Logic students sometimes struggle with understanding and remembering immediate inferences. The more opportunities they have to see them used, the more likely they are to grasp them. Consequently, I want to give some examples of immediate inferences used in the Bible. Two equivalent immediate inferences for categorical statements are obverse and contrapositive. Continue reading Some Uses of Immediate Inference in Scripture
Teaching students how to translate syllogisms into standard categorical form occupies several lessons in Introductory Logic. Lessons 11 and 12 explain how to translate categorical statements into standard form, which is then emphasized while learning about the Square of Opposition in Lessons 13-18. Lesson 19 teaches students how to distinguish premises and conclusions, in part so that in Lesson 20 they will understand how to identify the major and minor premises, so that they may know how to arrange a syllogism in standard order. Finally, Lessons 21 and 22 teach them how to identify the syllogism form using mood and figure. All this occurs before the students begin to learn how to determine the validity of a syllogism. Continue reading Why Standard Form?
Lesson 10 of Introductory Logic discusses the possibility that two statements delivered by different people may seem to be inconsistent, but upon further examination turn out to actually be consistent. We can call these seeming disagreements, and they can happen in one of two ways. Continue reading A Seeming Disagreement
I teach logic online. In addition to my regular logic students I have several Classical Conversations tutors who audit my logic course. After I finish the lesson and my students leave, the auditors join the class live, turning on camera and mic, and we discuss the lesson. I appreciate these discussions, because I often learn as much from them as they do from me. Continue reading I Know London is the Capital of France
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The classical Christian school movement is seeking to revive a form of education that helped shape some the greatest minds of western civilization. But how do we know that our father’s were trained according to the Trivium? One delightful demonstration of this is William Shakespeare’s frequent and detailed use of the liberal arts of grammar, logic and rhetoric in his plays and poems, a use thoroughly identified by Sister Miriam Joseph in her book Shakespeare’s Use of the Arts of Language. In this well-researched book, she argues that Shakespeare’s application of formal logic is evidenced in his use of definition, genus and species, syllogistic vocabulary, applied syllogisms, enthymemes, and more. Let me give some of her clearer examples. Continue reading Shakespeare’s Use of the Liberal Arts: Logic
A good introductory logic course will discuss the importance of defining terms in any argument. One clear demonstration of using definition in argument is Martin Luther King Jr.’s “Letter from Birmingham Jail,” a letter which King directed at Christian pastors in Alabama in 1963 defending his campaign of nonviolent direct action. Continue reading Defining Terms from Birmingham Jail
The most recent edition of Intermediate Logic has two new sections, Unit 4 and Unit 5. I’ve included these new units in the text because I wanted to answer the important question, “What are some practical applications of the tools that we are learning about, i.e. truth tables, formal proofs, and truth trees?” I believe that the applications of these tools in the new units will deepen and solidify student understanding of the concepts that, up to that point, have been largely theoretical.
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Unit 4 (Lesson 28) gives logic students the opportunity to analyze chains of reasoning. The arguments to be analyzed are taken from Boethius’s The Consolation of Philosophy, the Apostle Paul’s argument proving the general resurrection of the dead in I Corinthians 15, and a section on angelic will from Augustine’s City of God. I work through this last one in full on the DVD.
An exercise not in the text that may be beneficial would be to have students write their own chains of reasoning, arguing for a conclusion of their choosing, in imitation of these authors. Their arguments must include at least one NOT, AND, and OR, and two IF/THENs. Tell them to include a truth-table or truth-tree analysis of their own chain of reasoning.
Unit 5 (Lessons 29-40) teaches students how to apply what they have learned to the fascinating topic of Digital Logic. Do not be intimidated by the 0’s, 1’s, and new symbols. It’s just the same old true, false, and logical operators that they have already learned about presented in a new way. Students often find this a fun application of what they have learned. It helps them to understand the electronic world around them, and it shows that the tools that they have learned apply not only to philosophy and theology, but to digital clocks and iPhones!
Formal proofs are hard, like many other things worth learning!
In this video, I talk through the difficulties of formal proofs of validity, and why it’s worth enduring the hardship to learn them.
YouTube version HERE.
Symbolic logic has five standard logical operators, each of which has a standard translation in English:
negation is “not”
conjunction is “and”
disjunction is “or”
conditional is “if/then”
biconditional is “if and only if”
While the translations of the first four logical operators are frequent in English, the phrase “if and only if” is used very infrequently, and then only occasionally among mathematicians, philosophers, and lawyers.
For instance, while it is easy to find hundreds of nots, ands, ors, and if/thens in the Bible, the phrase “if and only if” is completely absent. However, for those who look carefully, biconditional reasoning is used several times in scripture. Keeping in mind that p if and only if q means if p then q and if q then p — and remembering other equivalences we have learned — the following verses all reflect biconditional reasoning: Continue reading The Biblical Biconditional
One of the more practical parts of Introductory Logic is Lesson 31 on Hypothetical Syllogisms. Hypothetical syllogisms of all kinds are a very common form of reasoning, so we should not only be able to identify them quickly, but we should also learn to use the valid forms confidently.
A hypothetical statement is an “if/then” statement, such as this one: Continue reading Help with Hypotheticals