While teaching through Exercise 25, I was challenging my students on problem 3 to identify every possible syllogism making the fallacies of Two negative premises, and negative premise and affirmative conclusion, and no other fallacies. I had original concluded that there were 32 such forms: EEA, EEI, EOA, EOI, OEA, OEI, OOA, OOI — all four figures of each.
Suddenly one of my students said, “But don’t some of those forms make others fallacies as well?” I realized he was right, and together we followed this rabbit trail, carefully working through the question to determine that, in fact, six of these forms do make additional fallacies: EOA-1, 2 and OOA-1, 2 have an Illicit Minor, and OOA-3, OOI-3 have an Undistributed Middle. Consequently, I have corrected my previous post on this topic.
I have some truly impressive logic students!
My question has to do with Lesson 24. Exercise 22 has the students do a challenge, testing the validity of all 256 forms. I understand it’s to practice counterexample. Is there another reason not to put this challenge after lesson 26 after they’ve learned all the rules? (Which I think would make it easier.) Continue reading Counterexample challenge
Introductory Logic formally teaches two methods for determining the validity of a syllogism: rules of validity, and counterexamples. The rule that tells us that any AAO-4 syllogism is invalid is this: “A valid syllogism cannot have two affirmative premises and a negative conclusion.” But can we show the invalidity of AAO-4 with a counterexample? Here is the schema:
All P is M
All M is S
∴ Some S is not P
I contend that there is only one way to write a counterexample for a syllogism of that form. I challenge you to write a counterexample to AAO-4. Remember that a counterexample must be the same form, and have true premises and a false conclusion.
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
Lesson 12 is the final installment in this Old Western Culture video course on The Romans, unit 1, and it has been a grand adventure. Wes Callihan has taken us through the entire Aeneid, greatest of the Roman epics, and led us through large portions of Ovid’s mythical tales of Metamorphoses. In this final lesson we are introduced to the last three of the Roman epics, connected (oddly enough) by the theme of impiety: De Rerum Natura by Lucretius, Pharsalia by Lucan, and Thebaid by Statius. Continue reading Great Books Challenge Lesson 12
Ovid’s Metamorphoses is an encyclopedia of about 250 Greek and Roman myths from Creation to Julius Caesar, including Pyramus and Thisbe, Arachne, the Minotaur’s labyrinth, Icarus, Hercules, Pygmalion, Orpheus and Eurydice, King Midas, and more you will probably recognize. These otherwise independent stories are united by Ovid’s theme of change, along with other interesting interweavings, such as Daedalus being both the architect hired by Minos to hide the Minotaur and the engineer who designed the wings of wax and feathers that he and his son Icarus use to escape Crete.
Wes Callihan brings to light dozens of fascinating insights, finds connections with biblical events, and demonstrates the value to Christian students of understanding this ancient epic, among others. For example, in Ovid, man is made in the image of God to rule over the earth. Ovid’s version of the great Flood, following the ages of gold, silver, and bronze, and the violent age of iron, has surprising parallels and differences with scriptures story of Noah. The only survivors, Deucalion and his wife Pyrrha, survive on a small boat, land on a mountain, but repopulate the world by throwing rocks behind them, which then grow into people. This demonstrates both the historicity and superiority of the biblical account.
As someone who enjoys science, I was particularly intrigued by three further associations made by Wes Callihan. Continue reading Great Books Challenge Lesson 10-11
This lesson completes Vergil’s epic classic the Aeneid, with books eleven and twelve. These books are battle filled page turners, with gripping side tales and a satisfying conclusion. The side tales are sometimes tragic, as when King Evander mourns the loss of Pallas: “I, in living, have undone the fate of fathers: I survive my son”; maddeningly frustrating, as when Diomedes’ suggestion of a truce is received by all but Turnus: “I shall go bold against Aeneas”; or adventurous fun, as the story of Camilla, the warrior maiden: “At the center of the struggle, like an Amazon…”
Wes Callihan has noted many parallels between Vergil and Homer (modified to match the Roman mindset), as well as Vergil and the Bible. These parallels have been insightful and educational, and have added to the pleasure of the reading. And as Vergil imitated Homer, so later writers, such as Dante, used matter from Vergil. Continue reading Great Books Challenge Lesson 9
These lessons include books seven through ten of the Aeneid. We are now into the second half of this epic, which is as much like the Iliad as the first half was like the Odyssey: famous warriors boasting and battling until they fall, their armor ringing around them, while the gods watch and interfere, seeking their own advantage. The parallels between the books that I noted myself or that Wes Callihan reveals help make these lessons truly intriguing. Let me note a few. Continue reading Great Books Challenge Lessons 7-8
Books four through six of the Aeneid are some of the most fascinating and memorable of this epic tale! In these chapters we read of the tragedy of Dido, the funeral games of Achises, and the journey of Aeneas into the underworld. Wes Callihan once again brings to light many practical lessons and interesting insights from these stories, and I look forward to each new lesson from Old Western Culture, wondering what I will learn next.
Continue reading Great Books Challenge Lessons 5-6