• Logic and Writing

     

    USES OF LOGIC

    Logic means clear and orderly thought. In writing, logic is necessary to support an argument in any kind of persuasion, in answering an essay question, and in supplying evidence to support an opinion. There are two kinds of logical thought: deductive reasoning and inductive reasoning. We will also examine fallacies, or errors in logical thinking.

     

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    DEDUCTIVE REASONING

    Deductive reasoning begins with a generalization, adds a related statement, and ends with a conclusion that is necessarily drawn from the two statements.

    The three-statement argument in deductive reasoning is called a syllogism. There is a major premise, minor premise, and a conclusion. This is like the introductory paragraph of an essay.

     

         EXAMPLE/VALID:

              Major Premise:     All seniors at Shaw High School must take a course in 

                                          government.

              Minor Premise:     Floyd Bly is a senior at Shaw High School.

              Conclusion:           Floyd Bly must take a course in government.

        

    Truth and Validity

    A syllogism may look like a perfectly good argument, and yet the conclusion may be false. In order for the conclusion to be true, two requirements must be met.

    1. The major premise and the minor premise must both be true.

     

         EXAMPLE/INVALID:  Major Premise:     All red flowers are roses.

                                            Minor Premise:     This geranium is red.

                                            Conclusion:           This geranium is a rose.

     

    NOTE:  You can see immediately that the major premise of the preceding syllogism is false: it is not true that all red flowers are roses.  Therefore, the conclusion drawn from the premises is necessarily false.  You cannot arrive at a true conclusion when one or both of the premises are false.  If you start your essay off with false or inaccurate information, your thesis, and perhaps your entire paper, is illogical and wrong.

     

    2. The argument must be valid - that is, the argument must follow the rules of logic.

       

    NOTE:  One rule of logic is that no conclusion can be drawn unless the major premise states a universal. This means that the major premise must state or imply the words all, every, no, or none. The statement in the major premise must be true of every person or thing that the major premise mentions.

         EXAMPLES:  All suns are stars.

                              No mammals have gills.

                              All insects have six legs.

     

    NOTE:  A statement that contains a limiting word (such as many, most, some, several, few, usually, or sometimes) cannot lead to a valid conclusion, and it is best to avoid them in your writing.  For example, the following non-universal statements cannot be used as either a major or minor premise in a syllogism.

     

         EXAMPLES:  Most commercial breads contain preservatives.

                              Some spiders have four eyes.

                              Professional musicians usually play more than one instrument.

                              Many gothic stories have supernatural elements.

     

    The following syllogism has a non-universal major premise.

         EXAMPLE/INVALID:  Major Premise:  Most freshman take four courses.

                                            Minor Premise:  Julie Sizuki is a freshman

                                            Conclusion:         ?

     

    Both of the premises in the preceding syllogism are true, yet no valid conclusion is possible because the major premise contains the limited word most.  You don’t know whether Julie Sizuki is one of the “most freshmen”   who are taking four courses or one of the other freshmen who are taking three or five courses. 

     

    NOTE: A second rule of logic is that no conclusion can be drawn if the conclusion does not necessarily follow from the two premises. This can occur if the major and minor premises are both true, but are not related or are not necessarily connected.

     

    A second rule of logic is violated in the following syllogism.  Can you tell why the conclusion is not valid?

        

           EXAMPLE/INVALID:

               Major Premise:  All members of the Key Club visited the Allen Nursing Home on  

                                         Saturday.

               Minor Premise:  Jeffrey Michaels visited the Allen Nursing Home on Saturday.

               Conclusion:       Jeffrey Michaels is a member of the Key Club.

     

    The syllogism is not valid because the conclusion does not necessarily follow from the two premises.  Jeffrey Ruiz may have visited the nursing home for any number of reasons.  Perhaps a friend or relative is a patient there, or perhaps he had decided to volunteer some time in the nursing home.  The fact that Jeffrey’s visit coincided with that of the Key Club does not necessarily mean that he is a member of that club.  In fact, no conclusion is possible from the premise as stated. 

     

    Consider the following syllogism:

          EXAMPLE/VALID

               Major Premise:  All members of the Key Club visited the Allen Nursing Home on 

                                         Saturday.

               Minor Premise:   Jeffrey Ruiz is a member of the Key Club.

               Conclusion:         Jeffrey Ruiz visited the Allen Nursing Home on Saturday

                                         morning.

     

    The preceding argument is valid because the conclusion must necessarily be true if the first two premises are true.

     

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    INDUCTIVE REASONING

    In Inductive Reasoning a general conclusion is reached at the end of a process in which a whole series of facts or evidence is gathered and weighed.

    Inductive reasoning, then, moves from specifics to a general statement; in this it is opposite to deductive reasoning, which moves from a general premise to a specific conclusion.  This  resembles the body paragraphs and the concluding paragraph of an essay.

