Can more than one conditional proof be used in an argument?
Briefly yes, it is permissible to use C.P. more than once in a given formal proof. But either one must be “nested” fully within the other, or they must be completely distinct. They cannot “overlap.” Here is an example for an interesting argument: Continue reading Repeated Conditional Proof
In his Institutes of Oratory, the rhetorician Quintilian, in discussing the value of learning logic, mentions the “horn” problem, which evidently was this tricky syllogism:
“You have what you have not lost. You have not lost horns. Therefore you have horns.”
Initially I supposed that this was invalid, until I put it into categorical form:
All things you have not lost are things you have.
All horns are things you have not lost.
∴ All horns are things you have.
This is an AAA-1, and is thus valid. It could just as readily be written as modus ponens: Continue reading Watch your assumptions!
“You can only find truth with logic if you have already found truth without it.” – G. K. Chesterton
So, you have entered Unit 4! In this unit, you will be applying many of the tools you have learned up to this point to real-life arguments in written texts, texts that present what I call “chains of reasoning.”
This is a tough section, because we are no longer working with artificial arguments meant to teach the tools, but arguments that have been written in actual books from men like the philosopher Boethius, the Apostle Paul, Augustine, Martin Luther, and others.
Here are a few things you will want to note from the DVD for this lesson.
Some people believe that Jesus’ command to love your enemies is an absurd requirement because they are defining love to mean ‘believe the other to be a nice person,’ when in fact they know their enemies to be quite wicked and depraved. But biblically, love means ‘to treat the other person lawfully from the heart,’ which is to be our behavior toward all men. If this definition is made clear, the people may still think that the command is impossible, but at least they no longer should see it as absurd.
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
I recently read a Tweet from a friend quoting a respected theologian, saying, “Definitions are never a matter of life or death.” While given the explanatory context I agree with the claim, taken out of context (a perennial hazard of Twitter, and social media in general) this could be dangerously misunderstood.
For example, how does one define a person? Is an unborn fetus a person? As such, do they have a God-given right to life? Consequently, should elective abortion be defined as a species of murder? Or consider the key terms fought over in the Civil War. When it was declared that “all men are created equal,” how should man be defined? Was a slave property? Which is correct grammar: the United States is, or the United States are?
I discuss this issue in this 30-second clip from my Introductory Logic video, Lesson 1, on “The Purposes of Defining Terms.”
My point is that definitions are not purely academic. God cares how we define our terms. And sometimes it is a manner of life or death.
Hi Josiah,
Can you use simplification in this way?
(P • Q) ⊃ R
Therefore P ⊃ R
In other words can you simplify the statement P and Q even though it is the antecedent to the conditional?
Thank you!!!!
Continue reading Simplification in Parentheses
And yet the validity of logical sequences is not a thing devised by men, but is observed and noted by them that they may be able to learn and teach it; for it exists eternally in the reason of things, and has its origin with God.
– On Christian Doctrine II.32
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
