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The Basics of Formal Logic MGIMO University School of Government and International Affairs Syllabus approved Dean, The MGIMO School of Government and International Affairs Mikhail Troitskiy « » 2021 The Basics of Formal Logic Undergraduate Course Syllabus Instructor Prof. Nikolai Biryukov © Nikolai Biryukov, 2021 © MGIMO University, 2021 This syllabus is designed in accordance with the MGIMO Educational Standard for the Bachelor Program in Economics. Author ________________Prof. Nikolai Biryukov Director MGIMO Library__________Marina Reshetnikova Logic has been traditionally defined as the study of principles (laws), forms, methods and rules of thought, primarily reasoning. It should, however, be understood that even though principles (laws), forms, methods and rules of thought studied by logic can be traced to earlier practices of human thinking, their expounded versions have, in fact, been invented by logicians themselves in an attempt to develop and perfect a universal tool of theoretical thought. Logic is, therefore, better described and understood as an artificial language specially devised for and adapted to needs of theoretical discourse, including that of science. Scientific disciplines that lay at the core of university-level education can hardly be adequately comprehended without mastering this language. However, by the 19th century the language of traditional logic created and conceptualised by Aristotle more than two millennia earlier and sophisticated by generations of scholars throughout Antiquity, Middle Ages and Modern Times exhausted its potential and seized to fully meet the needs of sciences. A new language was required, more complex and more powerful, and that requirement has been met by mathematical (symbolic) logic. Nevertheless, since most classical scientific writings read at higher schools and universities date from the times that preceded symbolic logic, traditional formal logic suffices for their understanding as well as the understanding of their contemporary expositions. Mastery of the language of traditional logic likewise suffices for analysis of everyday public discourse, including political discourse, the bulk of theoretical political discourse being no exception, for the simple reason that the maJority of the discoursers have never studied and, hence, do not use the language of symbolic logic. In the meantime, such analysis is an essential part of political scientists’ routine work and the respective analytical skills are indispensable elements of their professional competence. The language of traditional formal logic was originally developed on the basis of ordinary (“natural”) languages and is, therefore, relatively easy to learn and use. However, due to its artificial nature and, particularly, its deliberate orientation to theoretical thought, it is unrealistic to expect that it can be learned spontaneously, least so properly, in the course of everyday mental work. Even the kind of logical intuition inadvertently developed in mathematical classes proves insufficient in the field of humanities the study of which constitutes the basis of MGIMO education. Hence the language of logic with its specific semantics, syntax, and pragmatics must be taught as a special discipline to all those whose vocations make thinking skills of theoretical level pertinent. Part 1. The Subject, Functions, Laws and Parts of Logic (1 lecture, 1 seminar). Traditional formal logic was conceptualised at the outset as the study (the term science had not yet been coined) of principles (rules, or laws, to use a later expression) and forms (as different from contents) of thought. Three principles (laws) of thought were initially formulated, viz. (1) the law of identity, (2) the law of contradiction (often referred to as the law of non- contradiction), and (3) the law of excluded middle (also known as the law of excluded third), and three forms of thought were initially identified, viz. (1) concepts, (2) propositions, (3) inferences. It is important to understand that even though the above three principles (laws) can be traced to common sense practices of everyday communications and, at least, the first two of the above three forms of thought closely resemble such lexical units of ordinary languages as words and sentences with their parts and word order, logic requires far greater accuracy and far greater rigour than those exhibited by “natural” languages, and this is precisely what makes it functional as the language of science. Unlike imprecise, often metaphorical and ambiguous words of “natural” languages, concepts that figure in logical discourse must be defined explicitly and understood unequivocally – this is precisely what the principle (law) of identity is about, Unlike sentences of ordinary languages, propositions