Logic Module 1 Lesson 3 PDF

Lesson 3: Deduction and Induction SHS-Ateneo de Cebu CEP-Logic UNIT 1: Basic Concepts of Logic Lesson 3: Deduction and Induction Prepared by Joerell P. Estillore || July 26, 2022 Magis day, Ateneo Hearters! Preliminary In our previous lesson, we lear...

Lesson 3: Deduction and Induction SHS-Ateneo de Cebu CEP-Logic UNIT 1: Basic Concepts of Logic Lesson 3: Deduction and Induction Prepared by Joerell P. Estillore || July 26, 2022 Magis day, Ateneo Hearters! Preliminary In our previous lesson, we learned that every argument involves an inferential claim in which the conclusion is supposed to follow from the premise. Every argument also makes a claim that its premises provide grounds for the truth of its conclusion. The question we now address has to do with the strength of this claim. Just how strongly is the conclusion claimed to follow from the premises. The reasoning process (inference) that an argument involves is expressed either with certainty or with probability. That is what the logician introduced the name deduction and induction for, respectively. If the conclusion is claimed to follow with strict certainty or necessity, the argument is said to be deductive; but if it is claimed to follow only probably, the argument is said to be inductive. Therefore, a conclusion may be supported by its premise in two very different ways. These two different ways are the two great classes of arguments: Deductive arguments and Inductive arguments. And the distinction between these two classes of arguments, because every argument involves an inferential claim, lies in the strength of their inferential claim. Understanding the distinction of these classes is essential in the study of logic. In this lesson, we will learn the broad groups of arguments, Deductive arguments and Inductive arguments, and the techniques of distinguishing one from the other. LEARNING OUTCOMES After the successful accomplishment of this lesson, you will be able to: Understand the meaning, nature, and forms of a deductive argument. Understand the meaning, nature, and forms of an inductive argument. Distinguish deductive arguments from inductive arguments, and vice versa. Dear Ateneo Hearters, how do you define a deductive argument? How do you define an inductive argument? Stated more precisely, a deductive argument is an argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true. On the other hand, an inductive argument is an argument incorporating the claim that it is improbable that the conclusion be false given that the premises are true. Two examples: Bro. Joerell P. Estillore Lesson 3: Deduction and Induction SHS-Ateneo de Cebu CEP-Logic The meerkat is closely related to the suricat. The meerkat is a member of the mongoose family. The suricat thrives on beetle larvae. All members of the mongoose family are carnivores. Therefore, probably the meerkat thrives on beetle Therefore, it necessarily follows that the meerkat is a larvae. carnivore. The first of these arguments is inductive, the second deductive. In deciding whether an argument is inductive or deductive, we look to certain objective features of the argument. These features include (1) the occurrence of special indicator words, (2) the actual strength of the inferential link between premises and conclusion, and (3) the form or style of argumentation. However, we must acknowledge at the outset that many arguments in ordinary language are incomplete, and because of this, deciding whether the argument should best be interpreted as deductive or inductive may be impossible. The occurrence of special indicator words is illustrated in the examples we just considered. The word “probably” in the conclusion of the first argument suggests that the argument should be taken as inductive, and the word “necessarily” in the conclusion of the second suggests that the second argument be taken as deductive. Additional inductive indicators are “improbable,” “plausible,” “implausible,” “likely,” “unlikely,” and “reasonable to conclude.” Additional deductive indicators are “certainly,” “absolutely,” and “definitely.” (Note that the phrase “it must be the case that” is simply a conclusion indicator that can occur in either deductive or inductive arguments.) Inductive and deductive indicator words often suggest the correct interpretation. However, if they conflict with one of the other criteria (discussed shortly), we should probably ignore them. Arguers often use phrases such as “it certainly follows that” for rhetorical purposes to add impact to their conclusion and not to suggest that the argument be taken as deductive. Similarly, some arguers, not knowing the distinction between inductive and deductive, will claim to “deduce” a conclusion when their argument is more correctly interpreted as inductive The second factor that bears on our interpretation of an argument as inductive or deductive is the actual strength of the inferential link between premises and conclusion. If the conclusion actually does follow with strict necessity from the premises, the argument is clearly deductive. In such an argument it is impossible for the premises to be true and the conclusion false. On the other hand, if the conclusion does not follow with strict necessity but does follow