Greek and Roman Logic

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry

The intersection between Descriptivism and Meliorism in reasoning research: further proposals in support of 'soft normativism'

The rationality paradox centres on the observation that people are highly intelligent, yet show evidence of errors and biases in their thinking when measured against normative standards. Elqayam and Evans (e.g., 2011) reject normative standards in the psychological study of thinking, reasoning and deciding in favour of a ‘value-free’ descriptive approach to studying high-level cognition. In reviewing Elqayam and Evans’ position, we defend an alternative to descriptivism in the form of ‘soft normativism’, which allows for normative evaluations alongside the pursuit of descriptive research goals. We propose that normative theories have considerable value provided that researchers: (1) are alert to the philosophical quagmire of strong relativism; (2) are mindful of the biases that can arise from utilising normative benchmarks; and (3) engage in a focused analysis of the processing approach adopted by individual reasoners. We address the controversial ‘is–ought’ inference in this context and appeal to a ‘bridging solution’ to this contested inference that is based on the concept of ‘informal reflective equilibrium’. Furthermore, we draw on Elqayam and Evans’ recognition of a role for normative benchmarks in research programmes that are devised to enhance reasoning performance and we argue that such Meliorist research programmes have a valuable reciprocal relationship with descriptivist accounts of reasoning. In sum, we believe that descriptions of reasoning processes are fundamentally enriched by evaluations of reasoning quality, and argue that if such standards are discarded altogether then our explanations and descriptions of reasoning processes are severely undermined

G\"odel's Notre Dame Course

This is a companion to a paper by the authors entitled "G\"odel's natural deduction", which presented and made comments about the natural deduction system in G\"odel's unpublished notes for the elementary logic course he gave at the University of Notre Dame in 1939. In that earlier paper, which was itself a companion to a paper that examined the links between some philosophical views ascribed to G\"odel and general proof theory, one can find a brief summary of G\"odel's notes for the Notre Dame course. In order to put the earlier paper in proper perspective, a more complete summary of these interesting notes, with comments concerning them, is given here.Comment: 18 pages. minor additions, arXiv admin note: text overlap with arXiv:1604.0307

After the Great Recession: Law and Economics\u27 Topics of Invention and Arrangement and Tropes of Style

AFTER THE GREAT RECESSION: LAW AND ECONOMICS’ TOPICS OF INVENTION AND ARRANGEMENT AND TROPES OF STYLE by Michael D. Murray Abstract The Great Recession of 2008 and onward has drawn attention to the American economic and financial system, and has cast a critical spotlight on the theories, policies, and assumptions of the modern, neoclassical school of law and economics—often labeled the Chicago School —because this school of legal economic thought has had great influence on the American economy and financial system. The Chicago School\u27s positions on deregulation and the limitation or elimination of oversight and government restraints on stock markets, derivative markets, and other financial practices are the result of decades of neoclassical economic assumptions regarding the efficiency of unregulated markets, the near-religious-like devotion to a hyper-simplified conception of rationality and self-interest with regard to the persons and institutions participating in the financial system, and a conception of laws and government policies as incentives and costs in a manner that excludes the actual conditions and complications of reality. This Article joins the critical conversation on the Great Recession and the role of law and economics in this crisis by examining neoclassical and contemporary law and economics from the perspective of legal rhetoric. Law and economics has developed into a school of contemporary legal rhetoric that provides topics of invention and arrangement and tropes of style to test and improve general legal discourse in areas beyond the economic analysis of law. The rhetorical canons of law and economics—mathematical and scientific methods of analysis and demonstration; the characterization of legal phenomena as incentives and costs; the rhetorical economic concept of efficiency; and rational choice theory as corrected by modern behavioral social sciences, cognitive studies, and brain science—make law and economics a persuasive method of legal analysis and a powerful school of contemporary legal rhetoric, if used in the right hands. My Article is the first to examine the prescriptive implications of the rhetoric of law and economics for general legal discourse as opposed to examining the benefits and limitations of the economic analysis of law itself. This Article advances the conversation in two areas: first, as to the study and understanding of the persuasiveness of law and economics, particularly because that persuasiveness has played a role in influencing American economic and financial policy leading up to the Great Recession; and second, as to the study and understanding of the use of economic topics of invention and arrangement and tropes of style in general legal discourse when evaluated in comparison to the other schools of classical and contemporary legal rhetoric. I examine each of the rhetorical canons of law and economics and explain how each can be used to create meaning, inspire imagination, and improve the persuasiveness of legal discourse in every area of law. My conclusion is that the rhetorical canons of law and economics can be used to create meaning and inspire imagination in legal discourse beyond the economic analysis of law, but the canons are tools that only are as good as the user, and can be corrupted in ways that helped to bring about the current economic crisis