On X, thanks to @Le_Master, I just discovered a great app from @TimotheusKearns for studying Aristotelian–Scholastic Logic. It includes interactive exercises.
Ars Syllogistica(Latin for “The Art of the Syllogism“) is being developed by Dr. Timothy Kearns, who is professor at Legion of Christ College of Humanities.
What I’ve seen of it is excellent. It’s still a work-in-progress. Check it out.
It’s already pretty comprehensive! There are exercises on division and definition, diagramming propositions and syllogisms, evaluating validity and enthymemes, and more.
Not only that, it actually covers modal propositions and modal syllogisms. This interactive tutorial covers the broad scope of Scholastic Logic, which goes beyond just Aristotle.
I wondered how he created it. Professor Kearns’s response:
“I used Claude Fable 5 and just coached it exactly on what to do and then had it revise what it produced according to what I wanted changed. Sort of like I’m the architect and Fable is the civil engineer!
“Please let me know if you find any doctrinal problems or infelicities!”
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.
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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.
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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.
When thinking about philosophy and religion, it becomes clear that logic can only take one so far. For instance, a “perennial” view of the world religions, which I once attempted to entertain, rapidly falls apart on any serious investigation. Religions claim contradictive things vis-a-vis each other, and thus they cannot all be true. It is just a matter of logic that, if Islam is true, Christianity must be false (as Islam denies the divinity of Jesus), though it is logically possible that Islam and Christianity are both false. By analogy, in traditional logic with the square of opposition, “contraries” cannot both be true but both can be false.
Hence, either a “perennial” view embraces logical contradictions or must water down the major religions to such an extent that it must trivialize them all so as to attempt to rid all of the contradictions. Yet if it trivializes them all, that is just another way to infer that these religions are not really true after all. Or if it embraces logical contradictions, this is enough to claim that the “perennial” view is false. By analogy, in logic and pure mathematics, an “indirect proof” (aka reductio ad absurdum*) essentially shows that if a contradiction can be derived from a set of internally consistent premises, then the assumption that led to that contradiction must be false. It’s a common proof making move in number theory and abstract algebra, though it is a valid move when thinking about anything.
Nevertheless, logic alone cannot get us far. It cannot get us true premises. It’s only with true premises that we can then derive new true propositions via valid inferences in logic.
Add more responsibilities, you get more thinly spread out.
With serious health issues, job issues, and the genesis of new major projects (including a business project!), I just never seem to get the chance to add things to my website.
So, sorry about that.
In my defense, however, I have continued as “The Amateur Logician” mainly on my YouTube channel. Have you been following it? All the smart kids already do!
Though I’ve taken intermittent hiatuses, I am (very) slowly working on creating a new logic course. My thinking is to create multiple courses – and seeing if there’s a market to sell them. Education is so lacking today; it’s largely a joke. Alternatives are needed! And I do have a math degree and education degree.
For now, there’s lots on YouTube to watch! What have I been doing?
You will not find any videos like mine – this is not mere boasting.
Nobody else has covered traditional modal logic on YouTube.
Modal Logic Playlist
Also, the Philosophy of Rene Descartes Series is complete! If I may say so, I believe Part I and Part II are the best of the bunch. It goes in-depth with several references to great Thomist philosophers and those outside of that camp – like Sir Roger Scruton and Bertrand Russell.
It’s the holiday season. That’s why it seems like a good idea to do more book reviews. I’m just about to upload a review and study of Boolean Algebra by R. L. Goodstein.
Look below for some notes from that book; it’s just a preview, though!
Other recent videos include one on the passions: there you’ll get the traditional perspective with input from Plato and C. S. Lewis. Another video looks into relations (with the logic of reflexivity, symmetry, transitivity, etc.). There’s a video on a fortiori arguments and oblique syllogisms – with also a review of Jacques Maritain’s classic book Formal Logic. And I have something on biases (cognitive, memory-related, social-and-behavioral biases, philosophical biases, etc., etc.).