probably, it is often best to consider the argument inductive. Examples: All entertainers are extroverts. The vast majority of entertainers are extroverts. Stephen Colbert is an entertainer. Stephen Colbert is an entertainer. Therefore, Stephen Colbert is an extrovert. Therefore, Stephen Colbert is an extrovert. In the first example, the conclusion follows with strict necessity from the premises. If we assume that all entertainers are extroverts and that Stephen Colbert is an entertainer, then it is impossible that Stephen Colbert not be an extrovert. Thus, we should interpret this argument as deductive. In the second example, the conclusion does not follow from the premises with strict necessity, but it does follow with some degree of probability. If we assume that the premises are true, then based on that assumption it is probable that the conclusion is true. Thus, it is best to interpret the second argument as inductive. Occasionally, an argument contains no special indicator words, and the conclusion does not follow either necessarily or probably from the premises; in other words, it does not follow at all. This situation points to the need for the third factor to be taken into account, which is the character or form of argumentation the arguer uses. 1. Deductive Argument Forms Many arguments have a distinctive character or form that indicates that the premises are supposed to provide absolute support for the conclusion. Five examples of such forms or kinds of argumentation are arguments based on mathematics, arguments from definition, and categorical, hypothetical, and disjunctive syllogisms. An argument based on mathematics is an argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement. For example, a shopper might place two apples and three oranges into a paper bag and then conclude that the bag contains five pieces of fruit. Or a surveyor might measure a square piece of land and, after determining that it is 100 feet on each side, conclude that it contains 10,000 square feet. Since all arguments in pure mathematics are deductive, we can usually consider arguments that depend on mathematics to be deductive as well. However, arguments that depend on statistics are a noteworthy exception. As we will see shortly, such arguments are usually best interpreted as inductive. An argument from definition is an argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion. For example, someone might argue that because Claudia is mendacious, it follows that she tells lies, or that because a certain paragraph is prolix, it follows that it is excessively wordy. These arguments are deductive because their conclusions follow with necessity from the definitions of “mendacious” and “prolix.” Bro. Joerell P. Estillore Lesson 3: Deduction and Induction SHS-Ateneo de Cebu CEP-Logic A syllogism, in general, is an argument consisting of exactly two premises and one conclusion. Categorical syllogisms will be treated in greater depth in Module 3, but for now we will say that a categorical syllogism is a syllogism in which each statement begins with one of the words “all,” “no,” or “some.” Example: All ancient forests are sources of wonder. Some ancient forests are targets of the timber Arguments such as these are nearly always best industry. treated as deductive. Therefore, some sources of wonder are targets of the timber industry. A hypothetical syllogism is a syllogism having a conditional (“if... then”) statement for one or both of its premises. Examples: If estate taxes are abolished, then wealth will If Fox News is a propaganda machine, then it accumulate disproportionately. misleads its viewers. If wealth accumulates disproportionately, then Fox News is a propaganda machine. democracy will be threatened. Therefore, Fox News misleads its viewer. Therefore, if estate taxes are abolished, then democracy will be threatened. Later in this course, the first of these arguments will be given the more specific name of pure hypothetical syllogism because it is composed exclusively of conditional (hypothetical) statements. The second argument is called a mixed hypothetical syllogism because only one of its component statements is a conditional. Later in this book, the second argument will be given the more specific Latin name modus ponens. A disjunctive syllogism is a syllogism having a disjunctive (“either... or...”) statement. Example: Either global warming will be arrested, or hurricanes will become more intense. Global warming will not be arrested. Therefore, hurricanes will become more intense. As with hypothetical syllogisms, such arguments are usually best taken as deductive. Hypothetical and disjunctive syllogisms will be treated in greater depth in the final discussion of this course. 