Inductive Logic Unit 2 PDF

INDUCTIVE LOGIC UNIT 2  Outline – Differentiate between inductive and deductive logic – Distinguish between arguments from authority and induction by enumeration – Use Mills methods to reach conclusions – Apply the scientific way of reasoning – Construct arguments from ana...

INDUCTIVE LOGIC UNIT 2  Outline – Differentiate between inductive and deductive logic – Distinguish between arguments from authority and induction by enumeration – Use Mills methods to reach conclusions – Apply the scientific way of reasoning – Construct arguments from analogy  Inductive and Deductive logic Logic is the study of methods for evaluating whether the premises of an argument adequately support its conclusion There are two kinds of logic: – Deductive logic Studies methods for evaluating whether the premises guarantee its conclusion – Inductive logic Studies methods for evaluating whether the premises of an argument make its conclusion probable without guaranteeing it  Inductive logic Inductive logic is the part of logic that is concerned with the study of methods of evaluating arguments for strength and weakness.  Inductive logic A strong argument is one in which it is probable (but not necessary) that, if the premises are true then the conclusion is true. A weak argument is one in which it is not probable that, if the premises are true, then the conclusion is true. A cogent argument is a strong argument in which all of the premises are true. An uncogent argument is one that is either weak or strong with at least one false premise. Inductive logic Inductive and Deductive logic  Deductive vs. Inductive Logic There are some important differences between the two: 1. Inductive strength comes in degrees. Deductive validity does not. 2. Inductively cogent arguments can have false conclusions. Deductively sound arguments cannot. 3. An inductively strong argument can be made either stronger or weaker by adding new premises. Adding new premises cannot affect a deductively valid argument  Deductive vs. Inductive Logic 1. Inductive strength comes in degrees. Deductive validity does not. Example: Inductive/Deductive Ninety percent/All of the cars in the parking lot were vandalized last night. My car was in the parking lot so my car was vandalized last night.  Statistical Syllogism Statistical syllogism: x percent of A are B c is an A So, c is a B [where x is between 50-100 exclusive]  Statistical Syllogism The strength of an inductive argument is determined by Statistical Syllogism. In a statistical syllogism, the percentage is greater than 50 and less than 100. The statistical generalization need not be stated numerically: – ‘Almost all’, ‘most’, ‘very often’, ‘hardly ever’, and other similar expressions are frequently used.  Statistical Syllogism Two Standards of the Strength of Statistical Syllogisms: 1. Percentage - the closer the percentage in the generalization is to satisfy the conclusion, the stronger the statistical syllogism is (a is a G, a is a non-G) 2. Relevance of the reference class to the attribute class.  The Fallacy of Incomplete Evidence (Cherry-picking) The fallacy of incomplete evidence is committed when one fails to consider all available relevant evidence when choosing the reference class for one’s statistical syllogism. – Argument appear to be strong when it could be weak because the relevant information has been omitted.  The Fallacy of Incomplete Evidence If one knowingly omitted the relevant information, a clear logical error has been committed. However, consider the following cases where information is available, but the arguer illness, ignorance, poor investigation or other circumstances prevent awareness. Should we say that a fallacy has been committed? Arguments from Authority and Argument Induction by Enumeration Two types of inductive argument about which there is general agreement.  Argument by Authority  Induction by Enumeration – a conclusion about all of the members of the class is drawn from premises that refer to observed members of that class.  Arguments from Authority This argument form is as follows: 1. R sincerely asserts that S So, 2. S Where: R is any source of information such as a person, or reference work (dictionaries, encyclopedia, maps etc. (the more reliable the source the stronger the argument). and S stands for any statement  Arguments from Authority Criteria for Arguments from Authority: – Is the authority reliable on the subject at issue? unreliable authority fallacy committed – Are there authorities (other than R) that assert that S is false? If so, are these authorities more, less or equally reliable on the subject at issue? Fallacies of incomplete evidence – Is the authority being misquoted or misinterpreted? Even reliable authorities can make mistake, therefore argument from authority is not valid  Argument: Induction by Enumeration This argument form is as follows: 1. ____ percent of a sample of A are B So, 2. Approximately ____ percent of A are B Example: Eighty-two percent of a random sample of 200 UTECH students are sleep-deprived. Therefore, approximately 82% of UTECH students are sleep- deprived  Argument: Induction by Enumeration Criteria for Induction by Enumeration: – Is the sample random? each member of population has equal chance of being included in sample – Is the sample of an appropriate size? larger is better, 1500 = ±3% – Is the sample inaccurate due to psychological factors? The nature of questions asked – This type of argument can be strong, but these errors should be avoided.  