Work on analogy has been done from a number of disciplinary perspectives throughout the history of Western thought. This work is a multidisciplinary guide to theorizing about analogy. It contains 1,406 references, primarily to journal articles and monographs, and primarily to English language material. classical through to contemporary sources are included. The work is classified into eight different sections (with a number of subsections). A brief introduction to each section is provided. Keywords and key expressions of importance to research on (...) analogy are discussed in the introductory material. Electronic resources for conducting research on analogy are listed as well. (shrink)

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...) assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​. (shrink)

More or less explicitly inspired by the Aristotelian classification of arguments, a wide tradition makes a sharp distinction between argument and proof. Ch. Perelman and R. Johnson, among others, share this view based on the principle that the conclusion of an argument is uncertain while the conclusion of a proof is certain. Producing proof is certainly a major part of mathematical activity. Yet, in practice, mathematicians, expert or beginner, argue about mathematical proofs. This happens during the search for a proof, (...) then when the proof is presented and discussed by experts, and finally when it is taught or used in didactical contexts. (shrink)

The works of the Tibetan logician Phya pa Chos kyi seng ge (1109–1169) make abundant use of a particular type of argument that I term ‘argument by parallels’. Their main characteristic is that the instigator of the argument, addressing a thesis in a domain A, introduces a parallel thesis in an unrelated domain B. And in the ensuing dialogue, each of the instigator’s statements consists in replicating his interlocutor’s previous assertion, mutatis mutandis, in the other domain (A or B). I (...) show that such a dialogue involves two parallel arguments that develop in an intersecting zigzag pattern, and discuss the principles involved in the establishment of the conclusion from the perspective of parity of reasoning and analogical argument. I examine the overall rhetorical strategy directing the use of arguments by parallels and the pedagogical and explanatory functions they can serve. I also evaluate the plausibility of their use in Phya pa Chos kyi seng ge’s works mirroring a contemporary practice of oral debate, and reflect on the status of such arguments in the framework of Indo-Tibetan logic. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Analogical reasoning projects a property taken to hold of something or things (the source) to something else (the target) on the basis of just those similarities premised in the analogy. Standard similarity-based accounts of analogical reasoning face the question: Under what conditions does a collection of similarities sufficiently warrant analogical projection? One answer is: When a thing’s having the premised similarities somehow determines its having the projected property. Standardly, this answer has been interpreted as claiming that a formally defined determination (...) relation exists between the variables of which the determining properties are values and the variable of which the determined property is a value. This paper supplies another answer: Analogical projection is warranted when an item’s having the projected property is grounded in its having the premised similarities. Drawing on the metaphysics of grounding, we propose a model of grounded analogy on which analogical reasoning is valid under metaphysical necessity. Our model thus provides one answer to John Stuart Mill’s question of how analogical reasoning based on limited information about a single source case can provide an indefeasible justification for analogical projection. Once a relation of total grounding is ascertained to hold between some similarities and the projected property, no other properties bear on the projectability of the projected property from the source to the target. (shrink)

Arguments from analogy are pervasive in everyday reasoning, mathematics, philosophy, and science. Informal logic studies everyday argumentation in ordinary language. A branch of fuzzy logic, approximate reasoning, seeks to model facets of everyday reasoning with vague concepts in ill-defined situations. Ways of combining the results from these fields will be suggested by introducing a new argumentation scheme—a fuzzy analogical argument from classification—with the associated critical questions. This will be motivated by a case study of analogical reasoning in the virtual friendship (...) debate within information ethics. The virtual friendship debate is a disagreement over whether virtual friendships are genuine friendships. It will be argued that the debate could move away from its current impasse, caused by unproductive metaphysical and logical assumptions, if extant arguments are reinterpreted as fuzzy analogical arguments from classification, and subjected to a new set of critical questions which would replace the quest for facts of essence about friendship with an emphasis on empirical data, persuasion, and definitional power. (shrink)