Skip to content

Category: course

Logic Course …and Tutorial on Quadrivium: Arithmetic

George Wick
“The Amateur Logician”

A new course on traditional logic is approaching fast! Most videos have been filmed. This is a systematic course filled with optional exercise sets (and answer keys!).

I plan to release it around Christmas or shortly afterward.

Stay tuned!

Learn logic through ordinary language—not math. This verbal-style, practical approach helps you tackle everything from everyday arguments to deep philosophical questions.

(One of the Main References)

There will be a primary text that you’ll be able to download. The course will also include extra bonus exercises from Dr. Peter Kreeft’s classic Socratic Logic, reflecting my commitment to using the best source materials.

Logic is an instrument for thinking. This new course is about developing that instrument.

You’ll learn how to:

• Distinguish terms, propositions, and arguments
• Identify hidden assumptions in debates
• Recognize valid and invalid reasoning
• Master categorical logic and syllogisms
• Detect common (and not-so-common!) logical fallacies
• Analyze real-world arguments with precision and confidence
• And much more!

Once this is out, AmateurLogician.com will be in phase 2.0.

It’s the next “leap” forward. And I hope you join me.

“Triangular Numbers”

Another project under construction is mathematical.

Slowly I’ve been typing up Quadrivium tutorials.

Plato thought that studying arithmetic (number theory) and geometry, for example, are means to help the mind study higher things in philosophy – and even theology. Medieval minds like Boethius carried on this educational tradition.

In the Traditional Quadrivium. . .
◆ Arithmetic is the study of number in itself.
◆ Geometry studies size and shapes. Number in space.
◆ Music concerns itself with numbers found in sounds. Number in time.
◆ Astronomy studies heavenly bodies in motion. Number in space and time.

There’s something magical when diving into arithmetic.

It wasn’t an area of mathematics I was particularly interested in before. The more I’ve studied it, though, the more fascinating it has become. Don’t dismiss it!

(One of the Main References)

Nicomachus’ Introduction to Arithmetic (around 200 AD) is greatly philosophical. Within a Platonic context, studying number theory takes on added weight. These are eternal truths to be rigorously discovered.

Part of the tutorial is directly based on that reference.

Euclid’s Elements (around 300 BC), while mostly known for its geometry, contains important number theory insights. That’s another reference.

And this tutorial integrates modern number theory. For example, Carl Friedrich Gauss’ contributions (1777 – 1855) will be explored. We’ll sample a host of unresolved questions in the process.

It’s not a tutorial suck-in-the-past. It’s about moving forward from the greats, synthesizing deep insights from them. We’ll use our developing skills in logic to uncover these insights.

The tutorial assumes some knowledge of high school algebra but will teach you to construct proofs, equipping you to explore the richness of number theory. Some entries will be basic, others far more advanced.

Here’s a sample (all of which are drafts being worked upon):
✷ Even vs. Odd Numbers
✷ Plane Numbers
✷ Divisibility & Euclid’s Algorithm

I’m here to learn with you. Thank you for your readership and viewership.

Getting closer to the new logic course, new videos will be added to The Amateur Logician YouTube channel. The new course is a major steppingstone for this online project. There will be several traditional logic videos. But also, I have lots of references to share when exploring the Quadrivium in both a classical and modern sense. I think you’ll enjoy looking through the references. (And the new course!)

The newsletter will get back in gear from a long hiatus.

Finally, note that I do regularly post content on X.

Consider following me and saying “hello.”

I hope you find these new endeavors valuable!

New Logic Course Coming! Updates…

Working on a New Logic Course!

It’s a slow process, to be sure, to create a new course complete with exercise sets. But I’m giving it a go! As I spend some of my weekends on this project, please consider supporting me or keeping me accountable.

My initial plan of a modern logic course has been scrapped in favor of traditional logic. That basically means I’m throwing away around 15 video recordings. But, hey, I already have a modern logic course on YouTube.

Aristotelian-Scholastic Logic is the most grounded and practical science to learn. Studying it will help anyone increase skills in the art of reasoning. Intellectual virtues will be cultivated and extended.

In my view, it’s more important than modern mathematical logic.

Logic is something you actively do or don’t do. Aristotle referred to it as “the instrument.” We have to practice it! I’m doing my best to compile exercise sets. Recently, I made an answer key for all 71 enthymeme problems from Peter Kreeft’s famous textbook Socratic Logic. Other textbooks are being utilized. The primary textbook will be out of copyright so everyone can view it online for free.

Of course it’s up to you if you want to work through all exercises.

But I promise you this: if you do just 10% of them, you’ll be better at reasoning and logic than most people.

***

Other than that, I want to let you know that my latest content has mostly been appearing on X. Follow me here! Drop me a line.

I’ve been posting some outlines of math history, puzzles, logic notes, updates, and more.

***

On YouTube, I have a video featuring Bishop Fulton Sheen on logic, a preview of abductive logic (which is about inference to the best explanation), and Toulmin’s model of argumentation.

We’re all, hopefully, learning – and growing! I make mistakes. There’s a lot I don’t know. Feel free to point out any errors I’ve made. For example, my video on abductive logic has a big typo that I only noticed after I uploaded it.

© Copyright 2026. AmateurLogician.com. All Rights Reserved.
AmateurLogician.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.