Logic PDF

## Main Content ### Definition of Logic There are different conceptions of logic, some of which we are familiar with from everyday conversations. According to Francis Offor, the term logic can be used in at least three different and correct senses: 1. **The totality of all the laws guiding human...

## Main Content ### Definition of Logic There are different conceptions of logic, some of which we are familiar with from everyday conversations. According to Francis Offor, the term logic can be used in at least three different and correct senses: 1. **The totality of all the laws guiding human thoughts.** This is predicated on the fact that the ability to think or reason forms a basic and fundamental part of the nature of human beings. Though some animals, like dolphins, have been found to possess a good measure of rationality, humans are known to be gifted with the highest measure of reason. The laws guiding human thoughts are mostly self-evident, so much so that for human reasoning to make sense, it must conform to some basic laws. When any part of the laws is violated in the course of an argument or reasoning, the listener would most likely identify that something was wrong. Therefore, the laws need not be written down anywhere as we can have direct and immediate knowledge of their violations in expressions. For example, a right thinking person would frown at any assertion which affirms and denies a claim at the same time. For instance: "it is raining but it is not raining" or "this is a statue but it is not a statue." No formal education is needed for a reasonable person to identify that such claims as made above are against reason and should not be taken seriously. 2. **The principles guiding the operation of mechanism.** This is a description of the pre-designed codes or programs which control how a particular gadget functions. By this, no gadget such as a computer, phone or watch can function beyond what it has been designed or programed for, otherwise, it would be said to be malfunctioning. When this happens, that particular gadget would require the services of a technician in the same way we say that a person whose reasoning violates the laws of thought needs the services of a psychologist or a psychiatrist. 3. **The branch of philosophy that deals with the study of the basic principles, techniques or methods for evaluating arguments.** This is a description of logic in the professional sense. Here, logic is concerned with the nature of statements, how statements are combined to form arguments, the inferences that follow from the arrangement of statements in arguments as well as the determination of the validity or invalidity and soundness or unsoundness of such arguments. Therefore, logic as the study of the principles for evaluating arguments is aimed at distinguishing good arguments from bad ones, as well as justifying the conditions that make it so. ### The Laws of Thought The laws or principles of thought are those rules guiding human reasoning. They are: 1. **The Law of Identity:** This law states that every statement is identical with itself in such a way that if it is the case that "the sky is blue," then "the sky is blue." 2. **The Law of Contradiction:** This law states that a statement cannot be the case, and not be the case at the same time. This means that no statement can be true and false at the same time. 3. **The Law of the Excluded Middle:** This law states that a statement can be either true or false. Therefore, while for the law of contradiction, a statement cannot be both true and false, for the Excluded Middle, a statement cannot be neither true nor false. ### The Meaning of Argument The term "argument" as used in logic is different from the term "quarrel" that it ordinarily connotes. An argument has a structure which is defined by the terms "premises" and "conclusion" and the nature of the relationship between them. Going by this definition, there is the need to state what a statement or a proposition is and how they relate to arguments. A statement or a proposition makes a claim that is verifiable as being true or false and it is the arrangement of statements or propositions in the form of premise(s) and conclusion that makes up an argument. It should be noted that an argument could only have one conclusion, however, it can have more than one premise. ### Types of Arguments There are two types of argument. They are: 1. **Inductive Argument:** An inductive argument is that argument whose premise(s) provide partial or probable grounds for accepting its conclusion. This means that an inductive argument is not conclusive as it leaves room for some uncertainties. Example: "Nairobi is a beautiful city and it is in Kenya. Nakuru is a beautiful city and it is in Kenya. Kisumu is a beautiful city and it is in Kenya. Therefore, probably, Kenya is a beautiful Place." In this argument, we can see that from the observation of a number of cities, a probable conclusion that Kenya is a beautiful place was drawn. This conclusion is probable because it is only when all the cities, towns and villages in Kenya have been observed and discovered to be beautiful without exception that one could validly infer that Kenya is a beautiful place. It is for this inconclusiveness that an inductive argument cannot be described as valid or invalid but rather as either strong or weak depending on the weight of support offered by the premises. 