Activity Exercise 10.2 Identifying Inductive Arguments  Mill’s Methods Mill’s Method – inductive reasoning to help conclude that “A causes B” This method of reasoning is not valid but, provide significant support for the conclusion. The word “causes” is ambiguous and sometimes refer to sufficient or necessary condition “causes” can refer to conditions that is neither sufficient or necessary. Mill’s Methods - Sufficient Condition Sufficient condition: if x is a sufficient condition of y, then if x occurs, y occurs For humans, being beheaded is a sufficient condition for death. This is not a necessary condition as death could be caused by other means e.g., strangulation, bullet wound etc. Mill’s Methods - Necessary Condition Necessary condition: if x is a necessary condition of y, then y occurs only if x occurs. For flowers, water is a necessary condition for growth. When an event or phenomenon occurs, all the necessary conditions must be present. If the event can occur without the event or phenomenon then it would not be a necessary conditions.  Mill’s Methods John Stuart Mills developed five methods for establishing conclusions of the form “A causes B” as follows: 1. Method of agreement – involves identifying a common factor, that is, one that is present whenever the effect is present. 2. Method of difference – involves comparing two cases, one in which the effect is present and one in which it is absent; if when the effect is absent, the possible cause C is also absent, the test lends support to C as the cause.  Mill’s Methods 3. Joint method – involves combining the method of agreement and the method of difference. 4. Method of concomitant variation – involves showing that as one factor varies, another varies in a corresponding way. 5. Method of residues – involves “subtracting out” those aspects of the effect whose causes are known and concluding that the rest of the effect (“the residue”) is due to an additional cause.  Scientific Way of Reasoning Mill’s Method leads to scientific reasoning which involves: – Describing the problem – Formulating hypothesis – Testing the hypothesis  Arguments from Analogy Argument from Analogy / Analogical Reasoning 1. A is similar to B 2. B has property P So, 3. A has property P  Examples of Analogy The Tempest and A Midsummer Night’s Dream are both plays written by William Shakespeare. These two plays are very similar in length. Hudson was able to read A Midsummer Night’s Dream in the space of an evening. So, Hudson is able to read The Tempest in the space of an evening. Parrots and humans can both talk. Humans can think rationally. Therefore, parrots can think rationally. 28  Assessing analogies In assessing the logical connection between the premises and the conclusion, it usually helps to ask the following three questions: What are the respects in which A and B are similar and are they relevant to the issue at hand? Are A and B dissimilar in any relevant respects? Are there things (other than A) that are similar to B in the relevant respects? 29  Criteria for analogies Question 1: What are the respects in which A and B are similar and are they relevant to the issue at hand? Ideally, the more relevant respects A and B share, the stronger the argument. Question 2: Are A and B dissimilar in any relevant respects? That is, does the analogy between A and B break down at any relevant points? Dissimilarities are relevant if they decrease the likelihood of A’s having property P. Relevant differences between A and B tend to weaken the argument. Question 3: Are there things (other than A) that are similar to B in the relevant respects? If so, do these things have property P? To the extent that there are things relevantly similar to B that lack P, the analogy breaks down. To the extent that there are things relevantly similar to B that have P, the analogy holds up. 30  Analogies Arguments from analogy are often used in moral and legal reasoning. Activity: Consider an argument from analogy on a very controversial issue, not with a view to settling the issue but simply to illustrate the process of evaluating such arguments. 31