It’s rightly said to be bad etiquette to type on the Internet with ALL CAPS. Not only is to do so ungrammatical, it is an unsightly thing to do. Who wants to read that? Maybe the message has gotten out. In my own experience, I don’t see it often these day.
Now I’m well aware that my own experience rounds to 0% of the Internet experience, but I can still talk about it. It’s an experience, at the very least, that means something to me. Only others can judge if my encounters parallels theirs.
There actually may be something worse than typing in ALL CAPS. That’s having lots and lots of sentences crammed into a single paragraph. Talk about a reader’s nightmare! Heck, I think I could stand reading an ALL CAPS message, as long as it was nicely broken into smaller paragraphs.
In my own small online corner, I observe a greater number of people engaging in this example of bad etiquette. They write a wall of text. It has no breaks, no breathers. It’s just one sentence after another. It’s frankly a horrible sight.
People could learn a lot by reading a good newspaper column. The writer often will have an entire paragraph be only a single sentence. The thing is, it totally works! Things flow in readability with the breaks between paragraphs. Imagine if the column’s paragraphs decreased in number. Rather than making it a better read, it would become far worse.
Want a good example? Dr. Thomas Sowell! Read his shorter essays… Concise. Flawless word choices. Paragraph size is perfect. Educational. And packed with info!
There’s deductive logic and then there’s inductive logic.
Recently, on my YouTube channel, I’ve uploaded a number of videos on the latter!
Anyone wanting to expand their thinking skills needs to learn both.
First, here’s a general overview of induction. . .
Second, I quickly review an excellent good book on the subject.
An Introduction to Probability and Inductive Logic by Ian Hacking is extremely accessible. I highly recommend it! To be sure, it’s more of a book on probability theory than inductive logic as a whole. This is NOT for you if you have no interest in studying probability.
Yet, please don’t dismiss it too fast! We often make logical inferences about probabilities. Generally speaking, logic helps us determine if a specific conclusion “follows from” given premises. Logic is about good vs. bad reasoning. And we often derive conclusions that are probabilistic.
A lot of people might not realize, for example, that the study of statistics really is a study of probability. Inductive logic partly concerns making inferences about a population-as-a-whole FROM a mere sample. That requires statistics and probability.
Third, I have a video that connects induction with the “hard” sciences.
Other things being equal, we should judge the likelihood that a theory is true by the Simplicity Criterion and the Coherence Criterion.
I also discuss Sir Isaac Newton’s thoughts on the subject, the Scientific Method, and give some basic guidelines about forming hypotheses.
Finally, I reference the Principle of Sufficient Reason (PSR).
The PSR makes sense of our experiences! Things don’t just mysteriously pop in/out of existence. Indeed, if PSR is false, our experiences would make no sense; they would become totally inexplicable.
And if the PSR is false, we would have no reason to trust that the “hard” sciences provide any explanations about reality around us. In fact, while we might think physics gives us explanation X for why Y occurred, it could be that Y occurred for no reason at all (if the PSR is false).
Conclusion: we better accept the PSR!
Fourth, I present what everybody needs to know about induction.
At the heart of induction is what’s called “Partial Enumerative Induction” and “Abstractive Induction.” So, be sure to watch it!
Fifth, I cover an important logical fallacy in induction!
Ludwig von Mises, the great economist, has some excellent coverage of the Gambler’s Fallacy in his treatise Human Action. Probability theory is often counterintuitive, but Mises brilliantly explains a fallacy that many commit.
Wow! It’s been a while since the last blog post, right?
Excuses can be given, but are they good excuses?
Hey, I do have over 200 videos on my YouTube channel. It’s not like I haven’t been productive as “The Amateur Logician!” The playlistfor the series on Basic Symbolic Logic has been completed with around 50 videos. Anyone wanting to learn the basics of Propositional Logic and Predicate Logic can avail themselves of it.
More is to come! I’m in the process of creating a Traditional Logic Course. A series on the philosophy of Rene Descartes is to come. Also, a series on David Gordon’s textbook on economics is in the works.
