EXPLORING THE NATURE OF MODELS IN SCIENCE, PHILOSOPHY OF SCIENCE, AND SCIENCE EDUCATION BY JEREMY J. BELARMINO Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Educational Policy Studies in the Graduate College of the University of Illinois at Urbana-Champaign, 2017 Urbana, Illinois Doctoral Committee: Professor Nicholas Burbules Associate Professor Christopher Roy Higgins Professor Emeritus William F. Brewer Professor Fouad Abd-El-Khalick, University of North Carolina at Chapel Hill ABSTRACT The term model is ubiquitous in science, philosophy of science, and science education. Although there is no general consensus regarding its definition, the traditional approach in all of these disciplines has always been to view models as some kind of representation of reality. Recently, however, there has been a move towards non- representational and deflationary accounts of modeling that eschew the notion that models must come equipped with both necessary and sufficient conditions. Following the philosophy of the later Wittgenstein, I develop my own narrative concerning modeling called the integration account. The integration account maintains that models are comprised of various elements that are organized in a distinctive way in order to solve scientific problems. Some of these elements include, but are not limited to: theories, laws, theory-ladenness of ideas, choice, funding availability, feasibility, social relationships, and even serendipity. The integration account encounters some difficulty when it is applied to the field of science education, in particular science teaching. The latter’s pedagogical project appears to run contrary to the integration account’s commitment to solving scientific problems. As a result, I propose that pedagogical models and scientific models be viewed as separate kinds of models, each replete with their own separate function. Scientific models should only be used by professional scientists to solve scientific problems and not used as teaching tools by science teachers. The reverse is also true. Pedagogical models can still be used by science teachers even if they have run their course when it comes to solving scientific problems. ii For my wife Amanda Belarmino and my parents Jesus and Nora Belarmino iii ACKNOWLEDGMENTS This project would not have been possible without the guidance and feedback of my Dissertation Committee. Bill, your thought-provoking comments have certainly given me a lot to think about when it comes to the cognitive science of science and how students represent their knowledge. Chris, we have known each other for a long time now. Our discussions on Plato, Aristotle, Arendt, and MacIntyre have been some of the most exhilarating in my life. Fouad, I would like to personally thank you for embracing me into your NOS (Nature of Science) circle. Had we not met, I never would have pursued my interest in philosophy of science, let alone written a dissertation in the field. And last, but certainly not least, I would like to acknowledge Nick Burbules, my advisor and dissertation Chair. Thank you for always believing in this project and me. There were several moments when I had serious reservations about both, but your undeterred confidence in me never allowed me to give up. Most importantly, I need to express my gratitude to my family, especially my wife, Amanda, who has been a constant source of inspiration and reassurance. The completion of this project is a testament of your unrelenting care and support. I would also like to recognize my parents, whose lives were the very embodiment of eudaimonia. May you rest in peace. iv Table of Contents Chapter 1. Introduction ..................................................................................................................... 1 Part I Chapter 2. Three Accounts of Representation ................................................................................ 10 Chapter 3. The Integration Account of Modeling .......................................................................... 43 Chapter 4. Pierre Duhem’s Critique of Modeling .......................................................................... 76 Part II Chapter 5. The Role of Models in Science Education .................................................................... 95 Chapter 6. Three Case Studies on Modeling ................................................................................ 122 Chapter 7. Models Revisited ........................................................................................................ 152 Bibliography ................................................................................................................................. 