Thesis advisor: Arthur Madigan / Since at least Galileo, not only the technological abilities of natural science but the meaning of science's claims have been shaken to their very foundations, according to Edmund Husserl. We know what scientists say, but we do not know what they mean. Nor, Husserl claims, do they know what they mean. They do what works. They measure, they tabulate, they calculate. But they do not thereby really know the world. And since they are the standing authorities of knowledge in our culture, we do not have a reliable referent to which we can turn for an appropriate standard of meaning. At some level we realize that this piece of paper in my hand is not precisely a geometrical rectangle, in which all four angles are exactly ninety degrees and both sets of sides are exactly parallel to each other, but for the most part we simply identify it as a rectangle and move on. In our everyday experience, Husserl would say, we tend to conflate geometrical space and experiential space. We do not, however, have any real idea why we can do so effectively, even if we are engineers or physicists. Geometrical shapes are categorically different from the shapes we daily experience in our interactions with the world. No matter how carefully I draw lines or cut edges, I can never make a piece of paper (or, for that matter, a cow) that exactly meets the requirements of a geometrical rectangle. Even the fact that geometrical rectangles are, by definition, plane figures, which means they only have two dimensions, rather than the (at least) three that structure any perceptible thing, prevents perceptible things from ever meeting the strict requirements of geometrical figures. Given this basic disparity, what is it that justifies our using these geometrical figures to describe the perceptible world in which we live? If we want to know the world, Husserl tells us, we need to know what our scientific claims mean. This, he claims, is the only way we can meaningfully ground our increasingly science-governed lives. Plan of the Dissertation In this dissertation, then, I undertake the project of identifying more precisely what this problem is and offering some solution to it. My argument will have three steps. I shall argue first that to solve the problem Husserl so helpfully lays out, we need to go back to Aristotle's Metaphysics; second, that although Aristotle proposes a solution for the metaphysical problems implied by using mathematics to know perceptible things, this solution fails to answer the questions as he presents them, even if it is broadly interpreted; and, finally, that there are within Aristotle's metaphysical thought implicit resources for constructing this missing metaphysical justification, and that these can be found explicitly in his way of thinking about the distinction between actuality and potency, in his discussion of the metaphysical implications of knowing, and in his discussion of material causality. The basic problem is that mathematical objects and perceptible things are different kinds of things. We would not say that `Joe's idea is hungry' in anything other than a very metaphorical way, because we recognize that ideas are not the kinds of things that get hungry. Hunger is the province of animals. Ideas are not animals. Ideas, then, cannot be hungry. Mathematical objects and perceptible things, though, while also different kinds of things, are regularly combined. We do say, `This piece of paper is rectangular', although it would seem that pieces of paper (or cows) are not the kinds of things that could be rectangles. In this dissertation, I begin in chapter one with a careful recapitulation of Husserl's articulation of this problem of thoughtlessly conflating mathematical and experiential things. Husserl takes this to be the root of the crisis, not only of the meaning of the sciences, but also of all human meaning. I use Husserl's articulation, rather than simply explaining the problem as I understand it and moving directly to Aristotle's Metaphysics, where I see the roots of its solution, in part because Husserl's work was so influential in shaping my own understanding of the problem. More importantly, though not unrelatedly, Husserl helpfully contextualizes the problem both culturally and historically. He tells us why this matters, and he tells us how it seems to have happened. Both of these seem to me to be crucial to any ultimately successful resolution to the problem. In Husserl's articulation of the problem, he identifies Galileo as responsible for taking it as `obvious' that the `universally valid' shapes of geometry constituted the objectively real component of all things. He argues that Galileo inherits a tradition in which our approximations to `limit shapes' and the increased precision in replicating these made possible by technological advances gradually meld together, such that we learn to take the world to be fundamentally a mathematical manifold. In taking over this tradition, Galileo simply presumes that the world is fundamentally mathematizable and sets about developing methods by which even the concrete sensory plena through which any experienced shape is necessarily presented can be mathematized. Since we take as `given' these assumptions, whose origin Husserl attributes to Galileo, and which remain unjustified metaphysically, Husserl's tracing of the development of these assumptions can help us notice and evaluate them. This will be helpful in recovering the meaning of our mathematical scientific claims, and, ultimately, in recovering the meaning of our non-scientific claims. While Husserl helpfully identifies the problem and begins the historical tracing he proposes with his analysis of Galileo's assumptions, he does not complete the latter project, in part because he died so soon after beginning it. His project in the Crisis, as with many of the projects he undertook as a scholar, gets developed in many different directions, without any of these being completed. He proposes a philosophical-historical