2. Inductive Argument Forms In general, inductive arguments are such that the content of the conclusion is in some way intended to “go beyond” the content of the premises. The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that little is known about. Such an argument may take any of several forms: predictions about the future, arguments from analogy, inductive generalizations, arguments from authority, arguments based on signs, and causal inferences, to name just a few. A prediction is an argument that proceeds from our knowledge of the past to a claim about the future. For example, someone might argue that because certain meteorological phenomena have been observed to develop over a certain region of central Missouri, a storm will occur there in six hours. Or again, one might argue that because certain fluctuations occurred in the prime interest rate on Friday, the value of the dollar will decrease against foreign currencies on Monday. Nearly everyone realizes that the future cannot be known with certainty; thus, whenever an argument makes a prediction about the future, one is usually justified in considering the argument inductive. An argument from analogy is an argument that depends on the existence of an analogy, or similarity, between two things or states of affairs. Because of the existence of this analogy, a certain condition that affects the better-known thing or situation is concluded to affect the similar, lesser-known thing or situation. For example, someone might argue that because Christina’s Porsche is a great-handling car, it follows that Angela’s Porsche must also be a great-handling car. The argument depends on the existence of a similarity, or analogy, between the two cars. The certitude attending such an inference is probabilistic at best. A generalization is an argument that proceeds from the knowledge of a selected sample to some claim about the whole group. Because the members of the sample have a certain characteristic, it is argued that all the members of the group have that same characteristic. For example, one might argue that because three oranges selected from a certain crate were especially tasty and juicy, all the oranges from that crate are especially tasty and juicy. Or again, one might argue that because six out of a total of nine members sampled from a certain labor union intend to vote for Johnson for union president, two-thirds of the entire membership intend to vote for Johnson. These examples illustrate the use of statistics in inductive argumentation. An argument from authority is argument that concludes something is true because a presumed expert or witness has said that it is. For example, a person might argue that earnings for Hewlett-Packard Corporation will be up in the coming quarter because of a statement to that effect by an investment counselor. Or a lawyer might argue that Mack the Knife committed the murder because an eyewitness testified to that effect under oath. Because the investment counselor and the eyewitness could be either mistaken or lying, such arguments are essentially probabilistic. Bro. Joerell P. Estillore Lesson 3: Deduction and Induction SHS-Ateneo de Cebu CEP-Logic An argument based on signs is an argument that proceeds from the knowledge of a sign to a claim about the thing or situation that the sign symbolizes. The word “sign,” as it is used here, means any kind of message (usually visual) produced by an intelligent being. For example, when driving on an unfamiliar highway one might see a sign indicating that the road makes several sharp turns one mile ahead. Based on this information, one might argue that the road does indeed make several sharp turns one mile ahead. Because the sign might be misplaced or in error about the turns, the conclusion is only probable. A causal inference is an argument that proceeds from knowledge of a cause to a claim about an effect, or, conversely, from knowledge of an effect to a claim about a cause. For example, from the knowledge that a bottle of wine had been accidentally left in the freezer overnight, someone might conclude that it had frozen (cause to effect). Conversely, after tasting a piece of chicken and finding it dry and tough, one might conclude that it had been overcooked (effect to cause). Because specific instances of cause and effect can never be known with absolute certainty, one may usually interpret such arguments as inductive. Further Considerations It should be noted that the various subspecies of inductive arguments listed here are not intended to be mutually exclusive. Overlaps can and do occur. For example, many causal inferences that proceed from cause to effect also qualify as predictions. The purpose of this survey is not to demarcate in precise terms the various forms of induction but rather to provide guidelines for distinguishing induction from deduction. Keeping this in mind, we should take care not to confuse arguments in geometry, which are always deductive, with arguments from analogy or inductive generalizations. For example, an argument concluding that a triangle has a certain attribute (such as a right angle) because another triangle, with which it is congruent, also has that attribute might be mistaken for an argument from analogy. Similarly, an argument that concludes that all triangles have a certain attribute (such as angles totaling two right angles) because any particular triangle has that attribute might be mistaken for an inductive generalization. Arguments such as these, however, are always deductive, because the conclusion follows necessarily and with complete certainty from the premises. One broad classification of arguments not listed in this survey is scientific arguments. Arguments that occur in science can be either inductive or deductive, depending on the circumstances. In