The Trivium - Lost Method of Learning

TH Dialectic

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As a preface, I am not sure who first derived this method and do not think we will ever know. For me this doesn’t matter, the content speaks louder than its creator.

Etymologically, the Latin word trivium means "the place where three roads meet" (tri + via); hence, the subjects of the trivium are the foundation for the quadrivium, the upper division of the medieval education in the liberal arts, which comprised arithmetic (number), geometry (number in space), music (number in time), and astronomy (number in space and time). Educationally, the trivium and the quadrivium imparted to the student the seven liberal arts of classical antiquity.

I was introduced to this a few years back and have been hooked since, some call it a tool for free will, others a way of living, driven through virtuous logic and discernment. I would like to think of it as defence against the dark arts, a way to break free from the shackles of our Orwellian masters.

Grammar teaches the mechanics of language to the student. This is the step where the student "comes to terms," defining the objects and information perceived by the five senses. Hence, the Law of Identity: a tree is a tree, and not a cat.

Logic (also dialectic) is the "mechanics" of thought and of analysis the process of identifying fallacious arguments and statements and so systematically removing contradictions, thereby producing factual knowledge that can be trusted.

Rhetoric is the application of language in order to instruct and to persuade the listener and the reader. It is the knowledge (grammar) now understood (logic) and being transmitted outwards as wisdom (rhetoric).

The Trivium can be analogised to a great tree; the roots that absorb the facts from the world around us, logic like the branches of a tree and your output like the fruit or flowers of said tree.

16525


The Roots—Grammar—Soaking in Knowledge

There are three things going on: First, the tree takes in lots of nutrients and water through its roots. This is like our brain absorbing lots of facts. We are designed to absorb millions of facts from the moment we are born. We are naturally wired to do enormous amounts of fact absorbing through age eleven. Classical educators call this stage the grammar stage, and they make the most of this time by encouraging children to soak in (memorise) many facts about science, geography, history, Latin, and English grammar.

The Trunk—Logic—Growing in Understanding

Secondly, the oak tree grows a trunk, branches, and leaves that put the nutrients to work. This is similar to how a student begins to put together, understand, and use the individual facts they have absorbed. We refer to this stage as the dialectic stage. Students in this stage use the facts in discussion and in processing new ideas. Classical educators make the most of this stage by focusing their studies on the relationships between facts and dialoguing with their students about the how and why of history and science and other subjects. We also want to teach clear reasoning and debate in this stage.

The Fruit—Rhetoric—Bearing Fruit in Wisdom

Once the oak tree has developed good roots, stems, and leaves and has proper nourishment, it will begin to bear fruit (acorns). This is the third stage. A child who is given the nutrients of knowledge and develops the skills needed to process, understand, and apply those facts should be able to bear fruit in the form of original ideas and solutions to problems. They need to develop skills for communicating their ideas and solutions, of course, and they will need lots of practice. We teach the skills of public speaking and writing as early as possible; then, when they reach the age of fifteen and they have a desire to think deeply and originally, they have the skills to do so.

16526


The trivium: the liberal arts of logic, grammar, and rhetoric: understanding the nature and function of language / by Sister Miriam Joseph

(If anyone would like a virtual copy)

16527


This is a book for me at first was a real head scratcher, I had to read it about 5 / 6 times to get my head around what Sister Miriam was trying to say. But, when it clicked, it clicked. I found it really difficult trying to understand something so complex when not having read a book in probably over 6 years. I started to write dialogues with myself on how certain things in our natural world work, how things in nature work. The Trivium method is not only useful for the practical world but for philosophical questions too. It has lead me down a wonderful path of inquiries and I am forever grateful for how much use it has now served me when defending myself against TPTB and other hierarchal structures or regimes.

I am singular, I do not appeal to censuses, I make my own choices, I come to my own conclusions, I don’t hold convoluted or dogmatic views on anything that I know to be objectively true. I invite you to do the same, through rationale, logical decisions based on clear thought and quantifiable understanding of our objective world. We all been blessed with conscious thought and the ability to make decisions. In our dualistic world it’s usually one way, or the other; make sure your decision is correct. Choose wisely.