retracing of the assumptions of geometry, from its earliest inception through the present. He proposes a simultaneous careful consideration of the metaphysical assumptions at work in mathematical science and the justification necessary for it. He proposes transcendental phenomenology as the way to correctly understand the correlation between mathematical claims and the perceptible world they describe. While the development of transcendental phenomenology and the ways that it can help us come to understand more correctly our interaction with the world are fascinating, in this dissertation I want to focus on Husserl's other proposals toward a solution, namely the philosophical-historical retracing of assumptions and the metaphysical analysis. Specifically, I want to focus on the metaphysical analysis that Aristotle performs on the problems generated by presuming that one can use mathematical objects to know perceptible things. In chapter two, then, I explain more thoroughly the first two proposals toward a solution that Husserl proposes, and defend my claim that this metaphysical analysis in Aristotle is an appropriate continuation of Husserl's project. For completeness, Husserl's project needs, in addition to his tracing of the historical sources of lazy assumptions, an Aristotelian metaphysical analysis of what material and mathematical things are, to clarify whether and how mathematics could be appropriately (or inappropriately) applied to material things. In chapter three, I turn to Aristotle's Metaphysics and cull from its pages, primarily from Books III and XIII, the basic metaphysical questions and problems that arise in Aristotle's discussion of the use of mathematical objects to know perceptible things. I organize these into six central questions: 1) What exactly are the mathematical objects Aristotle discusses? 2) Are these mathematical objects substances? 3) Are these mathematical objects separable from perceptible things? 4) Are these mathematical objects constituents of perceptible things? 5) Are these mathematical objects principles or causes of perceptible things? 6) Is knowledge of these mathematical objects somehow knowledge of perceptible things? From these six questions, the basic problem that emerges is that knowledge of mathematical objects requires these objects to be exact, unchangeable, and indivisible, whereas the perceptible things of which they are supposed to provide knowledge are less determinate, changeable, and divisible. It seems like the mathematical objects would have to be separate from these perceptible things to be objects of mathematical knowledge, but if they were so, it is unclear how knowledge of them could be taken to also be knowledge of the perceptible things. These mathematical objects would have to somehow be part of the causal structure of these perceptible things for knowledge of them to be knowledge of these perceptible things. In chapter four, I take up the solution that Aristotle proposes for these difficulties, the `insofar as'/ `qua' (hêi) structure of knowing. Various attributes belong to a given perceptible thing in virtue of various ways of its being. Being green belongs to a plant, for example, insofar as it is a surface. The method of abstraction (aphairesis) allows us to separate out in thought the relevant way of being of the thing, so as to make the appropriate attribution to it. We can know a thing as something, even if that `something' is not itself actually separable. This proposal of Aristotle's begins to resolve some of the metaphysical problems that chapter three articulated. It is not itself, however, metaphysically justified. While it seems that we do regularly make these kinds of claims about perceptible things, it is not clear what justifies us in separating in thought what is not separate in fact, nor just how these various ways of being belong to the unified perceptible thing such that knowledge of them provides knowledge of the thing. This difficulty in giving a metaphysically coherent account of Aristotle's model of abstraction pervades the scholarly literature. Aristotle, it seems, does not have a satisfactory solution to the troubling metaphysical problems he raises about using mathematical objects to know perceptible things. In my fifth, and final, chapter, I undertake to construct from other texts in Aristotle's corpus a metaphysical justification for his model of abstraction that can, in fact, resolve the metaphysical problems that he and Husserl have raised. I find this metaphysical justification in an implicit claim of Aristotle's, to be found in the same section where he proposes his model of abstraction as a solution (Met XIII.3): the claim that mathematical objects are potential substances. I examine what these potential substances are, how they are related to their own actualizations and how they are related to the perceptible things of which they are supposed to provide knowledge, relying primarily on Metaphysics VIII and IX. I consider how knowledge of these could be possible, using texts from De Anima III, and then explore a connection between these potencies and the material cause of perceptible things in Physics II.9. I conclude at last that we are, in fact, justified in using mathematical objects to describe perceptible things. These objects, however, are mathematically describable only insofar as they are material, by which Aristotle means, insofar as they are potential, rather than actual. / Thesis (PhD) — Boston College, 2010. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Philosophy.
| Identifer | oai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_101718 |
| Date | January 2010 |
| Creators | Stackle, Erin |
| Publisher | Boston College |
| Source Sets | Boston College |
| Language | English |
| Detected Language | English |
| Type | Text, thesis |
| Format | electronic, application/pdf |
| Rights | Copyright is held by the author, with all rights reserved, unless otherwise noted. |
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