Question from Intermediate Logic, Lesson 7, Exercise 7a: 1-6:
Is this exercise to help students visually see a tautology vs. a self contradiction? Or do they need to write out truth tables to find the truth-value?
The purpose of this exercise is to train students to understand the truth-functionality of compound propositions; that is, so they can see how the truth value of the proposition depends on the truth value of the component parts and the logical operators. Part of that is recognizing tautologies. But yes, I have students create truth tables to solve some of these.
Note that the number of rows in the truth table only depends on the number of variables (with unknown truth value). This means that the truth table for #3, for example, must be four rows long (two variables, P and Q), but #6 need only be two rows long (one variable, P). The other truth values will be rows of T (for A, B) or rows of F (for X, Y). For example, a truth table for #2 would start like this:
(P ⊃ P) ⊃ ~A
T T FT
F F FT
You would then finish the truth values under the conditionals. If done correctly, the final column (under the second horseshoe) is FF.
It has been maintained that Martin Luther King Jr. was the last American orator to use the grand level of style appropriately. In my rhetoric text Fitting Words, I define the grand level as that “in which the stylistic devices are intended to be dramatic, apparent, and impressive. Its purpose is not only to inform the mind and persuade the will, but to grip the emotions and heart. It is most appropriate for speeches delivered on formal occasions.”
Anyone who has listened to (or at least read) some of his speeches – especially his most famous “I Have a Dream” – is aware that MLK uses stylistic devices in a dramatic and impressive way, a way that can grip the mind and heart of his hearers. Here are some quotes from my text which shows his skill in using the grand level of style. Continue reading King’s Grand Style
Logic is a symbolic language. It is also a very precise language, every term well defined and unambiguous. English, on the other hand, is a somewhat ambiguous language. The same word can have multiple meanings: a pen is a writing utensil and an enclosure for livestock.
One key term in logic is the disjunction “or”. In English, the word “or” has two meanings. The first is the inclusive or, which means basically “this, or that, or both.” If someone said, “Most Bible students read the King James or the NIV,” this statement is still true for a student who reads both the King James and the NIV. The “or” includes both possibilities.
The exclusive or basically means “this or that, but not both.” This is the sense used in this classic argument for the deity of Christ: “Jesus was either God or a bad man.” If Jesus was God, then He was not a bad man. If He was a bad man, then He was not God.
Symbolic logic deals with the ambiguous “or” this way. The logical operator OR is taken in the inclusive sense. “A or B” is true if A is true, B is true, or both A and B are true. To represent the exclusive or, we use the compound proposition “A or B, but not both A and B.”
My student has a question on Exercise 4 number 14. Her answer for was ~C ⊃ S instead of S ⊃ ~C. Can the statements “I will go swimming only if the water is not cold” be considered logically equivalent to “If the water is not cold, I will go swimming”?
Also, how can I explain the difference between “If the water is not cold I will go swimming” and “I will go swimming unless the water is cold”?
Thank you! Continue reading Question about Conditionals
Fitting Words: Classical Rhetoric for the Christian Student is arranged around the five canons of rhetoric: invention, arrangement, style, memory, and delivery. In the first half of this course, after laying the Christian philosophical and historical foundation of the subject, we concentrated on constructing the first two canons: invention, and arrangement (primarily the six parts of a discourse). We also studied the three artistic modes of persuasion: ethos, pathos, and logos (including the special lines of argument: forensic, political, and ceremonial oratory).
In the second half of this course, we will continue to learn about logos by constructing general lines of argument. In Unit 5 we will review the applicable parts of logic: defining terms, determining truth, employing maxims, and using inductive and deductive arguments. We will also considering the destruction of our opponents’ arguments in refutation, including identifying informal fallacies.
In Unit 6 we will learn about Style: understanding the nature of the soul, speaking with clarity and elegance, the levels of style, and figures of speech and thought. In Unit 7 we will learn the essential skills of memory and delivery.
We will continue to see examples of all of these concepts in historical and biblical speeches and other discourse. Click HERE to learn more.
Logic gives us standards and methods by which valid reasoning can be distinguished from invalid reasoning. It teaches students to think in a straight line, and to justify each step of their thought. Intermediate Logic does this using a symbolic language to represent the reasoning inherent in the language of argument. It is more flexible than syllogistic logic, and can thus apply to more real-life arguments.
Intermediate Logic Unit One teaches the powerful method of truth tables to determine the validity of propositional arguments. Unit Two takes these methods and teaches students how to deduce a conclusion from a set of premises, so they are able not only to show that an argument is valid, but also prove why it is valid. Unit Three teaches these same concepts using the modern method of truth trees. Unit Four applies these methods to the analysis of real-life arguments from 1 Corinthians 15, Hebrews 2, Boethius’ The Consolation of Philosophy, Augustine’s City of God, and more (including a scene from the movie “Get Smart”). Unit Five teaches the fascinating application of these methods to the logic of digital electronics.
Today marks the 75th anniversary of one of the most significant orations in American history: Franklin D. Roosevelt’s Declaration of War Upon Japan. The speech is significant for several reasons. Continue reading Remembering a Speech – 75 Years Later
Comic strips are a great place to find examples of informal fallacies. It seems that we tend to find improper reasoning funny. In the “Peanuts” comic strip below, Lucy is ad baculum incarnate.
Note that the fallacy is not really made by Lucy making the threat, but by Charlie Brown, who is convinced by her “argument.”
Here is another example, where Lucy persuades Linus to memorize his lines using “five good reasons”: Continue reading Fallacies in Comics
Would you like to be a fly on the wall in my logic class? Want to improve your understanding and/or teaching of logic by watching me teach and interact with my students, discussing the lesson after the class, and having the recorded class sessions available? If so, click HERE to audit Intermediate Logic for the 2017 school year!
What’s included for Auditors? First, you have access to all the live classes. During the discussion, you will not be called upon as I do with my regular students. You are free to watch in the background by muting your mic and camera, but you also have the option of appearing to ask a question or make a comment if you’d like.
After the regular class time has ended, students leave the virtual classroom while auditors are invited to stick around for a few minutes to ask “Teacher Questions”! This is when you would have me all to yourselves as teachers. Turn on your webcams and mics, and discuss the lesson, teaching logic in general, or whatever questions you might have.
We will meet together live for online recitations Monday/Thursday from 8:00-9:30 AM (PST), or Tuesday/Friday from 8:00-9:30 AM (PST). The spring semester starts January 5/6, 2017, and goes to May 18/19, with a Winter Break in mid-February and an Easter Break in mid-April.
I hope to see you there!
As I teach for the first time through Fitting Words: Classical Rhetoric for the Christian Student, I am pleased with what my students are producing.
We have been learning about forensic (or judicial) oratory, including the definition of wrongdoing, the elements of proving wrong, the state of mind of wrongdoers, non-technical modes of persuasion, and more. The most recent assignment was this:
Here is the forensic speech of one of my students, Daniel Seifert, defending Bucky Barnes (from “Captain America: The Winter Soldier”) of the alleged murder of Tony Stark’s parents and others.