A Primer on Logic

Reason and the Pursuit of Truth

By Buddy Williams — October 4th, 2025

Letter to My Children
The Pursuit of Truth
What Is Logic?
The Three Acts of the Mind
The Road of Reason
The Structure of an Argument
The Kinds of Reasoning
Common Errors of Reason
How to Practice Logic in Daily Life
The Character of a Rational Mind
The Enemies of Reason
Closing Letter

Letter to My Children

To my beloved children: Emma, Isaac, and Griffin,

Since our mock debates in the car yesterday, I’ve been thinking that I wanted to help you improve your reasoning skills. I know there are other books you may have read, but I wanted to give you a shorter version in my own words.

This short primer on Logic [rules for reason] will help you learn to use your reason in pursuit of truth [agreement with reality]. I was introduced to this topic by Isaac Watts when I was around sixteen, near your age. It forever changed how I think by teaching me to reason well. Everything we do in life is either limited or expanded by our ability to reason. Improving your reasoning will help you see things more clearly.

A note about my writing style: when you see a word, say truth [agreement with reality], brackets will surround my definition. If you see me use parentheses (My name is Buddy.), that means I’m giving an example. This will help you understand my meaning.

I have some practical advice for how to read this primer. Grab a pen. As you read, circle words you find interesting. Underline sentences that stand out to you. Write your questions and insights in the margins. Make this booklet your own. When you are done, it should look like a mess! Have fun with it.

P.S. There will be mistakes in this primer. As you will soon see, making mistakes is a wonderful yet frustrating part of being human. There is always room for growth and discovery!

Love,

Dad

The Pursuit of Truth

So, where shall we begin our search for truth? Let’s start with our shared human nature — and how that makes it difficult to find truth [agreement with reality].

The first thing to know about being human is that it’s hard to see the truth. The human species is estimated to be about 300,000 years old, but our earliest ancestors have existed for around 2.5 million years. For most of that time, we were hunter-gatherers. Humans lived in nomadic [traveling from place to place] tribes — small groups that survived better together. Our survival depended on our ability to cooperate.

It turns out that harmony within small groups is often strengthened by falsehoods [myths, fictions, and white lies]. This may sound evil, but consider: if a friend asks you if their new haircut looks good, would you tell them it’s terrible? Probably not. Why? Because kindness often protects friendship. We build each other up because we want to belong and feel safe. This is just one example of how falsehoods can be helpful.

Since falsehoods help us work more effectively in groups, humans have evolved to use them in abundance. Myths, stories, and fictions have shaped our minds. Human beings first seek community. In our minds, truth often takes a backseat to belonging, emotion, and belief [fictions, myths, and falsehoods].

So, a study of truth [agreement with reality] is also a study of Logic [rules for reason] — and of how it is hard for humans to perceive [to see] truth. Out of all you may learn from Logic, the most important is this: it is tough to see well. I hope you learn to see better. I can only show you the way; you must walk the path.

What Is Logic?

There are two kinds of Logic: deductive and inductive. Deductive Logic concerns certainty [true or false; yes or no; rules of valid reasoning]. Inductive Logic concerns probability [uncertainty; maybe; likelihood].

Deductive Logic tells us what must be true when the premises are true. Inductive Logic teaches us to make informed guesses based on patterns or evidence.

(Example of deduction: All phones need batteries. My iPhone is a phone. Therefore, my iPhone needs a battery. If the premises are true and the form is valid, the conclusion must be true.) (Example of induction: Every day this week, my dog has barked at the mail carrier. Therefore, my dog will probably bark again tomorrow. The conclusion is probable, not certain.)

The vast majority of human claims are inductive — they deal in likelihood, not certainty. In fact, there is very little we can know for sure. Some philosophers believe that the only certainties are the laws of Logic themselves.

You can test this. Think of anything you believe with certainty and ask whether it can be doubted. With a bit of creativity, nearly everything can. Did yesterday exist? It seems so, but how can you be certain? What if the world were created today with memories of yesterday? It is impossible to know for sure. Thus, most “facts” are really just high probabilities.

The Three Acts of the Mind

The mind performs three acts when it thinks: simple apprehension (forming ideas), judgment (affirming or denying), and reasoning (inferring from judgments). These acts correspond to term, proposition, and syllogism/argument.