    Most inductive arguments contain a mixture of personal observations, published statistics, and opinions of authorities. Any paper you write that requires evidence uses inductive reasoning.

     

    EXAMPLE:  Assume that Jenny Gagarin was trying to decide how cacti are different from other kinds of plants.  She visited a number of gardening shops, and made the following observations. 

    Evidence:  The ball cactus has spines.

                    The prickly pear cactus has spines.

                    The Indian fig cactus has spines.

                    The crown cactus has spines.

    Her Conclusion:  All cacti have spines.

     

    On the basis of her research, Jenny made the following generalization: “All cacti have spines.”  This is an example of inductive reasoning.  In this example, the evidence is a series of personal observations.  Most sound inductive arguments contain a mixture of personal observations, published statistics, and opinions of authorities.  In the case of the cacti argument, for instance, Jenny should have also checked a reference book or several on-line sources, because not all cacti have spines. 

     

    Working with Evidence

    In inductive reasoning the word population is used to refer to the group or class of things that is being studied.

     

    Jenny’s population is “all cacti.”  Anything in the world – from seventeenth-century English poetry to white dwarf stars to Americans living in Tokyo today – may be the population (or the subject under study) in an inductive argument.

     

    The conclusion in an inductive argument is reached by making what is called an inductive leap. This leap is the process of moving from the specific evidence to a generalization about the entire population. The inductive conclusion is never certain, because you can never study every single member of the population.

     

    The sampling is the number of specific cases of the population that are examined as evidence. In order to ensure a sound inductive argument, two criteria must be met. First, the sampling must be large. Second, the sampling must be random.

     

    When the sampling is too small, as in the case of Jenny’s cacti study, you cannot reach an accurate conclusion.  A too-small sampling is a fallacy called hasty generalization.  If Jenny had gone to examine forty or fifty different kinds of cacti, she would probably have discovered that some species of cacti do not have spines.  Reference works are good sources of support for inductive arguments because they report the results of large samplings.  Second, the sampling must be random.  This ensures the chances of gathering accurate evidence.  People involved in public opinion polls, television ratings, or market research are especially concerned about getting a random sampling of the population.  The evidence in an inductive argument can never be considered as absolute proof that the conclusion is true.

     

      

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    FALLACIES: ERRORS IN LOGIC

    Being aware of common errors that people make in logical thinking will help you evaluate the soundness of arguments you hear and read, as well as those you write. These errors in reasoning, called fallacies, are found in both deductive and inductive arguments.

     

    1. Post Hoc, Ergo Propter Hoc

    This means "After this, therefore because of this." This fallacy occurs when one event is assumed to have caused a second event just because the two events occurred in sequence.

         Example:  President _____ was just elected to office, and now the economy is 

                          improving.  President _____ caused the upswing.

        

    2. Only-Cause fallacy & Only Solution fallacy

    It is an oversimplification; to name a single cause or solution for a complex situation.

         Example:  We could eliminate crime by banning all guns.

         Example:  The American education crisis and low test scores can be resolved by spending

                         more money on schools.

     

    3. Non Sequitur

    This means "It does not follow." Whenever a conclusion does not logically and necessarily follow from the premises or evidence, a non sequitur occurs.

         Example:  All living things require water.  An automobile requires water, so it must be

                          a living thing.

     

    4. Hasty Generalization

    A conclusion based on too small a sampling is called a hasty generalization. Remember that generalizations should only be made after an adequate and random sampling.

         Example:  I ate Mexican food last night, and it was awful.  So, all Mexican food is bad.

     

    5. Stereotype

    A hasty generalization about groups of people is called a stereotype.  Stereotypes are almost always negative.

         Example:  All southerners are hicks.

     

    6. Unreliable Authority (Ipse Dixit)

    "He said it." is the fallacy of citing an unreliable authority, a person who is not an expert in the field being discussed.

          Example:  I don’t need to see a doctor about my sore muscles because my best friend

                           says I can just take some herbal remedies.  

          Example:  Halle Barry the movie star recommends Revlon cosmetics, so their

                           products must be great.

                    

    7. Irrelevance or Distraction

    In any argument, look out for reasons or facts that are not really related to the argument. Such reasons are irrelevant and distracting, and weaken the argument. Often the irrelevance or distraction involves emotional appeals, which have no place in a logical argument.

         Example: A person arguing that there should be more women Supreme Court judges 

         submits the following evidence.  Which two are irrelevant?

         a. the opinion of members of the Supreme Court.

         b. the opinion of her family.

         c. the present number of women and men holding positions as federal jobs.

         d. the present number of women lawyers and men lawyers in the nation as a whole.

         e. the percentage of women judges on various state, county, and local levels.

         f. biographical data about women who have served as a federal judge.

     

         b and f  have no place in the argument and offer no sound relevant opinion or sound 

         and supportive evidence.