THE METAPHYSICS OF SIMILARITY AND ANALOGICAL REASONING A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAI‘I AT MĀNOA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHILOSOPHY by Jarrod Brown August 2018 Dissertation Committee Members: Tamara Albertini Aridam Chakrabarti (chairperson) Vrinda Dalmiya George Tsai Amy Schafer Jesse Knutson Keywords: analogy, similarity, comparative philosophy, relations 1 ABSTRACT This work introduces the importance of similarity and analogy to philosophy, argues that analogy should be seen as “similarity based reasoning,” overviews different philosophical discussions to illustrate the scope of similarity-based reasoning, and introduces the assumptions for similarity-based reasoning that form the central topics of the present work. It demonstrates that approaches that reduce or identify relations to non-relational ontological categories fail primarily through the strategy of seeking truthmakers for relational claims. It takes up the related problems of co-mannered relations, substitution instances, individuating relations and similarities. It attacks the notion that substitution instances provide a non-relational account of relations and provides a proof that similarity is a more fundamental concept than substitution. Given, however, that similarity is relational, it argues relations are non-reducible to non-relational entities, but that if given the notion of relating in general and of similarity, one can construct a non-reductive theory of relations that can individuate all relations, including similarity relations themselves. This provides a workable theory of relations, but does not solve problems related to the epistemology of relations and similarity. Sanskritic debates concerning the metaphysical nature of similarity and its knowability are explored through contrasting the views of four Indian schools of thought: the Buddhist, Nyāya-Vaiśeṣika, Bhaṭṭa Mīmāṃsāka, and Prābhākara Mīmāṃsā. Within the Islamic tradition, analogy is rejected as a valid tool for legal reasoning by the Ẓāhirī school, and this is contrasted with the very tempered defense by the Shāfiʿī school. The Islamic debates bring out more clearly the hermeneutical challenges, but it is argued that these challenges of interpretation are bound up in the challenges of the epistemology of relations and similarities. The work concludes that an epistemic virtue-theoretic account can help us better understand how analogical arguments can be true and non-vacuous, and argues we should cultivate the virtue of similarity and relation sensitivity. i. 2 TABLE OF CONTENTS Abstract …......... i Table of Contents …......... ii Chapter One: The Importance and Scope of Analogy and the Relation of Similarity …......... 1 Chapter Two: The Metaphysical Basis of Analogy I: Relations as Universals or Tropes …......... 29 Chapter Three: The Metaphysical Basis of Analogy II: Theories of Relations …......... 87 Chapter Four: The Metaphysical Basis of Analogy III: Theories of Relations Continued …......... 107 Chapter Five: The Epistemology of Relations and Similarity: Knowing Relations, Knowing Analogies …......... 141 Chapter Six: The Epistemology of Relations and Similarity II: Seeing Analogies ......... 214 References …......... 228 ii 3 CHAPTER ONE: THE IMPORTANCE AND SCOPE OF ANALOGY AND THE RELATION OF SIMILARITY ANALOGY AS CENTRAL TO ALL PHILOSOPHICAL PURSUITS The problem of analogical reasoning is, simply put, the most fundamentally important problem in philosophy, and one that straddles the full range of philosophical areas of inquiry—metaphysics, epistemology, aesthetics, ethics, logic, philosophy of mind, and philosophy of language, and it therefore finds itself implicated in every philosophical discussion. The full complexity of the problem is brought to the foreground when one acknowledges that analogical reasoning is simply that which depends on the relation and recognition of similarity. Once we realize that an explanation of analogical reasoning requires an explication of the relation of similarity and its recognition, we are forced to confront the fact that we must take such reasoning for granted in any attempt to explain it. One would be unable to recognize the words on these pages as words one knows if one does not have the epistemic ability to detect and cognize similarity; without similarity, we are rendered ineludibly mute. One could not speak of “types of things” since types depend on similarities holding between the particulars of that type. One could not speak of persistence over time since knowledge of persistence would depend on the ability to recognize relevant similarity through time. We would be left with a language of proper names (which is no language at all): without