Often, as I see it, individuals take a partial truth but then stretch it out of proportion turning it into an untruth. There’s no reason why cat absolutely must have the spelling “cat.” The sign “cat” is an English convention.
As the brilliant essayist Theodore Dalrymple writes in his book Life at the Bottom, throwing away the supposed “oppressive” forms of conventional language standards, based on an egalitarian worldview, will entrap a poor family into remaining poor: “Linguistic and educational relativism helps to transform a class into a caste – a caste, almost, of Untouchables.”
It’s difficult to think of a better way to destroy someone’s social, intellectual, and economic mobility. Isn’t it ironic?
Of course, language is not a static thing. It changes! And a good writer sometimes does play fast-and-lose with the standard rules.
Shakespeare’s English is not our English.
Grammar can be better or worse in a time and place, and that surely affects the quality of someone’s speech or writing. There’s a kind of underlying logic in simply understanding the subject-predicate relationship. We can definitely write incoherently!
While there are borderline disputes in “higher” grammar or spelling, there are traditional conventions that everyone accepts – and these conventions allow you and me to talk to each other.
A good vocabulary increases successful communication. It makes it more efficient and sophisticated. Picking the right word cuts down on wordiness. It is thus economical. Things read more authoritatively and thereby it psychologically adds persuasive ethos to your writings. It adds precision and depth.
How, though, do we increase our vocabulary?
Without having a sufficient size, we don’t have much to draw from. My answer is to write down unfamiliar words in a notebook. I’m admittedly not always consistent, but I have begun to do this while reading. When I see a word I don’t know, I look it up, and then write it down. It doesn’t have to be a word I don’t know, actually, just something unfamiliar or unusual. Such a word sometimes gives the air of familiarity when an expert writer places it into a flawless context, yet alone it is actually unfamiliar or unusual. So look it up and write it down.
A thesaurus is a useful tool, though it’s inadequate. Like randomly searching a dictionary, a thesaurus unlikely will help you find a word that represents a complex idea you want to convey but which you cannot simplify to a specific word. That’s why you need to build your mind’s vocabulary.
This “green-eyed logic puzzle” kind of reminds me of a logic joke I’ve seen.
Four logicians walk in a bar. The host asks the question, “Do you all want a drink?” The first logician says, “I don’t know.” The second logician says, “I don’t know.” The third logician says, “I don’t know.” And the fourth logician says, “Yes!”
The fourth logician can respond with a “Yes” because if logician one, two, or three didn’t want a drink, their answer would have been a “No.” And if the fourth logician didn’t want a drink, he could have said “No.”
(Here we have three, not four, logicians!)
The “green-eyed logic puzzle,” to be sure, is more complicated than the bar joke.
Yet when you consider two prisoners, the puzzle is not too hard. It just seems hard when you have 100 people. So, when it comes to these problems, it is always a good idea to attempt to simplify it and then try to solve it. And if you can do that, you can extrapolate and tackle the seemingly more difficult problem with its greater numbers involved.
In the easy case, since it is known that “at least one person has green eyes,” person A and person B can figure out things and leave on the second night. That’s because person A knows that if person B left the first night, that would only be because B saw that A is non-green. That didn’t happen! Ergo, person A realizes that he must have green eyes.
The same logic applies to person B. Ergo, person B realizes that he must have green eyes. As the number of people increase, the number of days increases proportionally as it takes as many days to observe as there are people so as to watch their actions, and those actions reveal needed information. With three people, it takes three nights. With n people, it takes n nights. We can see this modeled after induction by generalizing from two people to n people.
The video references David Lewis (who is famous in philosophy for his ideas about “possible worlds” in logic) and suggests that the “common knowledge” being shared to everyone at once makes a difference. It makes a difference because now everyone is keeping track of everyone else based on the “common knowledge.” In other words, the video suggests, for everyone to keep track of everyone during these days with a success rate of 100 is for the simultaneity of watching at that point when the “common knowledge” was broadcasted.
