibility is a staple of Euclidean geometry: space must be divisible into infinitely smaller parts because indivisibles or points cannot compose extension. Without reconciling these metaphysical and mathematical principles, one can call into question the integrity of mathematics and metaphysics. Metaphysical contradiction results from the application of metaphysical simplicity to the composition of material bodies that occupy infinitely divisible space. How can a simple being constitute a material object while occupying a space that lacks a smallest part? Should we assume that a composite material object (such as the paper in front of the reader) exists in an infinitely divisible space, then the simple beings must occupy a space that consists of ever smaller spaces. The simple being thereby appears to consist of parts simpler than itself—a metaphysical contradiction. Philosophers resolve this contradiction by either modifying the metaphysical principle of simplicity to allow for the occupation of infinitely divisible space, or have simply dismissed one principle for the sake of preserving the other principle. The rejection of one principle for preserving the other principle is an undesirable path. Philosophers would either forfeit any attempt to account for the composition of material reality by rejecting simplicity or deny understanding of geometry heretofore via the rejection of space’s infinite divisibility. My objective in this dissertation is two-fold: 1.) to provide an historical analysis of various philosophers’ attempts to reconcile simplicity and infinite divisibility or to argue for the exclusive nature of the said principles; 2.) to articulate a reconciliation between simplicity and infinite divisibility. Underlying both objectives is my attempt to draw a connection between the metaphysical principle of simplicity and the metaphysical principle of sufficient reason. Having shown in the historical section that each philosopher implicitly references a modified version of the principle of sufficient reason when articulating their theories of metaphysical simplicity, I will use this common principle to develop a Neo-Aristotelian solution to the problem of material divisibility. This Neo-Aristotelian solution differs from other accounts in the historical section by including a potential parts theory of material divisibility while modifying the principle of simplicity: simple beings are no longer conceived as constitutive parts of a material thing, but as the sources of unity for a natural composite being. Table of Contents 1. Dissertation Introduction and Synopsis 1 2. Chapter One: The Priority of Metaphysical Principle of Simplicity 26 in Hume, Berkeley, and the Pre-Critical Kant -Chapter One Introduction 27 - Section A-John Locke and Negative Ideas 37 -Section B-Berkeley, Negative Ideas, and Perceptual Minima 51 -Section C-Hume, Negative Ideas, and Minimum Sensibles 71 -Section D-Berkeley versus Hume on the Nature of Minima 102 -Section E-Immanuel Kant and Force-Shells 130 -Chapter One Conclusion 165 3. Chapter Two: Leibniz and Phenomenal Matter and Space 167 -Chapter Two Introduction 168 -Section A-Pseudo Qualitative Intellectual Divisibility 172 -Section B-The Principle of Simplicity and the Principle of Material 176 Sufficient Reason -Section C-Leibniz’s Theory of the Divisibility of Matter and Space and his 186 Affirmation of SIMT -Chapter Two Conclusion 192 4. Chapter Three: Kant and the Antinomy of Matter’s Divisibility 194 -Chapter Three Introduction 195 -Section A- The Metaphysical Foundations of Natural Science: 197 The Plenum Principle and Matter’s Infinite Divisibility -Section B- The Second Antinomy and the Principle of Simplicity 218 -Chapter Three Conclusion 234 5. Chapter Four: A Defense of Neo-Aristotelian Potential Parts Doctrine 236 -Chapter Four Introduction 237 -Section A- The Problem of Divisibility in the Actual and 240 Potential Parts Doctrines: The Arguments from Divisibility -Section B- Argument against the Actual Parts Theory 253 -Section C- Substantial Form and Neo-Aristotelian Potential Parts 259 -Section D- Aristotelian Substantial Form and PPT: 263 The Reconciliation between Simplicity and Infinite Divisibility -Chapter Four Conclusion 266 6. Appendix: Interpretations of Leibnizian Space and Matter 268 References 295 1 Dissertation Introduction and Synopsis 2 During the 17th and 18th centuries, philosophers witness a conflict between proponents of the truths of mathematics and proponents of the truths of metaphysics. This conflict is not only metaphysical in nature, but also epistemic in character. In this debate, one must either deem that the conflict leaves either set of principles irreconcilable, eschewing a truth of metaphysics in order to preserve a truth of mathematics or vice-versa; or one must find some way to reconcile the seemingly conflicting principles; or one might believe that the conflict is unsolvable, casting both sets of principles into the region of knowledge that is unattainable by feeble human reason. The clash centers on the question of whether material bodies that occupy infinitely divisible space must be infinitely divisible. The principles at stake in this dispute are the metaphysical truth of simplicity and the mathematical truth of space’s infinite divisibility. The metaphysical truth of simplicity states that all beings must either be simple beings or be composed of simple beings. It is a principle traceable to the Neo-Platonic philosopher named Proclus. Proclus argues in the Elements of Theology that there must be what he calls “The One” or pure unity. Without something that is one or is considered one being, no composition or multitude could exist. Proclus writes: “For if it in no respects participates of The One, neither will the whole be one whole, nor each of the many of which the multitude consists; but there will also be a certain multitude arising from each of these, and this will be the case to infinity.”1 Unity or simplicity enables the something to be called a thing; otherwise, nothing at all would exist. The principle of simplicity thereby is a fundamental principle of metaphysics that must be true in order for there to exist anything at all since composition presupposes simplicity. 1 Proclus. Proclus: Elements of Theology. Thomas Taylor, ed. Frome, Somerset, UK: The Prometheus Trust, 1998. Proposition I. 3 The mathematical truth of space’s infinite divisibility states that space can be divided without limit since there is no smallest and indivisible part of space. It is a truth propounded in Euclid’s Elements from Euclid’s notion of a line as “…a breadthless length.”2 Since Euclid conceives a point as “…that which has no part”, it could not possibly be the sole constituent of a line or any geometrical objects because partless things cannot be aligned next to one another as we will explore later in this dissertation.3 It would be absurd to consider the Euclidean principle of the infinite divisibility false since a number of mathematical theorems are based on such a principle, including the Pythagorean theorem. Without infinitely divisible space, it would be very difficult for a mathematician to prove the Pythagorean theorem because no irrational numbers would be possible. Thus, a rejection of space’s infinite divisibility would result in a repudiation of commonly accepted mathematical theorems. The affirmation of both of these principles is integral to the preservation of the coherence of human knowledge and the value placed on the disciplines of metaphysics and mathematics. Should one deny one principle in favor of the other principle, then the result is an exclusive field of human knowledge: metaphysical knowledge and mathematical knowledge collide. The affirmation of both principles is thereby necessary for the preservation of the human intellect. Without compatibility of knowledge systems, human knowledge rests in subjectivity rather than objectivity. Knowledge is not about the
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