Logical Fallacies (common types of errors in reasoning):
Fallacies are broken down into two categories: formal and informal. Formal fallacies are based strictly on the logical formation of an argument (deductive). Informal fallacies, which are the most commonly recognized and easiest to learn, take into account the non-logical content of an argument (inductive); they are false for epistemological, dialectical or pragmatic reasons, and typically fall under three categories: relevance, presumption, and ambiguity. The first formation of logical fallacies comes to us from Sir Thomas Aquinas and “The Scholastics”.

List of Logical Fallacies Below:
  1. Ad Hominem
  2. Ad Hominem Tu Quoque
  3. Appeal to Authority
  4. Appeal to Belief
  5. Appeal to Common Practice
  6. Appeal to Consequences of a Belief
  7. Appeal to Emotion
  8. Appeal to Fear
  9. Appeal to Flattery
  10. Appeal to Novelty
  11. Appeal to Pity
  12. Appeal to Popularity
  13. Appeal to Ridicule
  14. Appeal to Spite
  15. Appeal to Tradition
  16. Bandwagon
  17. Begging the Question
  18. Biased Sample
  19. Burden of Proof
  20. Circumstantial Ad Hominem
  21. Composition
  22. Confusing Cause and Effect
  23. Division
  24. False Dilemma
  25. Gambler’s Fallacy
  26. Genetic Fallacy
  27. Guilt By Association
  28. Hasty Generalization
  29. Ignoring A Common Cause
  30. Middle Ground
  31. Misleading Vividness
  32. Personal Attack
  33. Poisoning the Well
  34. Post Hoc
  35. Questionable Cause
  36. Red Herring
  37. Relativist Fallacy
  38. Slippery Slope
  39. Special Pleading
  40. Spotlight
  41. Straw Man
  42. Two Wrongs Make A Right
Stay sharp folks.

TH
 
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Qmeta

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Excellent topic. I'm currently writing an education book for children and will reference this method extensively. The change from the 'classical' way of learning has probably been among the most detrimental to our society, I think.
 
OP
TH Dialectic

TH Dialectic

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Excellent topic. I'm currently writing an education book for children and will reference this method extensively. The change from the 'classical' way of learning has probably been among the most detrimental to our society, I think.
Would love a copy when it's complete, let me know where I can grab one!

TH
 

Paracelsus

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More of a Quadrivium fan myself. Rumor has it Pythagoreans secret handshake was mathematical equations. Numbers don't lie, talented rhetoricians often do.
 

Qmeta

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Numbers don't lie
Isn't maths the only discipline that doesn't need evidence? Mathematicians conjecture, and illustrate logic that they themselves have created. Axioms, the foundation of maths, cannot be experimented upon. Maths is not scientific, yet it is considered a science. It is entirely based on assumptions, which science seeks to avoid. Curious.

If I create a system of logic that uses, for example, 22 variables I could devise a method for the variables to relate together (e.g., calculation). I could then say that the variables don't lie. This could be true, but the system itself is still something that I made up and is not based on reality or experience. Reality is irrelevant to it, as would 'lies' be.

With maths, we are essentially saying "The numbers don't lie, so therefore they must be true" without mentioning that maths is an abstraction, and it can neither lie nor tell the truth.
 

Paracelsus

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Isn't maths the only discipline that doesn't need evidence? Mathematicians conjecture, and illustrate logic that they themselves have created. Axioms, the foundation of maths, cannot be experimented upon. Maths is not scientific, yet it is considered a science. It is entirely based on assumptions, which science seeks to avoid. Curious.

If I create a system of logic that uses, for example, 22 variables I could devise a method for the variables to relate together (e.g., calculation). I could then say that the variables don't lie. This could be true, but the system itself is still something that I made up and is not based on reality or experience. Reality is irrelevant to it, as would 'lies' be.