2. **Deductive Argument:** A deductive argument is that argument whose premise(s) provide full grounds for accepting its conclusion. This means that a deductive argument is conclusive, as it leaves no room for some uncertainties. Example: "All Kenyans are Africans. Oluoch is a Kenyan. Therefore, Oluoch is an African." In this argument, we can see that from the general knowledge that all Kenyans are Africans it was possible to conclusively infer that Oluoch is an African because he is a Kenyan. It is for this conclusiveness that a deductive argument is described as either valid or invalid. In a valid deductive argument, once the premises of the argument are accepted as true, it becomes impossible to reject or deny its conclusion without violating the law of contradiction, whereas it is possible for the premises of an invalid argument to be true while its conclusion is false. ### Divisions of Logic #### Formal Logic Formal logic, according to Ekanola, is the aspect of logic that deals primarily with the formal structures of statements and arguments. Its main focus is to determine the status of statements in relation to their logical truths and that of arguments in relation to their validity. In formal logic, the form otherwise known as structure of an argument is very important. This is because the content of a statement or an argument is not necessary in the determination of the truth of that statement or necessary in the determination of the validity of that argument. There are different formal conditions for statements that are: 1. **conjunctions** 2. **disjunctions** 3. **conditionals** 4. **bi-conditionals** ...without any consideration to their content. 1. **Conjunction:** a conjunction is any expression that brings two statements together using words like 'and', 'though', 'but' and so on. In such an expression, it does not matter what the contents of that statements are, the moment both conjuncts are true, then resulting expression must be true. For example, given that there is a statement 'R' and a another statement ‘S', where R stands for ‘the pear is ripe' or any statement whatsoever a nd S stands for 'the pear is sweet' or any statement whatsoever; provided that such state ments (conjuncts) are joined by any of the words 'and', 'though' or 'but' and given that both conjuncts are true, then the resulting expression 'the pear is ripe and the pear is swe et' must be true. Any other condition represented by such a statement would be false. Th erefore, 'R and S' is true only when R is true and S is true at the same time. 2. **Disjunction:** in any statement that is a disjunction, it the case that the disjuncts ar e joined by words like ‘or', ‘nor', 'either or', as the case may be. It does not matter wha t the content of that statement is, anytime both disjuncts are false, then the resulting expr ession must be false. For example, given that there is a statement ‘R or S', where R stan ds for 'the pear is ripe' or any statement whatsoever and S stands for 'the pear is sweet' or any statement whatsoever; provided that such disjuncts are joined by any of the word s 'or', 'nor' as the case may be, and given that both disjuncts are false, then the resulting expression 'the pear is ripe or the pear is sweet' must be false. Any other condition repre sented by such an expression would be true. Therefore, ‘R or S' is false only when R is f alse and S is false at the same time. 3. **Conditional :** a conditional statement is one in which the antecedent (the part of t he statement which serves as the condition for the other part to follow) and the consequ ent (the part that follows after the condition) are joined by words like ‘if...then...', 'only if' as the case may be. It does not matter what the content of that statement is, anytime t he antecedent is true and the consequent is false, then the resulting statement must be fal se. For example, given that there is a statement ‘if R then S', where R stands for 'the pea r is ripe' or any statement whatsoever and S stands for ‘the pear is sweet' or any stateme nt whatsoever; provided that such a statement is constructed by any of the words 'if...th en...', 'only if' as the case may be, and given that the antecedent is true and the consequ ent is false, then the resulting expression must be false. Any other condition represented by such a statement would be true. Therefore, ‘if R then S' is false only when R is true a nd S is false at the same time. 4. **Bi-conditional:** a bi-conditional statement is one in which the component stateme nts are joined by words like ‘if and only if', or its equivalents. It does not matter what th e content of that statement is, provided that the components have equal truth values, in which case, they are either both true or both false, then that statement must be true. For example, given that there is a statement ‘R if and only if S', where R stands for ‘the pear is ripe' or any statement whatsoever and S stands for 'the pear is sweet' or any statemen t whatsoever; provided that such statements are joined by the word 'if and only if' as the case may be, and given that both components are either both false or both true, then the r esulting statement must be true. Any other condition represented by such a statement wo uld be false. Therefore, ‘R if and only if S' is true when the components have equal truth values and false when they do not have equal truth values. For arguments, there are certain forms that are already known to be valid. What this means is that any argument that takes the form of any of them would necessarily be valid. Examples are; 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Simplification 6. Constructive Dilemma 7. Destructive Dilemma 8. Addition 9. Conjunction 1. **Modus Ponens:** Example; "If John studied law (P) THEN John is a lawyer (Q) John studied law (P) Therefore, John is a lawyer (Q)" This form of argument is stating that when we have a conditional statement as the first premise of an argument and we also have a second premise which is an affirmation of the antecedent of the first premise, we can validly infer a conclusion which is an affirmation of the consequent. 