The most important concepts to understand in Formal Logic is the concept of validity. All logic students should memorize and come to understand these three different (but related) ways of defining validity:
“The worse your logic, the more interesting the results you obtain from it.” – Lord Russell
“Against logic there is no armor like ignorance.” – Laurence J. Peter
“You can’t be very good at philosophy if you’re very bad at logic” – Peter Kreeft
Some time ago on this blog, I challenged my readers to translate this syllogism from Quintilian into standard categorical form, and to determine its validity:
“Virtue is the only thing that is good, for that alone is good which no one can put to a bad use: but no one can make a bad use of virtue.”
Let’s see what we can do. The word “for” is a premise indicator, so the conclusion is the first statement. Re-arranging into standard order, we get: Continue reading Syllogism challenge
Mr. Nance,
On the Square of Opposition, the particular affirmative is “Some S is P” and the particular negative is “Some S is not P.” Why does the universal “All S is P” not have the contrary universal “All S is not P”? Why instead do you use “No S is P”?
Just curious! Continue reading Logic and Biblical Ambiguities
Mr. Nance,
In the Introductory Logic video Lesson 12, you write this sentence on the white board: “Some days the sun just doesn’t shine.” The first rule to put this sentence into the proper form states: Identify and write the complete subject. You identified “days” as the subject. Essentials taught me to ask, “Who or what does (not) shine?” Doesn’t that mean that “the sun” is the subject? How imperative is it that the subject be identified correctly? Continue reading Categorical form & getting the subject right
Mr. Nance,
In the Intro Logic course, the answer guide shows that a past tense statement, “God created heaven and earth” was converted to the present tense, “God is the Creator of heaven and earth.” I clearly see that the subject of the sentence (God) is like no other subject…is that why? Or would you have done this with a similar sentence? “Jane Austen authored Pride and Prejudice.” –> “Jane Austen is the author of Pride and Prejudice.” (I am wondering if you have an exception to the Caution printed on the previous page.) Thank you!
Mr. Nance,
1. Where does the A E I O come from for the four categorical statement types?
These are simply the first four vowels in English. I have been told that A and I come from the Latin “Affirmo” and the E and O from the Latin “Nego,” but I cannot confirm this.
2. If two statements say “Red is my favorite color” and “All my shirts are red” is their relationship independence or implication? Continue reading On Relationships Between Statements
![bible_with_books_med[1]](https://i0.wp.com/logiccurriculum.com/wp-content/uploads/2015/07/bible_with_books_med1.jpg)
Logic students regularly struggle with immediate inferences, and (as is often the case when students have more than usual difficulty) they can begin to wax philosophical about the value of learning this particular concept. As an initial response to such students, I want to give a couple of examples of immediate inferences used in the Bible. Two equivalent immediate inferences for categorical statements are obverse and contrapositive.
Obverse changes the quality of the statement, and takes the complement of the predicate. It gives equivalent statements for all four forms of categorical statement:
All S is P ≡ No S is non-P
No S is P ≡ All S is non-P
Some S is P ≡ Some S is not non-P
Some S is not P ≡ Some S is non-P
Jesus uses the obverse in Mark 2:22, where He says,
“No one pours new wine into old wineskins. Otherwise, the wine will burst the skins, and both the wine and the wineskins will be ruined. No, they pour new wine into new wineskins.”
Contrapositive switches the subject and predicate of the statement, and changes both to their complements. It gives equivalent statements for universal affirmative and particular negatives:
All S is P ≡ All non-P is non-S
Some S is not P ≡ Some non-P is not non-S
Paul uses something like the contrapositive in Romans 11:6 when he argues,
“And if by grace, then it is no longer of works; otherwise grace is no longer grace. But if it is of works, then it is no longer grace; otherwise work is no longer work.”
This is more obviously the contrapositive when the conditional statements are translated into categorical form.
All Christian parents want their children to know how to learn something new, to understand the world around them, and to have insight into the character of its Creator. One way they can help their sons and daughters along this educational path is to teach them propositional logic.
Propositional (or symbolic) logic provides powerful methods by which students can learn how to learn, beyond the methods of categorical logic. Tools such as formal proofs of validity teach students how to reason in a straight line, while providing them with standards and methods by which they can judge and correct their own arguments, and analyze the arguments of others. The study of propositional logic can help them understand the history of thought, while giving them insight into the modern digital age. Many Christian thinkers have found propositional logic to be interesting and valuable, and have contended that an inquiry into modern logic can aid us in understanding the nature and character of the God of the Bible.
To see a good example, watch this excerpt from my video lessons on truth tables:
Propositional Logic