With maths, we are essentially saying "The numbers don't lie, so therefore they must be true" without mentioning that maths is an abstraction, and it can neither lie nor tell the truth.
2+2=x
Solve for x
 

ISeenItFirst

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For....

Illustrating the abstraction that is maths?
For... X.

See, it says it right there. Solve FOR X.

I took it as illustrating that the abstraction is so close to the actual reality as to be indistinguishable in most cases. Especially when dealing with arithmetic and algebra. Now when you get to some higher levels, things can get quite abstract.

I like to blame things on the maths too. The maths is always up to no good. When you need 4 apples though, and there's 2 here and 2 there, you might just oughta sum them up, and thank the maths you could. You can curse them under your breath afterwords, I know I would.
 

Paracelsus

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For....

Illustrating the abstraction that is maths?
Don't worry, the answer will come to you, like Archimedes in the bathtub!

Srinivasa Ramanujan was flummoxed by two plus two for his entire life.
For... X.

See, it says it right there. Solve FOR X.

I took it as illustrating that the abstraction is so close to the actual reality as to be indistinguishable in most cases. Especially when dealing with arithmetic and algebra. Now when you get to some higher levels, things can get quite abstract.

I like to blame things on the maths too. The maths is always up to no good. When you need 4 apples though, and there's 2 here and 2 there, you might just oughta sum them up, and thank the maths you could. You can curse them under your breath afterwords, I know I would.
Now there's a resonable answer!

I did substitute an unknown variable for the answer instead of a numerical value. And a great strawman redirect!
 
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ISeenItFirst

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Don't worry, the answer will come to you, like Archimedes in the bathtub!

Srinivasa Ramanujan was flummoxed by two plus two for his entire life.

Now there's a resonable answer!

I did substitute an unknown variable for the answer instead of a numerical value. And a great strawman redirect!
I did calc 3 at uni when I was not old enough to vote.

So many of these rants against the maths, remind me of elementary schoolers, talking about having to do algebra when they get to higher grade, and they heard there are numbers AND letters, and it sounds mystical and scary. So they focus on their grammar and vocabulary until they learn how to deride the unconscionable and likely illegal use of letters for maths as 'abstract'.

I certainly dont intend to be casting aspersions. I was just always naturally math oriented. I can see how someone could get stuck on 2 + 2. It's not that much different than "This statement is False".

 
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Paracelsus

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I did calc 3 at uni when I was not old enough to vote.

So many of these rants against the maths, remind me of elementary schoolers, talking about having to do algebra when they get to higher grade, and they heard there are numbers AND letters, and it sounds mystical and scary. So they focus on their grammar and vocabulary until they learn how to deride the unconscionable and likely illegal use of letters for maths as 'abstract'.

I certainly dont intend to be casting aspersions. I was just always naturally math oriented. I can see how someone could get stuck on 2 + 2. It's not that much different than "This statement is False".

I limped through grade school - and most of college with functional, albeit deficient mathematics. It wasn't until I picked up the Wooden Books "Quadrivium" that everything about qualitative and quantitative numbers truly clicked. Your anecdote typifies the experience of those who intuitively grasp the nature of numbers. It's truly a case of comprehension or ignorance, until mathematical gnosis is achieved, one remains a hopeless ignoramus.

The Trivium isn't a bad place to start, but the profundity that lies beyond polemics is inexpressible in words. Musical theory alone has convinced me beyond any fathom of a doubt that God exists.

 
OP
TH Dialectic

TH Dialectic

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Mathematics in modern terms is a formal language, it's used to describe. Mathematics applied naturally with provable axioms and assumptions is what actual mathematics is.

Just like @Qmeta was saying above, when you have a set of foundations that are not provable in our objective reality is when the falacious reasoning takes over. Sophisters spinning locked rhetoric in the form of mathematical sums and unquantifiable axioms to confuse seems to be the only way that modern "psyence" can be proven.

TH
 
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cavedweller

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As a preface, I am not sure who first derived this method and do not think we will ever know. For me this doesn’t matter, the content speaks louder than its creator.