2. **Modus Tollens:** Example; "IF John studied law (P) THEN John is a lawyer (Q) John is not a lawyer (Q) Therefore, John did not study law (P)" This form of argument is stating that when we have a conditional statement as the first premise of an argument and we also have a second premise which is a denial of the consequent of the first premise, we can validly infer a conclusion which is a denial of the antecedent. 3. **Hypothetical Syllogism:** Example; "IF John studied law (P) THEN John is a lawyer (Q) IF John is a lawyer (Q) THEN John wins the case (R) Therefore, IF John studied law (P) THEN John wins the case (R)" This form of argument is stating that when we have two related conditional statements making up the first and second premises of an argument in such a way that the consequent of the first is the antecedent of the second, then we can validly infer a conclusion which is a conditional statement from the antecedent of the first and the consequent of the second. 4. **Disjunctive Syllogism:** Example; "EITHER John studied law (P) OR John is a lawyer (Q) John n did not study law (P) Therefore, John is a lawyer (Q) OR EITHER John studied law (P) OR John is a lawyer (Q) John is not a lawyer (Q) Therefore, John studied law (P)" This form of argument is stating that when we have a disjunctive statement as the first premise of an argument and a second premise which is a denial of any of the disjuncts, we can validly infer a conclusion that is an affirmation of the other disjunct. 5. **Simplification:** Example; "John studied law (P) AND John is a lawyer (Q) Therefore e, John studied law (P) OR John studied law (P) AND John is a lawyer (Q) Therefore, John is a lawyer (Q)" This form of argument is stating that when we have two statements joined with a conjunction as the premise of an argument, then we can validly infer a conclusion that is an affirmation of any of the conjuncts. 6. **Constructive Dilemma:** Example; "If John studied law (P) then John ia a lawyer (Q) AND If John wins the case (R) then John will rejoice (S) EITHER John studied law (P) OR John wins the case (R) Therefore, EITHER John is a lawyer (Q) OR John will rejoice (S)" This form of argument is stating that when we have two conditional statements joined by a conjunction as the first premise of an argument and given that there is a second premise which is a disjunction of their respective antecedents, we can validly infer a conclusion which is a disjunction of their consequents. 7. **Destructive Dilemma:** Example; "If John studied law (P) then John is a lawyer (Q) AND If John wins the case (R) then John will rejoice (S) Either John is not a lawyer (Q) OR John will not rejoice (S) Therefore, either John did not study law (P) OR John does not win the case (OR)" This form of argument is stating that when we have two conditional statements joined by a conjunction as the first premise of an argument and given that there is a second premise which is a disjunction of their negated consequents, we can validly infer a conclusion which is a disjunction of their negated antecedents. 8. **Addition:** Example; "John studied law (P) Therefore, John studied law (P) OR John is a lawyer (Q) OR John studied law (P) John is a lawyer (Q) Therefore, John studied law (P) OR John is a lawyer (Q)" This form of argument is stating that you can form a disjunction of which that statement is a part or you can form a disjunction of two existing statements. 9. **Conjunction:** Example; "John studied law (P) John n is a lawyer (Q) Therefore, John studied law (P) AND John is a lawyer (Q)" This form of argument is stating that from two separate statements, you can infer a conclusion that is a conjunction of the two premises. #### Informal Logic Informal logic is the aspect of logic that deals primarily with the nature of arguments in our everyday discourses. The basic concern here is on logical consistencies, persuasiveness and reasonableness of arguments. In this case, when any of these concerns are violated, it leads to fallacy. Kahane defines a fallacy as "an argument that should not persuade a rational person to accept its conclusion", while in Hamblin's view, "a fallacious argument is one that seems to be valid but is not so." For Irving Copi, a fallacy is a type of argument that may seem to be correct but which proves upon examination not to be so. There are two types of fallacies. They are formal and informal fallacies. As discussed under formal logic, arguments that violate the formal structures or rules of formal arguments already known to be valid, commit formal fallacies . In the same manner, when arguments in informal settings present logical inconsistencies or appear to be valid when they are indeed invalid, they commit informal fallacies. We shall now consider a number of informal fallacies broadly grouped into: 1. Fallacies of Relevance 2. Fallacies of Ambiguity 3. Fallacies of Presumption 1. **Fallacies of Relevance:** usually in fallacies of relevance, the premise(s) of such an argument has no logical connection with its conclusion and is therefore irrelevant for accepting the conclusion. 1. **Appeal to Force (argumentum ad baculum)** This fallacy is committed when, rather than appealing to the rational status of an argument in influencing the acceptance or rejection of the claim made, the influence of force is invoked upon. An example is found in the persuasion of UN members by America to endorse Jerusalem as the capital of Israel or forfeit US aids. US went on to say; we will ‘take names of those who vote to reject Jerusalem recognition.’ Here, the rationale behind voting for or against the motion was subdued and US threatened to withdraw aids as a measure to force the compliance of members. 2. **Appeal to Pity (argumentum ad misericordiam)** When in an argument, a person appeals to pity rather than to reason as a way of influencing others to consider their position, one commits this fallacy. An example is when a woman approached a bank for a business loan without a business plan or collateral. When asked to state why her request should be granted, she simply said, 'because I am a widow.' Being a widow in this case is not the condition required for getting a loan from the bank as she was rather appealing to pity. 3. **Appeal to Emotion (argumentum ad populum)** When a person beclouds the reasoning processes of people in making informed judgments by appealing to their emotions, one commits this fallacy. An example is a Nigerian politician from the northern part of the country who visits the southern part on a campaign rally dressing like a southerner. The intention being to look like the people and showing that he or she appreciates their culture. But as soon as elections are over with, they do away with the materials. 4. **Appeal to Authority (argumentum ad verecundiam)** According to Francis Offor, this fallacy "involves the mistaken supposition that there are some connections between the truth of a proposition and some features of the person who asserts or denies it. When the opinion of someone famous or accomplished in another area of expertise is appealed to in order to guarantee the truth of a claim outside of the province of that authority's field, this fallacy is committed." An example is found in the Sultan of Sokoto personally immunising his grandchildren against polio as a way of convincing his people to accept polio immunisation. In other words, if the Sultan of Sokoto personally immunised his grandchildren against polio Then, immunisation against polio is not harmful. In this situation, it is possible for a professor of medicine to educate the people of the importance of polio immunisation and not to be taken seriously. However, when the Sultan who probably knows nothing about medicine but because he is highly respected makes the same claim, his opinion is respected beyond that of the expert. 5. **Argument Against the Man (argumentum ad hominem)** Argumentum ad hominem could be either 'abusive' or 'circumstantial'. In the first instance, we attack the messenger rather than the message while in the second we argue against the circumstance of the opponent. Examples: "John's argument that abortion should be rejected is meaningless, because he doesn't think straight.(Abusive). You should agree with me that the Yorubas are well educated. After all, you are a Yoruba person (Circumstantial)." 6. **Appeal to Ignorance (argumentum ad ignorantiam)** This fallacy is committed when a person claims that a statement is true for the reason that it has not been proven to be false or that it is false because it has not been proven to be true. An example is: "The notion of heaven is a fiction because no one has been able to prove that heaven exists." 2. **Fallacies of Ambiguity:** fallacy of ambiguity results when a particular word or an idea is used in more than one sense in a single argument. 1. **Fallacy of Equivocation** Example includes; "A bank is a place where money is kept. A river has a bank. Therefore, the bank of a river is a place where money is kept." 2. **Fallacy of Division** This fallacy occurs when the features of a group is assumed to be possessed by the individual members of the group. Example includes; "All Nigerians smile in the face of poverty. Jide is a Nigerian. Therefore, Jide smiles in the face of poverty." 3. **Fallacy of Composition** This fallacy occurs when the features of individual members of a group are attributed to the entire group. Example includes; "Lagos is a beautiful city and it is in Nigeria. Abuja is a beautiful city and it is in Nigeria. Port Harcourt is a beautiful city and it is in Nigeria. Therefor e, Nigeria is a beautiful Place." 3. **Fallacies of Presumption:** these kinds of fallacies result from the imprecisions or uncertainties in the use of words. 1. **False Cause** There are two forms of this fallacy. • Non causa pro causa: This fallacy results when we assume that A is the cause of B when there is no causal connection between A and B. Example; "The parrot sang beautifully during planting season and the harvest was bountiful. Therefore, the parrot caused the increase." • Post hoc ergo propter hoc: This fallacy occurs when one particular event follows immediately after another and we assume that the one is the cause of the other when indeed, it is not the case. Example; "Thunder usually follows after a bright lightning. Theref ore, the lightning is the cause of thunder." 2. **Complex Question** A complex question is one which contains at least two questions, one of which is implied, and in which an affirmative answer to the implied question is already presupposed, irrespective of whether or not the main question is answered in the affirmative or in the negative. In other words, this fallacy is committed when one draws a conclusion from a yes or no answer to a question that is loaded. A complex question, therefore, is one in which a simple yes or no does not absorb a person of guilt. Example; "Question -: Have you stopped stealing? Answer-: Yes. (This would imply that the person used to steal) Answer-: No. (This would imply that the person still steals)" 3. **Begging the Question** This fallacy is committed when one assumes as a premise of an argument the conclusion to be proven. Example; "The universe is an endless space because the universe is endless."