Simple Apprehension [the forming or conceiving of an idea without affirming or denying] — when you first think of something. (Example: Thinking of a “tree” or a “robot” without saying anything about it.)
Judgment [joining or separating ideas] — when you declare that one idea agrees or disagrees with another. (Example: “Robots can learn.”)
Reasoning [comparing judgments to form new ones] — when you compare two or more judgments to reach a conclusion. (Example: Premise 1: All humans need water. Premise 2: I am human. Conclusion: Therefore, I need water.)

Logic guides these acts so that each is performed rightly. Clear ideas, sound judgments, and valid reasoning are the pillars of correct thinking.

The Road of Reason

This list may feel overwhelming at first, but you can always refer back to it. It describes how knowledge is formed and communicated — how the mind translates the world into understanding. This is also known as Epistemology [the theory of knowledge, especially about its methods, validity, and scope].

Each step moves us a little further away from raw reality and closer to human thought, where errors can creep in. To see clearly, we must understand each step — and where it can go wrong.

Reality [world, cosmos, existence] Reality is what is, whether or not anyone perceives it. (Example: The sun was shining even before you looked outside to see it.) Reality does not depend on belief or awareness. It simply is. Error: Confusing what exists with what we wish existed.
Perception [our five senses: sight, hearing, touch, taste, and smell] Perception is the process by which reality reaches the mind through the senses. (Example: You hear thunder and assume it’s close, but it’s miles away.) Our senses are powerful, yet limited. They show us only appearances. Error: Mistaking perception for reality — believing things are precisely as they seem.
Idea [a conception that may or may not exist in reality] An idea is the mind’s image or concept of something it has perceived. (Example: After meeting several dogs, you form the idea of “dog” — even though each dog looks different.) Ideas are the building blocks of thought — they can be true or false, clear or vague. Error: Confusing the idea with the thing itself. (The word “fire” cannot burn you.)
Judgment [the mental act joining two ideas by affirmation or denial — declaring that one either agrees with or differs from the other] Judgment compares two ideas and declares their relationship. (Example: Idea 1 — people who study usually pass tests; Idea 2 — I studied for my test; Judgment — I will probably pass my test.) This is the foundation of truth and falsehood — where thinking moves from knowing things to knowing statements about things. When expressed in words, a judgment becomes a proposition. Error: Forming judgments without evidence, or confusing emotion for truth.
Argument [a series of judgments, or premises, that lead to a conclusion] Argument is reasoning — connecting judgments to form new knowledge. (Example: Premise 1: All electric cars need charging. Premise 2: My Tesla is an electric car. Conclusion: Therefore, my Tesla needs charging.) Arguments can be valid or invalid, sound or unsound. Error: Believing that because a conclusion feels right, the reasoning must be right.
Word [a spoken or written sign that signifies an idea] Words are the symbols we use to share ideas. They allow minds to connect. (Example: The word “game” might mean “video game” to you but “football” to someone else.) Words are tools, but imperfect ones — they must be defined and used carefully. Error: Assuming words always mean the same thing to everyone.
Term [a word with a precise meaning within reasoning or argument] A term is a word used carefully and consistently in Logic. (Example: “You’re being salty.” Here, salty doesn’t mean full of salt — it means annoyed.) Defining terms clearly prevents confusion and arguments built on misunderstanding. Error: Using vague or shifting terms — what logicians call equivocation.

Remember: After step one, Reality, we make mistakes at every following step. We may misperceive the world. We may form false ideas. We may make bad judgments, poor arguments, or misuse words.

To reason well is to recognize these mistakes — first in yourself, and then in others. This is how clarity grows.

The Structure of an Argument

An argument is a set of premises offered for a conclusion. Its parts can be described as follows:

Term — a word or phrase expressing an idea (e.g., student, homework, effort).
Proposition — a statement that can be true or false (e.g., Effort improves performance.).
Premise — a proposition offered in support of a conclusion.
Conclusion — the proposition claimed to follow from the premises.

A classical syllogism is a deductive argument with two premises and a conclusion:

All students who practice get better.
Emma practices guitar every day.
Therefore, Emma gets better at guitar.

If the premises are true and the form is valid, the conclusion must be true. An argument is valid when it follows the rules of Logic correctly. It is sound when its premises are true and it is valid. Premises can be true or false. Arguments can be valid or invalid. An argument can be sound or unsound. A good argument is both valid and sound.

