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Symbolic Logic (Phl1 C03) SYMBOLIC LOGIC (PHL1 C03) I SEMESTER Core Course MA PHILOSOPHY (2019 Admission Onwards) UNIVERSITY OF CALICUT School of Distance Education Calicut University P.O., Malappuram, Kerala, India - 673 635 190403 School of Distance Education UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION Study Material I SEMESTER 2019 Admission Onwards MA PHILOSOPHY Core course (PHL1 C03) SYMBOLIC LOGIC Prepared by: Sri. Manoj K. R, Assistant Professor on contract, School of Distance Education, University of Calicut. Scrutinized by: Dr. Sheeja O.K, Assistant Professor of Philosophy, Sree Kerala Varma College, Thrissur Symbolic Logic 2 School of Distance Education UNIT – I INTRODUCTION 1.1 What is Logic Etymologically logic can be defined as the science of thought expressed in language. We get knowledge through our thought process or through our act of thinking. If we substitute reasoning with the word thought, it may be stated that the concern of logic is reasoning as expressed in certain language with a subsidiary process. The study of logic is a normative discipline. The reasoning process which go e s on in the mind is not visible, instead it is the verbal expression of such thoughts that are analysed. Copy and Cohen define logic as the study of methods and principles of distinguishing correct reasoning from incorrect reasoning. Logic is actually the method and principles in evaluating good reasoning from bad reasoning or correct reasoning from incorrect reasoning. Logic is considered the basic science of sciences, since correct reasoning is the basis of scientific study in any field. Logic is concerned with norms to distinguish between correct and incorrect reasoning; hence it is called normative study of reasoning. In our day-to-day life, we know the importance of ability to reason s i n c e it is through this ability that we draw appropriate conclusion from given evidence. It is source of most of our knowledge. Since most of our knowledge is not from direct observation instead it is through inference. We must know how to infer correctly. Primarily, Logic is about inferring, about reasoning in particular. It is the study of what constitutes correct reasoning. By studying logic one can recognize and use certain common forms of correct logical inference hence avoid making common logical errors. According to Creighton, logic is the science which treats the operations of the human mind in its search for truth. From this definition there are three facts that are stated here, firstly it states that logic is a science, then operations of human mind, then a concern for truth. Logic can be called science because, Logic shares the following characteristics of science a) Science deals with a particular department of study, like botany is the study of plants. b) Science is systematic and organised body of knowledge. c) Science renders true and exact knowledge through special means. Symbolic Logic 3 School of Distance Education Similarly, logic gives us systematic knowledge regarding correct thinking and knowledge given is correct and precise. Secondly the operations of the human mind with which logic is concerned is three processes of thinking known as conception,judgement and reasoning. Conception is the function of the human mind by which an idea or a concept is formed in the mind. Another function of the mind is judgement by which relation between things is established. It is the process of comparing concepts or ideas. Judgement is the process of affirmation or denial. When the idea of man and mortality is related, we have the idea of man is mortal. Reasoning is the process of passing from certain known judgement to a new judgement. The process by which one proposition is arrived on the basis of other proposition is called inference. Through the act of reasoning mind draws a new truth from given truth. From the given judgements a conclusion is reached. All men are mortal Socrates is a man ----------------------- Socrates is mortal The above three processes conception, judgement, inference expressed in language is called term, proposition and argument. Logic in primarily concerned with reasoning, reasoning presupposes concept and judgement, thought means processes and product of thinking. It is the is well established truth expounded by great minds which is the subject matter of logic. Creighton states that truth is the goal of logic, it can be either formal or material. In formal truth there is agreement of thought among themselves. In material truth there should be agreement to corresponding objects to the world outside. The positive science studies the nature of things or otherwise called natural science, it deals with things actual and real. While for normative science tells us about how a thing ought to be in order to agree with deal before us. Normative science is one which sets a norm to which the facts under study must conform. While positive science deals with things as they are. Examples of normative sciences are Ethics, Aesthetics etc. Regarding how our conduct ought to be to reach the ideal of goodness is the concern of ethics. Normative science is concerned with an ideal, there is a standard to which its material is directed and its value is estimated with reference to that standard then it is called regulative science. Logic teaches us how our thought ought to be to reach the ideal of truth. Here truth is made the ideal. Symbolic Logic 4 School of Distance Education 1.2 The Nature of Argument Logic is directly concerned with thought, but language is an indispensable medium to express what we think, arguments are expressed in language, and we should use the correct language to express the arguments in correct form. Verbal expression of judgement is termed proposition. Proposition is the basic unit of logical analysis; Proposition should be either true or false. A declarative sentence is part of the language to which it is spoken or written, while a proposition is not peculiar to the language in which it is expressed. Eg :- ‘The book is on the table’ in French and German language has the same propositional content, irrespective of the language in which it is spoken. While the same sentence can be uttered in different contexts to have different propositions. A statement can be expressed using different words. Utterance of a sentence in different contexts yields different statement. Statement and Propositions are not exact synonyms. An argument is comprised of a set of sentences consisting of one or more premises, which contain the evidence and a conclusion which is supposed to follow the premises. An argument may be defined as any group of propositions or statements, of which one is claimed to follow from the others, which are alleged to provide grounds for the truth of that one. Assertion do not cite reason for a particular event. There are s o m e differences between assertions and an argument. Assertion is only an opinion or a belief. In an argument there will be certain reason provided from which we have to infer the conclusion. The terms premise and conclusion are usually employed in analyzing the structure of the argument. The proposition which is affirmed on the basis of other propositions of the argument is the conclusion of that argument. Premises of an argument are sentences or claims containing the evidence, while conclusion is the claim that is supposed to follow the premises. An argument is a set of propositions arranged in terms of their relationship as premises and conclusion. The propositions of an argument are either the premises or the conclusion. Hence, an argument is defined as ‘a relational arrangement of premises and conclusion’. The conclusion of an argument is always the one proposition that is derived from one or more supporting propositions called premises. In other words, the propositions, which substantiate the conclusion, are the premises. The proposition which is drawn on the basis of the premises is a conclusion. Symbolic Logic 5 School of Distance Education Premise 1 - All men are mortal. Premise 2 - Socrates is a man. Conclusion - Therefore, Socrates is mortal. Raghu will win the game if he worked hard for it. Raghu worked hard for the game. Therefore, Raghu won the game 1.3 Truth and Validity Truth and Falsity apply only to propositions but never to arguments, while validity and invalidity is the logical property of deductive arguments, but not of propositions. There is relation between validity or invalidity of argument and truth or falsity of its premises and conclusion which are propositions. An argument can be valid even if one or more of its premises are false. Some valid arguments can contain only true premises In the following argument the premises and the conclusion are true All mammals have lungs. All whales are mammals. Therefore, all whales have lungs. For a valid deductive argument, it is impossible to have the premises true and the conclusion false. Validity of an argument depends upon the form of the argument. The validity does not depend upon the content of the argument, validity is function of the form of the argument. An argument is sound when it is factually correct and is valid. Even with false premises and false conclusion the argument can remain valid. All mammals have wings. All reptiles are mammals. ---------------------------------------------- Therefore, all reptiles have wings. In the above argument all of the premises and conclusion is false still the argument is valid.It makes us clear that truth or falsity of the conclusion of the argument does not by itself determine its validity or invalidity of that argument. The argument being valid does not guarantee the truth of the conclusion. But in a valid argument if the premises are true then necessarily the conclusion must be also be true.
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