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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
✷ Prime Numbers

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!

“Hello, World!”

It’s customary to launch a blog with “Hello, World!”

Hello, I’m George, the Amateur Logician. (See the about page.)

It’s my sincere hope that AmateurLogician.com is intellectually stimulating and enjoyable.

Feel free to contact me to say, “hello.”
If you have suggestions, requests, or find errors let me know.

Genuine philosophy is a spiritual quest for truth, goodness, and beauty.

Sister Miriam Joseph’s Classic Text

A desire to know must be grounded in good logic.

From there, the sky is the limit. Please join me in this quest!

Presently, allow me to point out my extensive tutorial on “Trivium Logic.” I may add to it in the future.

The “Propositional Logic” tutorial is in its earlier stages. It’s a work-in-progress, though it already contains the basics.

Subscribe to the Amateur Logician Newsletter here.

We can eventually form some kind of online community.

Also, consider following me on TikTok here and YouTube here. At present there’s some logic and philosophy on my TikTok. The YouTube channel is starting off with some mathematics (basic and advanced), but soon there will be an extensive series on basic propositional and predicate logic.

Here’s the major Amateur Logician website content as of November, 2023:

Traditional Scholastic (Verbal) Logic
  1. Trivium: Logic
  2. An Invitation to Logic
  3. Arguments in Brief
  4. Evaluating Arguments
  5. Laws of Thought
  6. Ontology & Logic
  7. Concepts, Signs, & Names
  8. Categorical Propositions: A, I, E, and O
  9. Negations & Complements with Categorical Propositions
  10. Distribution of Categorical Propositions
  11. Euler’s Circles & Venn Diagrams
  12. Predicables
  13. Categories
  14. Definitions
  15. Square of Opposition
  16. Equivalent “Immediate Inference”
  17. Traditional “Immediate Inference”
  18. Informal “Immediate Inference”
  19. The Categorical Syllogism
  20. Syllogisms & Venn Diagrams
  21. Moods & Figures of Syllogisms
  22. Polysyllogisms & the Sorites
  23. Enthymemes
  24. Compound Propositions
  25. Conditional Propositions & Conditional Syllogisms
  26. Conditional Contrapositions, Reductions, & Biconditionals
  27. Conjunctions, Disjunctions, & Disjunctive Syllogisms
  28. Dilemmas
  29. Modal Propositions
  30. Reductio ad Absurdum Arguments
  31. Deduction & Induction
  32. Inductive Abstraction
  33. Inductive Syllogisms
  34. Mill’s Inductive Methods
  35. Science & Hypothesis
  36. Formal Fallacies
  37. Testimony & Unsound Authority
  38. Informal Fallacies & Language
  39. Diversion & Relevancy Fallacies
  40. Presumption Fallacies
  41. Causal & Inductive Fallacies
Modern (Mathematical) Logic

1. Propositional Logic
2. Symbols & Translations
3. Basic Truth Tables
4. Complicated Translations
5. Introducing Rules of Inference
6. Equivalences (Replacement Rules)
7. Conditional & Indirect Proofs

1. Trivium: Grammar
2. Trivium: Rhetoric
3. Philosophy
4. Praxeology
(also contains Mises’ Regression Theorem)
5. Math & Physics

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