The Kinds of Reasoning

Deductive [from general to particular] All phones need batteries. My iPhone is a phone. Therefore, my iPhone needs a battery. Deduction offers certainty when the premises are true.
Inductive [from particular to general] Every time it rains, traffic gets worse. Therefore, it will probably be slower tomorrow if it rains. Induction gives probability, not certainty — the method of science.
Analogical [by resemblance] The brain is like a computer: both process information and can make errors. Analogy helps us see connections and can provide plausible, though not certain, support for conclusions.

Deduction demonstrates, induction discovers, and analogy illuminates and suggests. Each has its rightful use.

Common Errors of Reason

Errors arise when perception, language, or inference [reason] fail.

Errors of Perception — seeing wrongly. (Example: You think your friend ignored your text, but their phone died.) Our senses and first impressions can deceive us.
Errors of Words — speaking unclearly. (Example: Two people argue about what counts as “cheating” in a game. The problem isn’t moral — it’s definitional.) Define your terms before you debate.
Errors of Inference — reasoning badly. (Example: All cats are animals; therefore, all animals are cats.) The form appears valid, but the reasoning is reversed.

To reason well is to detect such errors — first in yourself, then in others. Logic is the art of seeing clearly.

How to Practice Logic in Daily Life

Logic is not a school subject; it is a discipline for living. To practice Logic is to cultivate the habit of questioning, defining, and testing your own thoughts.

Ask What You Mean — define your terms. (Example: “That’s unfair.” Ask, “What do I mean by unfair?”)
Ask How You Know — feelings are not reasons. If you say something “feels true,” pause. Why does it feel that way?
Separate Fact from Judgment — (Example: “He’s mean.” The fact may be “He interrupted me.” The rest is opinion.)
Test Your Conclusions — Try to disprove your own ideas. Truth survives testing.
Listen Generously, Think Independently — Listening is not agreement; it is respect. Reason begins with attention.
Reflect on Error Without Shame — Every corrected falsehood is progress toward truth.

Logic is the art of seeing the world as it is — and the courage to keep looking even when it’s hard.

The Character of a Rational Mind

A rational mind is not cold but clear; not proud but patient. Its strength lies not in certainty, but in seeking truth and harmony.

Clarity — prefers understanding to agreement.
Humility — doubts wisely; believes neither everything nor nothing.
Patience — waits for evidence; quick judgments often fail.
Integrity — loves truth more than comfort or pride. (Admitting when you are wrong is one of the highest acts of reason.)
Courage — thinks independently, even against the crowd.
Wonder — finds joy in discovery; delights in the order of the cosmos [universe].

The goal of Logic is not to make you clever but wise — to train the mind to see clearly, love truth, and act rightly. To think clearly is to make good decisions. Making good decisions is essential to living well.

The Enemies of Reason

If Logic is the art of seeing clearly, its enemies are what make us see dimly. They live not outside of us, but within.

Emotion [feeling before seeing] — Feel deeply, but do not neglect thinking. Emotions can blind us to the truth because they are powerful. Emotions help us act. Let us be sure we act in truth.
Pride [the love of being right] — The proud seek victory, not truth. Choose truth, even when it humbles you.
Bias [habit of unexamined belief] — We see the world not as it is, but as we perceive it to be. Be aware of your filters.
Haste [judging before understanding] — Slow thinking is deep thinking. Truth rarely rushes.
Conformity [agreeing to belong] — Truth is not found by counting opinions. Have the courage to stand alone if reason compels it.

Reason is not the absence of passion but the mastery of it.

Closing Letter

Dear Children,

You now hold in your hands the beginning of wisdom: the art of reasoning well. These writings cannot make you wise, but they can show you the path. Wisdom comes when you walk it.

Logic will teach you to see more clearly, but that sight will not always bring comfort. You will notice errors that others overlook. You will see falsehood where others find certainty. That may feel lonely at times — yet it is better to walk in truth alongside those who also wish to live in truth.

Be patient with those who do not see as well as you. Use your reason in acts of self-love and love of others. Love is the way. This will never be easy, since sometimes you must oppose others.

Reason is a flame that burns away confusion and pride, lighting the path toward understanding. As you follow it, you will not only become more intelligent but also more just, more patient, more kind, and more powerful.

When you reason well, you honor both truth and those who seek it with you. Logic is not about winning arguments; it is about living in harmony with reality [truth]. To see the world as it is, to think clearly about it, and to act rightly within it — that is the great art of being human.

Keep your mind sharp, your heart humble, and your curiosity alive.

With love and confidence in your reason,

Dad

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