the ability to recognize similarity diachronically, it would be a language of ever changing names. In fact, the very ability to recognize what you are reading now is the same text as what you were reading moments before, and your ability to recognize these words as words you already know, depends on your ability to recognize a sameness, and what is sameness if not absolute similarity? Your ability to find this manuscript, after having set it down for a while, and resume reading from where you left off depends on an enormous number of operations, an edifice of recognition and reasoning built upon a foundational ability to 4 perceive, to be aware of, and to reason with similarity relations. Indeed, it is the very sophistication with which we as human beings can perform these actions that forms part of our uniqueness as a species of “rational animal.” To group organisms together in taxonomic structures, or to see ideas falling under a concept, to recognize something as the same type as another previously experienced thing, or to see some particular as belonging to a category all depend necessarily on similarity. All philosophizing needs concepts. There are no concepts without similarity. Therefore, without similarity, there can be no philosophizing. It further seems that similarity is a necessary feature of the universe. Given any two unique entities, they are similar in that they are both not some other third unique entity. Similarity, then, is a given, but an incredibly significant one. To claim that “x is like y” demands some specifiable similarity: a particular resemblance, something that they are similar in respect to. This claim differs from, say, literary analogies—similes —which Donald Davidson rightly points out are trivially true.1 So love is like a red, red rose sprung in June because something can be found in common between any two things (freshness, beauty, et cetera), but as Davidson and others before him have pointed out, some commonality can be found between any two things. Hence we have the adage, “Everything is like everything else” or as Stuart Hampshire has formulated it, echoing Charles Sanders Peirce, "it is . necessarily true that everything resembles everything in some respect. Of any two things whatever, there is some respect in which they can be said to resemble each other and not to resemble some third thing."2 Douglas Greenlee has argued that indeed that this is a necessary and significant truth, whereas Davidson sees it, at least through the lens of similes, as a trivial truth.3 Greenlee calls this the Similarity of Discernables principle. So love is like a red, red rose but also like a rotting corpse. This triviality and generality of the similarity relation has cast analogical reasoning in a shadow of doubt and distrust, evident in some of the earliest theoretical discussions of the concept up to contemporary considerations. Semiotician Umberto Eco 1 Donald Davidson, “What Metaphors Mean,” Critical Inquiry, 1978, 245–64. 2 Stuart Hampshire, Thought and Action, vol. 11 (University of Notre Dame Press, 1983), 31. 3 Douglas Greenlee, “The Similarity of Discernibles,” The Journal of Philosophy, 1968, 753–63. 5 has remarked on this suspicion, echoing sentiments we will see were earlier expressed by Plato, that “[the] criterion of similarity displayed an overindulgent generality and flexibility. Once the mechanism of analogy has been set in motion there is no guarantee that it will stop . The image, the concept, the truth that is discovered beneath the veil of similarity, will in its turn be seen as a sign of another analogical deferral. Every time one thinks to have discovered a similarity, it will point to another similarity, in an endless progress. In a universe dominated by the logic of similarity (and cosmic sympathy) the interpreter has the right and the duty to suspect that what one believed to be the meaning of a sign is in fact the sign for a further meaning.4 This triviality, transitivity and universality, though, violates the norms we use in assessing analogies. To illustrate what is meant, consider the old analogy tests from standardized exams: a fish is to a school like a tree is to a ______. There is a specific resemblance between the first set (fish, school) and the second set (tree, forest) which one must deduce in order to answer correctly. Another example avoids language altogether. Consider the set of images. To correctly answer this visual analogy, it too relies on recognizing the relevant similarities. Fig. 1. The visual analogy above is important, because as much as the present work will have to say about language and reasoning, it is important to bear in mind the often overlooked fact that mental activity is 4 Umberto Eco and Stefan Collini,