178 v Chapter 1 Introduction 1.1 Plato’s Model Mythos In Book 7 of the Republic, Plato tells his audience an amazing tale. He welcomes them to use their imaginations to envision a cave that extends far beneath the Earth’s surface. Deep inside this cave, towards the very bottom, there are very unique prisoners. These prisoners are shackled in a way that they are forced to stare at the cave wall in front of them; they cannot move their heads from side to side or even look behind them. Far behind the prisoners, towards the cave’s entrance, is a burning fire. In between the fire and the prisoners there is a slightly elevated path. On this path, there are people carrying various statues of everyday objects from one side of the cave to the other. Now the statue carriers are holding the statues in such a way that the shadows of the statues are visible to the prisoners, but the statues themselves are not. Because the prisoners cannot turn their heads, they do not know who or what is producing the shadows. In fact, from their perspective, they do not even know that they are looking at shadows; for all they know, the shadows are the only genuine reality. One day, however, one of the prisoners breaks free from his shackles. Once unfettered, he immediately turns around and follows a path propelling him towards the entrance of the cave. As he is walking, he is astonished at what he sees; for he sees statues that resemble the ones he has been staring at his entire life. After considering the statues and their likenesses on the wall, he realizes that the two cannot be a coincidence. The objects on the wall are nothing more than the shadows of these statues. At this moment, the prisoner’s entire reality is turned upside down. 1 Everything he thought was real was only a mere likeness, a dismal chimera. For his entire life he had witnessed the most elaborate puppet show ever produced, unfortunately none of it was real. He wants to turn back the hands of time, return to his rightful place in front of the wall, and call out the names of shadows again. But he knows that this is impossible. Instead, he summons up the courage to keep climbing towards the entrance of the cave. As he approaches the entrance, he sees a burning fire and realizes that it is the mechanism that has been perpetuating the farce known as his life. He wants to put it out, but he cannot. So he keeps on climbing. As he gets closer to the entrance to the cave, his vision becomes more and more impaired. For his entire life he had grown accustomed to looking at things in the dark; and now, all of a sudden, he is inundated by light. As he begins to walk outside, his vision gradually returns. At first he is only able to see the shadows of objects on the ground and the reflections of objects on the water’s surface. Eventually he lifts his head and is able to look at the objects themselves, the ones producing the various shadows and reflections. He has never seen anything so beautiful in his entire life. But out of nowhere, he feels a sudden urge, an ineffable compulsion prompting him to gaze up to the heavens above him. And that is when he catches a glimpse of the sun, its radiance extending from one end of the horizon to the other. In that moment, he knows his journey is complete. What began as a day that was a kind of night, has become the one, true day. Those remotely familiar with Plato’s famous Allegory of the Cave recognize the philosophical impact that the myth has had on metaphysics, epistemology, aesthetics, politics, and education. What is rarely recognized, however, is the myth’s influence on philosophy of science, in particular, the philosophy of modeling. The shadows on the 2 wall of the cave are models of the statues being carried along the pathway, whereas the statues themselves are representations of the actual objects outside of the cave. Plato’s point is that the objects outside represent the true Reality, while the shadows on the wall inside the cave are the farthest removed from the realm of immortal, incorporeal, and unchanging Forms. Now there is a great deal of metaphysics in Plato’s myth, which makes it even more ironic that the scientific community, by and large, has adopted his philosophy of modeling. When Plato speaks of his Theory of Forms as being the ultimate Truth, he is referring to the abstract truths of mathematics. For Plato, all physical objects in the natural world are poor representations, or mere shadows, of their mathematical counterparts. Even though Plato developed his view of mathematics in the 4th century B.C.E, consider what Johannes Kepler, one of the most important astronomers to come after Nicholas Copernicus, said in the Mysterium Cosmographicum nearly two thousand years later, “The ideas of quantities have been and are in God from eternity, they are God himself; they are therefore also present as archetypes in all minds created in God’s likeness.”1 Or, more recently, consider the words of theoretical physicist Paul Dirac, one of the pioneers of quantum mechanics, “As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.”2 For Plato, Kepler, Dirac, and many others, mathematics is more than just a mirror of nature—it is the one, True Nature. 1. Johannes Kepler, Mysterium Cosmographicum, in Arther Koestler, The Watershed: A Biography of Johannes Kepler (New York: University Press of America, 1960), 65.