general, arguments aimed at the discovery of a law of nature are usually considered inductive. Suppose, for example, that we want to discover a law that governs the time required for a falling body to strike the earth. We drop bodies of various weights from various heights and measure the time it takes them to fall. Comparing our measurements, we notice that the time is approximately proportional to the square root of the distance. From this we conclude that the time required for anybody to fall is proportional to the square root of the distance through which it falls. Such an argument is best interpreted as an inductive generalization. Another type of argument that occurs in science has to do with the application of known laws to specific circumstances. Scientific laws are widely considered to be generalizations that hold for all times and all places. As so understood, their application to a specific situation is always deductive, even though it might relate to the future. Suppose, for example, that we want to apply Boyle’s law for ideal gases to a container of gas in our laboratory. Boyle’s law states that the pressure exerted by a gas on the walls of its container is inversely proportional to the volume. Applying this law, we conclude that when we reduce the volume of our laboratory sample by half, the pressure will double. This application of Boyle’s law is deductive, even though it pertains to the future. A final point needs to be made about the distinction between inductive and deductive arguments. There is a tradition extending back to the time of Aristotle that holds that inductive arguments are those that proceed from the particular to the general, while deductive arguments are those that proceed from the general to the particular. (A particular statement is one that makes a claim about one or more particular members of a class, while a general statement makes a claim about all the members of a class.) It is true, of course, that many inductive and deductive arguments do work in this way; but this fact should not be used as a criterion for distinguishing induction from deduction. As a matter of fact, there are deductive arguments that proceed from the general to the general, from the particular to the particular, and from the particular to the general, as well as from the general to the particular; and there are inductive arguments that do the same. For example, here is a deductive argument that proceeds from the particular to the general: Three is a prime number. Five is a prime number. Seven is a prime number. Therefore, all odd numbers between two and eight are prime numbers. And here is one that proceeds from the particular to the particular: Gabriel is a wolf. Gabriel has a tail. Therefore, Gabriel’s tail is the tail of a wolf. Bro. Joerell P. Estillore Lesson 3: Deduction and Induction SHS-Ateneo de Cebu CEP-Logic Here is an inductive argument that proceeds from the general to the particular: All emeralds previously found have been green. Therefore, the next emerald to be found will be green. The other varieties are easy to construct. Thus, the progression from particular to general, and vice versa, cannot be used as a criterion for distinguishing induction from deduction. Answer the following questions: 1. Briefly discuss the similarities and differences between deductive and inductive arguments. Support your discussion with your own examples. 2. Explain how we can distinguish deductive arguments from inductive arguments, and vice versa. In your class notebook, write a journal entry about the importance of evaluate the strength of the argument’s inferential claim—how strongly the conclusion is claimed to follow from the premises. Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i.e., the presence of indicator words, the nature of the inferential link between premises and conclusion, or the character or form of argumentation). 1. Because triangle A is congruent with triangle B, and triangle A is isosceles, it follows that triangle B is isosceles. 2. No e-mail messages are eloquent creations. Some love letters are eloquent creations. Therefore, some love letters are not e-mail messages. Bro. Joerell P. Estillore Lesson 3: Deduction and Induction SHS-Ateneo de Cebu CEP-Logic 3. Paying off terrorists in exchange for hostages is not a wise policy since such action will only lead them to take more hostages in the future. 4. The Wall Street Journal has an article on the new banking regulations. The Financial Times, like the Wall Street Journal, is a highly respected business publication. Therefore, the Financial Times probably also has an article on the new banking regulations. NOTE WELL: PUT YOUR ANSWER IN THE ASSIGNMENT THAT WILL BE POSTED IN OUR TEAM. DO NOT PUT YOUR ANSWER HERE. RUBRIC FOR GRADING Advanced – Main ideas are holistically and properly related to the lesson with no error in logic or flow of ideas. Proficient– Main ideas are adequately related to the lesson or have minor errors in logic or flow of ideas. Developing– Main ideas are related minimally to the lesson or have some errors in logic, flow of ideas, or grammar. Intervention required– Main ideas have weak or irrelevant focus on the lesson and are difficult to follow in logic, flow of ideas, or grammar. Bro. Joerell P. Estillore