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1 Bpy-002 Logic BPY-002 LOGIC: CLASSICAL AND SYMBOLIC LOGIC (4 credits) COURSE INTRODUCTION Cordial welcome to the BA Philosophy Programme of IGNOU. The curriculum prepared for this degree is relevant and significant. We have included latest scholarship on the course prepared by renowned scholars from across the country. The second course that you study is “Logic: Classical and Symbolic Logic.” The concept of logical form is central to logic; it is being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic, which is the study of natural language arguments, includes the study of fallacies too. Formal logic is the study of inference with purely formal content. Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two: propositional logic and predicate logic. Mathematical logic is an extension of symbolic logic into other areas, such as the study of model theory, proof theory, set theory, and recursion theory. This course presents 4 blocks comprising 16 units. Block 1 is an introduction to logic. In this block we have tried to explain the nature and scope of logic, concept and term, definition and division, and proposition. Block 2 deals with meaning and kinds of reasoning, deductive reasoning, syllogisms, and dilemma and fallacies. Block 3 studies induction, the history and utility of symbolic logic, compound statements and their truth values, and truth-functional forms. Block 4 probes into formal proof of validity with rules of inference and rules of replacement. This final unit also explains conditional proof and indirect proof, and quantification. All these four Blocks will enable you to know the core of logic explained in simple terms with profound insights taking into account the latest trends in the discipline. You will have to enhance your knowledge of the subject with the help of the suggested readings and by browsing through the various websites on the topic, especially through the Wikipedia on which many contributors depend for their reference. 1 BLOCK -1 INTRODUCTION Logic is the study of the principles of valid inference and demonstration. The word derives from Greek logike, meaning “possessed of reason, intellectual, dialectical, argumentative;” As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from the study of validity, fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. The present block, consisting of 4 units, introduces logic taking into account its basic nature. Unit 1 on “Nature and Scope of Logic” introduces and familiarizes the nature and scope of the subject to the students. Anyone who ventures to study logic must necessarily know its status among academic disciplines: is it a science or an art? Again, is it a positive science or a normative science? Debates on these cover the problem from various angles. Yet another concern of a student of logic would be the extension and scope of logic. This has been achieved by introspection into the relation between logic and various other sciences. Unit 2 highlights “Concept and Term.” Thought in logic means process or product of thinking concepts. This unit aims at examining major entities in the language of logic like concepts, words and terms. Concept is a word that carries a lot of philosophical significance. Words and terms connote different senses in the language of logic. It is essential that a student of logic gets familiarized with the usage of such technical terms. Unit 3 explains how Logic deals with thought, and thoughts are always expressed in language. Words we use must convey proper idea. If they have no fixed meaning it would be difficult to understand what one means in his use of a word. In such a situation error and confusion are not uncommon. We define a term according to the interest we have in it. But logic deals with correct thinking. Our thoughts can never be coherent unless we determine the meaning of each term. Now the tools which logic devises for the attainment of this purpose are definition and division. Unit 4 discusses “Proposition.” As we know inferential process is the main subject matter of logic. The term refers to the process by which a proposition is arrived at and affirmed on the basis of one or more other propositions accepted as the starting point of the process. To determine whether an inference is correct the logician examines the propositions that are the initial and end points of that process and the relationships between them. This clearly denotes the significance of propositions in the study of logic. Four units mentioned above teach us that knowledge is based directly on perception and indirectly on what we have been told. Much of the knowledge we have is justified by means of reasoning or logical argument, based on other knowledge we have. If we are not willing to use reasoning, our beliefs or values might well be inconsistent, and then we would have no knowledge or proper judgement at all. 1 UNIT 2 CONCEPT AND TERM Contents 2.0 Objectives 2.1 Introduction 2.2 Concept, Word and Terms. 2.3 Terms as a Name of Class 2.4 Extension and Intension 2.5 Inverse Variation 2.6 Classification of Terms 2.7 Let Us Sum Up 2.8 Key Words 2.9 Further Readings and References 2.10 Answers to Check Your Progress 2.0 OBJECTIVES Logic is said to be the study of argument as expressed in language. Language in general is highly ambiguous. In any language words are often used in various senses. For example, sometimes ‘thought’ and knowledge’ are used as synonymous terms. Therefore this unit aims at: • examining major entities in the language of logic like concepts, words and terms and thereby show that they carry lot of philosophical significance and at the same time carry different senses. • familiarizing the students with varieties of technical terms. Terms can be classified under different criteria. There are simple and composite terms, singular and general terms, collective and non-collective terms, absolute and relative terms, concrete and abstract terms, positive, negative and private terms and connotative and non-connotative terms. This unit undertakes a study of these various types of terms to procure a good undertaking of the language of logic with which the student is expected to be sufficiently acquainted. 2.1 INTRODUCTION Language is the external expression of intention, thought etc. It is the means of communicating our ideas to other people. In logic, by language we mean only the verbal expression of our ideas, either spoken or written. The Greeks seem to have used the word ‘logos’ to denote ideas as well as speech. This clearly shows the close relation between language and thought. As Grumbley has rightly pointed out, thought and language are closely connected just like how principles of life and activities of a living organism are connected. Clear thinking and accurate language help each other. Further, it is language that gives thought a name and an abiding reality as a permanent possession. It is popularly said: ‘Thought lives in language’. The multitudes of objects that we 1 see around cannot be remembered unless certain names are endowed to the ideas of those objects. The nature of thought is such that it gets dissolved unless we put them in words. Language not only structures thought by codifying them, but also does the service of preserving them for future generations. It enables us to split complex ideas into atomic ones to analyse and thereby understand them. Hence the philosophers often comment that logic and language are the two sides of the same coin. In order to understand complex ideas we split them into simple words. Words like chastity, nationality, religious are just a few examples to convince ourselves that words can stand representing condensed expression of complex thoughts pregnant with many ideas. In this unit an attempt is made to understand how words, concepts and terms play a decisive role in our study of logic. 2.2 CONCEPT, WORD AND TERM It is necessary to distinguish between word, concept and term. Concept means a general idea. There is difference between the two ideas represented by the terms ‘student’ and ‘a student’. The term ‘a student’ refers to a particular student in an indefinite manner and it is essentially singular in usage. The term ‘student’ is applied in general to all those who undertake studies. The common and essential attributes which are found in every particular individual of the class are thought of separately, and thus we get a concept. In brief, the concept stands for general ideas. When expressed in language concept becomes a term. Judgment is the process of relating two concepts. For instance, the two concepts ‘water’ and ‘cold’ may be related and the result is the judgement, ‘water is cold’. A judgment when expressed in language is called a proposition. Sometimes it is said that concepts are mental entities. They are not visible. Conception or simple apprehension is the function of human mind by which an idea of a concept is formed in the mind. It is a process of forming mental image of an object, e.g., you see an elephant and form an idea of the elephant in the mind. The formation of concepts involves the fallowing processes. (1) Comparison: Different entities are compared with one another so that the attributes they share in common and those on which they differ can be specified.
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