Etymologically, the Latin word trivium means "the place where three roads meet" (tri + via); hence, the subjects of the trivium are the foundation for the quadrivium, the upper division of the medieval education in the liberal arts, which comprised arithmetic (number), geometry (number in space), music (number in time), and astronomy (number in space and time). Educationally, the trivium and the quadrivium imparted to the student the seven liberal arts of classical antiquity.

I was introduced to this a few years back and have been hooked since, some call it a tool for free will, others a way of living, driven through virtuous logic and discernment. I would like to think of it as defence against the dark arts, a way to break free from the shackles of our Orwellian masters.

Grammar teaches the mechanics of language to the student. This is the step where the student "comes to terms," defining the objects and information perceived by the five senses. Hence, the Law of Identity: a tree is a tree, and not a cat.

Logic (also dialectic) is the "mechanics" of thought and of analysis the process of identifying fallacious arguments and statements and so systematically removing contradictions, thereby producing factual knowledge that can be trusted.

Rhetoric is the application of language in order to instruct and to persuade the listener and the reader. It is the knowledge (grammar) now understood (logic) and being transmitted outwards as wisdom (rhetoric).

The Trivium can be analogised to a great tree; the roots that absorb the facts from the world around us, logic like the branches of a tree and your output like the fruit or flowers of said tree.

View attachment 16525


The Roots—Grammar—Soaking in Knowledge

There are three things going on: First, the tree takes in lots of nutrients and water through its roots. This is like our brain absorbing lots of facts. We are designed to absorb millions of facts from the moment we are born. We are naturally wired to do enormous amounts of fact absorbing through age eleven. Classical educators call this stage the grammar stage, and they make the most of this time by encouraging children to soak in (memorise) many facts about science, geography, history, Latin, and English grammar.

The Trunk—Logic—Growing in Understanding

Secondly, the oak tree grows a trunk, branches, and leaves that put the nutrients to work. This is similar to how a student begins to put together, understand, and use the individual facts they have absorbed. We refer to this stage as the dialectic stage. Students in this stage use the facts in discussion and in processing new ideas. Classical educators make the most of this stage by focusing their studies on the relationships between facts and dialoguing with their students about the how and why of history and science and other subjects. We also want to teach clear reasoning and debate in this stage.

The Fruit—Rhetoric—Bearing Fruit in Wisdom

Once the oak tree has developed good roots, stems, and leaves and has proper nourishment, it will begin to bear fruit (acorns). This is the third stage. A child who is given the nutrients of knowledge and develops the skills needed to process, understand, and apply those facts should be able to bear fruit in the form of original ideas and solutions to problems. They need to develop skills for communicating their ideas and solutions, of course, and they will need lots of practice. We teach the skills of public speaking and writing as early as possible; then, when they reach the age of fifteen and they have a desire to think deeply and originally, they have the skills to do so.

View attachment 16526

The trivium: the liberal arts of logic, grammar, and rhetoric: understanding the nature and function of language / by Sister Miriam Joseph

(If anyone would like a virtual copy)

View attachment 16527

This is a book for me at first was a real head scratcher, I had to read it about 5 / 6 times to get my head around what Sister Miriam was trying to say. But, when it clicked, it clicked. I found it really difficult trying to understand something so complex when not having read a book in probably over 6 years. I started to write dialogues with myself on how certain things in our natural world work, how things in nature work. The Trivium method is not only useful for the practical world but for philosophical questions too. It has lead me down a wonderful path of inquiries and I am forever grateful for how much use it has now served me when defending myself against TPTB and other hierarchal structures or regimes.

I am singular, I do not appeal to censuses, I make my own choices, I come to my own conclusions, I don’t hold convoluted or dogmatic views on anything that I know to be objectively true. I invite you to do the same, through rationale, logical decisions based on clear thought and quantifiable understanding of our objective world. We all been blessed with conscious thought and the ability to make decisions. In our dualistic world it’s usually one way, or the other; make sure your decision is correct. Choose wisely.

