Logic: Syllogisms and Enthymemes Bridge between invention & arrangement Claims with reasons E. Wanczuk, adapted from: Carbone, Paula. AP Institute. California State University, San Marcos. CSUSM, San Marcos, CA. July 2009. Lecture. Syllogisms are considered ultimate logic, or logos, but also a way of structuring an argument

Inductive Reasoning Begins with particular facts and draws generalizations or conclusions from them. Sherlock Holmes Examples: The Scientific Method Pythagorean Theorem: Pythagoras examined a number of right triangles and observed the unvarying ratio of the sides and angles; from these observations of specific triangles, he induced a general formula.

Deductive Reasoning Uses a generalization to analyze a new particular situation. Examples: Pythagorean Theorem: in your math class, you may use deductive reasoning by applying Pythagoras’s general formula to specific triangles you encounter in math problems.

Syllogism MAJOR PREMISE: A = B A general principle or rule Shows formal logic; deductive reasoning No room for argument; not persuasively interesting because it cannot be challenged. If logical, it is accepted as fact. Lacks exigency. MAJOR PREMISE: A = B A general principle or rule MINOR PREMISE: C = A Introduction of new particular event; verifiable by specific evidence; usually a statement of fact CLAIM/CONCLUSION: C = B Conclusion, linking B to C Paula M. Carbone

Categorical Syllogism Example Usually begins with words such as “all” or “none” Includes the entire category—makes a categorical statement. MAJOR PREMISE: All men are mortal. MINOR PREMISE: Socrates is a man. CLAIM/CONCLUSION: Socrates is mortal. Covel, Robert. “The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement.” English Journal 99:6 (2010): 47-50. Print.

Conditional Syllogisms: “If - then” Example from Writing Arguments: MAJOR PREMISE: Persons who lack the strength and endurance needed for combat duty should be barred from combat units. MINOR PREMISE: Women are persons who lack the strength and endurance needed for combat duty. CLAIM: Women should be barred from combat units. If a person lack the strength and endurance needed for combat duty, then that person should be barred from combat units. Paula M. Carbone

Conditional Syllogism If you do not study, you will not pass. Bill did not study. Then Bill did not pass. Covel, Robert. “The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement.” English Journal 99:6 (2010): 47-50. Print.

Alternative Syllogism Expressed in terms of “either-or” Either you study, or you will be a failure in life. John studied. John was not a failure in life. Covel, Robert. “The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement.” English Journal 99.6 (2010): 47-50. Print.

Truth vs. Validity Truth = the accuracy of the conclusion Validity = method used to arrive at the conclusion A process may be correct, but the solution may be flawed. A syllogism may be true without being valid. Covel, Robert. “The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement.” English Journal 99:6 (2010): 47-50. Print.

Conditions for Validity Must follow proper order of steps: AB, CA, CB Major premise must be expressed in universal terms. If one premise is expressed in negative terms, the conclusion must be negative. If both premises are negative, no conclusion is possible (invalid). Covel, Robert. “The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement.” English Journal 99:6 (2010) 47-50. Print.

Homework: Read and write down the following syllogism by Ambrose Bierce and explain in one perfectly constructed paragraph why it IS or IS NOT valid. Be specific, referring to your PPT notes and the syllogism to explain your position. Major Premise: Sixty men can do a piece of work sixty times as quickly as one man. Minor Premise: One man can dig a posthole in sixty seconds, therefore Conclusion: Sixty men can dig a posthole in one second. Paula M. Carbone

Unstated Assumption A claim with reasons depends on logical completeness by relying on an unstated assumption. The unstated assumption is usually the major premise. Often, the unstated assumption needs to be supported in an argument. Formulating the major premise to check arguments helps to indicate the major assumption the audience has to accept for the argument to be persuasive. CLAIM: Women should be barred from military combat units. STATED REASON: Because women lack the strength and endurance needed for combat duty. UNSTATED ASSUMPTION: Persons who lack the strength and endurance needed for combat duty should be barred from combat units. For logical completeness, this claim with reason depends upon the audience accepting the unstated assumption. Paula M. Carbone