must adhere to strict uniform patterns that allow for clear and unmistakable understanding of logical relations between both concepts that appear in propositions and propositions themselves. Failure to meet these requirements deprives inferences of due rigorousness and destroys their demonstrative and convincing power. Lecture 1. The Subject, Functions, Laws and Parts of Logic. The essence and subject of logic. Functions of logic in theoretical discourse. Logic as an artificial language of theoretical discourse. The principles (laws) of thought: the principle of identity; the law of contradiction (non-contradiction), the law of excluded middle (excluded third), the principle of sufficient reason. The forms of thought in traditional logic: concepts, propositions, inferences. Traditional parts of logic. Seminar 1. The Subject, Functions, Laws and Parts of Logic. Why do we need logic? Can we do without logic? What are the functions of logic in scientific discourse? Is logic a specific branch or a universal tool of theoretical, more specifically scientific, knowledge? Is logic a theory or a language? Can science do without logic? Are laws of thought also laws of reality or Just rules of proper thinking about reality? What are the results of violating laws (rules) of logic? What is equivocation? Are the three forms of thought ordered properly? How do they relate to each other and to forms of ordinary speech and thinking? Is illogical thinking simply incorrect or is it to be seen as an alternative mode of thinking? Are other forms of thought possible and thinkable? Is there Just one universal logic or are there many different logics? Required reading: • Assadian B. Formal Logic in Philosophy // Introduction to Philosophy: Logic / Ed. by B. Martin. – Ch. 3. – Rebus Community, 2020. – P. 23–33; https://press.rebus.community/intro-to-phil-logic/chapter/chapter-3-formal-logic-in- philosophy/. • Biryukov N. I. The Basics of Formal Logic: A Multimedia Manual. – Topic 1. The Subject and Laws of Logic: PowerPoint presentation of lecture; https://nibiryukov.mgimo.ru//nb_english/nbe_teaching/nbe_teach_ppp/nbe_ppp_the_basic s_of_formal_logic/nbe_bfl01_the_subject_and_laws_of_logic.pptx. • Knachel M. What is Logic? // Introduction to Philosophy: Logic / Ed. by B. Martin. – Ch. 1. – Rebus Community, 2020. – P. 3–11; https://press.rebus.community/intro-to-phil- logic/chapter/chapter-1/. Further reading: • Code A. Aristotle’s Logic and Metaphysics // Routledge History of Philosophy. – Vol. II: From Aristotle to Augustine / Ed. by David Furley. – Ch. 2. – London & New York: Routledge, 1999. – P. 40-71. • Copleston F. A History of Philosophy. – Vol. 1: Greece and Rome. From the Pre-Socratics to Plotinus. – Ch. XXVIII. Logic of Aristotle. – New York et al.: Doubleday, 1993. – P. 277-286. • Russell B. A History of Western Philosophy. – Book I. – Ch. XXII. Aristotle’s Logic; http://archive.org/stream/westernphilosoph035502mbp#page/n225/mode/2up. Advanced reading: • Bobzien S. Ancient Logic // The Stanford Encyclopedia of Philosophy (Summer 2020 Edition); https://plato.stanford.edu/entries/logic-ancient/. • Gottlieb P. Aristotle on Non-contradiction // The Stanford Encyclopedia of Philosophy (Spring 2019 Edition); https://plato.stanford.edu/entries/aristotle-noncontradiction/. • Hofweber T. Logic and Ontology // The Stanford Encyclopedia of Philosophy (Spring 2021 Edition); https://plato.stanford.edu/entries/logic-ontology/. • Shapiro S. and Kissel T. K. Classical Logic // The Stanford Encyclopedia of Philosophy (Spring 2021 Edition); https://plato.stanford.edu/entries/logic-classical/. Part 2. Concept as a Form of ThouGht (2 lectures, 2 seminars). Traditional logic analyses concepts in terms of intensions and extensions and their interrelations. Intensions and extensions both “consist of” (refer to sets of) other concepts which are either predicated of the concept in question (the concept’s intension) or of which the concept in question is predicated (the concept’s extension). Elementary logical operations of generalisation and specialisation, as well as the principal methods of explicating concepts, such as definitions and classifications, are aimed at ascertaining exact and unequivocal logical relations between concepts for their subsequent use in propositions. Logical relations between concepts depend on the way their extensions interrelate, i.e. on the presence or absence of common elements in their extensions. Varieties of relations thus identified are conceptualised as different kinds of concepts. Lecture 2. Concept as a Form of Thought. The concept of concept: a form of thought that grasps the universal essence of a species or a genus. Intensions and extensions of concepts. The interrelation of intension and extension. Logical operations on
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