Logical Fallacies (common types of errors in reasoning):
Fallacies are broken down into two categories: formal and informal. Formal fallacies are based strictly on the logical formation of an argument (deductive). Informal fallacies, which are the most commonly recognized and easiest to learn, take into account the non-logical content of an argument (inductive); they are false for epistemological, dialectical or pragmatic reasons, and typically fall under three categories: relevance, presumption, and ambiguity. The first formation of logical fallacies comes to us from Sir Thomas Aquinas and “The Scholastics”.

List of Logical Fallacies Below:
  1. Ad Hominem
  2. Ad Hominem Tu Quoque
  3. Appeal to Authority
  4. Appeal to Belief
  5. Appeal to Common Practice
  6. Appeal to Consequences of a Belief
  7. Appeal to Emotion
  8. Appeal to Fear
  9. Appeal to Flattery
  10. Appeal to Novelty
  11. Appeal to Pity
  12. Appeal to Popularity
  13. Appeal to Ridicule
  14. Appeal to Spite
  15. Appeal to Tradition
  16. Bandwagon
  17. Begging the Question
  18. Biased Sample
  19. Burden of Proof
  20. Circumstantial Ad Hominem
  21. Composition
  22. Confusing Cause and Effect
  23. Division
  24. False Dilemma
  25. Gambler’s Fallacy
  26. Genetic Fallacy
  27. Guilt By Association
  28. Hasty Generalization
  29. Ignoring A Common Cause
  30. Middle Ground
  31. Misleading Vividness
  32. Personal Attack
  33. Poisoning the Well
  34. Post Hoc
  35. Questionable Cause
  36. Red Herring
  37. Relativist Fallacy
  38. Slippery Slope
  39. Special Pleading
  40. Spotlight
  41. Straw Man
  42. Two Wrongs Make A Right
Stay sharp folks.

TH

fantastic :) and thank you kindly for the PDF link.. I stumbled onto this bloke last year who put some quite brilliant youtube videos together, covering the Trivium and other important matters for consideration.


Harry Growler, looks like he hasn't posted in a wee while, worth looking into at some point if you're so inclined. ok cheers. 👍

bd
 

tupperaware

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Isn't maths the only discipline that doesn't need evidence? Mathematicians conjecture, and illustrate logic that they themselves have created. Axioms, the foundation of maths, cannot be experimented upon. Maths is not scientific, yet it is considered a science. It is entirely based on assumptions, which science seeks to avoid. Curious.

If I create a system of logic that uses, for example, 22 variables I could devise a method for the variables to relate together (e.g., calculation). I could then say that the variables don't lie. This could be true, but the system itself is still something that I made up and is not based on reality or experience. Reality is irrelevant to it, as would 'lies' be.

With maths, we are essentially saying "The numbers don't lie, so therefore they must be true" without mentioning that maths is an abstraction, and it can neither lie nor tell the truth.

Gödel's incompleteness theorems - Wikipedia
Math is seriously limited no matter how hard it tries to eat its tail. All of life is beyond math including slime molds. Maybe especially slime molds.
Like when Lucy goes 100% at 3:09






In Stephen Wolfram's book "A New Kind of Science" he devotes a chapter to the serious limitations of math.

A New Kind of Science: A 15-Year View
"One of the big ideas of A New Kind of Science is what I call the Principle of Computational Equivalence. The first step is to think of every process — whether it’s happening with black and white squares, or in physics, or inside our brains — as a computation that somehow transforms input to output. What the Principle of Computational Equivalence says is that above an extremely low threshold, all processes correspond to computations of equivalent sophistication."

That's the key. Above an extremely low threshold math fails. Almost all science and math works below this extremely low threshold.

I bought this huge book at Barnes and Noble for 2$. Anything above the low threshold just gets no respect because there formulas like 2+2=4 and way beyond just fail. Few will admit that math formulas are lower than the camouflaged cow pie I slid gracefully across on a recent hike in the woods.
 

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