The Enthymeme A compressed syllogism, expressing a syllogism in a single sentence; a syllogism with part of the argument presumed. For Example: Women should be barred from combat units because women in combat units will reduce the army’s fighting strength. Paula M. Carbone

Syllogism vs. Enthymeme Women should be barred from combat units because women in combat units will reduce the army’s fighting strength. Major Premise: Minor Premise: Conclusion: Paula M. Carbone

The enthymeme as syllogism MAJOR PREMISE: If a person lacks the strength and endurance needed for combat duty, then that person should be barred from combat units. MINOR PREMISE: Women are persons who lack the strength and endurance needed for combat duty. CLAIM: Women should be barred from combat units. A = person lacks strength and endurance B = barred from combat units C = women Paula M. Carbone

Syllogism vs. Enthymeme Major Premise: Authors who use too much detail ruin their stores. Minor Premise: Orwell does not go into too much detail in his Animal Farm. Conclusion: Therefore, Orwell did not ruin Animal Farm. George Orwell did not ruin Animal Farm by going into to much detail. Covel, Robert. “The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement.” English Journal 99:6 (2010): 47-50. Print.

Practice in Analyzing "I can urge them to disobey segregation ordinances, for they are morally wrong” MLK, Jr. Letter from a Birmingham Jail: discussing morally just and unjust laws. What is the unspoken assumption? Write as syllogism. Laws that are morally wrong should be disobeyed Segregation ordinances are morally wrong Segregation ordinances should be disobeyed Can this stand on its own? Is the major premise going to be accepted by everyone? He provides amplification in the form of backing: before this statement (in a periodic paragraph) used testimony, examples, and other enthymemes—see next slide Paula M. Carbone

Now, what is the difference between the two Now, what is the difference between the two?  How does one determine whether a law is just or unjust?  A just law is a man-made code that squares with the moral law or the law of God.  An unjust law is a code that is out of harmony with the moral law.  To put it in the terms of St. Thomas Aquinas: An unjust law is a law that is not rooted in eternal law and natural law.  Any law that uplifts human personality is just.  Any law that degrades human personality is unjust.  All segregation statutes are unjust because segregation distorts the soul and damages the personality.  It gives the segregator a false sense of superiority and the segregated a false sense of inferiority.  Segregation, to use the terminology of the Jewish philosopher Martin Buber, substitutes an "I-it" relationship for an "I-thou" relationship and ends up relegating persons to the status of things.  Hence segregation is not only politically, economically and sociologically unsound, it is morally wrong and sinful.  Paul Tillich has said that sin is separation.  Is not segregation an existential expression of man's tragic separation, his awful estrangement, his terrible sinfulness?  Thus it is that I can urge men to obey the 1954 decision of the Supreme Court [which outlaws segregation in the public schools], for it is morally right; and I can urge them to disobey segregation ordinances, for they are morally wrong. Rhetorical questions serve to close the gap between him and his audience, whom he knows to be opposed to him Definition employed to clarify his stance, that his actions, while breaking a law and leading to his imprisonment, are just because the law is unjust Enthymemes work as argumentative claims Syllogism: “A law that degrades human personality is unjust” - MAJOR PREMISE Segregation degrades the human personality. Therefore segregation is an unjust law. Note the backing, amplification, provided - use of aquinas, buber, tillich Two authorities pillars of Christian church, St. Augustine in previous paragraph, not shown, and Aquinas Draws of examples, Aquinas, and his definition; amplifies to bring definition back to support his stance Buber: applies segregation to objectification, extending his argument that segregation not only illegal, and unsound, but morally wrong Tillich: further supports his claim that segregation is a sin. Tilich’s definition of sin, and applies to segregation Paula M. Carbone

Limitations of Formal Logic in AP English Language Only deals with structure of argument, not with the inherent logic or acceptance of assumptions Nobody is perfect. I am nobody. Therefore, I am perfect. The syllogism is untrue, but valid. Please explain. Premise untrue, so illogical but correctly structured Formal logic of limited value in helping students to establish the truth of their claims Therefore, in writing arguments, looking for different ways to structure an argument has led to Toulmin as favored in AP Paula M. Carbone