A Primer on Logic

A Letter to My Children

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

Since our mock debates in the car yesterday, I’ve wanted to help you sharpen your reasoning. There are whole books on this, but I wanted to give you a shorter version in my own words.

This primer on Logic [the rules of good reasoning] will help you use reason in pursuit of truth [agreement with reality]. I was introduced to this subject by Isaac Watts when I was about sixteen, near your age. It changed how I think forever. Everything we do is limited or expanded by how well we reason.

A note on my style: when I define a word, the definition goes in brackets, like truth [agreement with reality]. When I give an example, it goes in parentheses (My name is Buddy.).

Grab a pen as you read. Circle words you find interesting, underline sentences that stand out, and write questions in the margins. When you’re done, this should look like a mess. Have fun with it.

P.S. There will be mistakes in this primer. As you’ll soon see, making mistakes is a wonderful and frustrating part of being human. There is always room to grow.

Love,

Dad

1. Why Truth Is Hard to See

Let’s start with something surprising: humans aren’t built to see truth clearly.

For most of our history, our ancestors lived in small, nomadic [moving from place to place] tribes. Survival depended on cooperating with the group. And harmony in small groups is often helped along by falsehoods [myths, fictions, and white lies].

That may sound wrong, but think about it. If a friend asks whether you like their new haircut, would you tell them it’s terrible? Probably not. Kindness protects the friendship. Because small falsehoods helped us get along, our minds grew comfortable with them. We seek belonging first, and truth often takes a back seat.

So the most important lesson in this primer is this: it is hard to see well. Logic can show you how to see better. I can only point the way; you have to walk it.

2. The Road of Reason

Knowledge travels a road, from the world outside us to the words we use to share it. Each step takes us a little further from reality and closer to our own thinking, and at each step errors can creep in. Philosophers call the study of this road epistemology [the theory of how we know things].

You don’t need to memorize it. Come back to it when you need it.

Reality [everything that exists]. Reality is what is, whether or not anyone notices it. (The sun was shining before you looked outside.) Error: confusing what exists with what we wish existed.

Perception [our five senses]. Perception is how reality reaches the mind. Our senses are powerful but limited. They show us appearances. (You hear thunder and think the storm is close, but it’s miles away.) Error: believing things are exactly as they seem. (You think a friend ignored your text, but their phone died.)

Idea [the mind’s picture of something]. An idea is how the mind holds what it has perceived. Ideas can be clear or vague, accurate or mistaken. (After meeting several dogs, you form the idea “dog,” even though each dog looks different.) Error: confusing the idea with the thing. (The word “fire” can’t burn you.)

Judgment [joining two ideas by saying yes or no]. A judgment says that one idea agrees or disagrees with another. This is where true and false first appear. (“Robots can learn” joins the idea robot with the idea learning.) Error: judging without evidence, or letting a feeling stand in for a reason.

Argument [judgments that lead to a conclusion]. An argument connects judgments to reach a new one. (All electric cars need charging. My Tesla is an electric car. So my Tesla needs charging.) Error: assuming the reasoning is good because the conclusion feels right.

Word [a sign for an idea]. Words let us share ideas, but they are imperfect tools. (“You’re being salty” has nothing to do with salt.) Error: assuming a word means the same thing to everyone.

Term [a word given a precise meaning for a discussion]. Before you argue about whether a game was fair, agree on what fair means. Many arguments are really about definitions. (Two people argue about whether something counts as “cheating.” The disagreement isn’t moral. It’s definitional.) Error: letting a word’s meaning shift partway through an argument. Logicians call this equivocation.

Notice that after the first step, reality, we can make mistakes at every step. To reason well is to catch those mistakes, first in yourself and then in others.

3. The Shape of an Argument

An argument has a few parts:

• A proposition is a statement that can be true or false. (Practice improves skill.)
• A premise is a proposition offered as support.
• A conclusion is the proposition the premises are meant to support.

Here is a classic form, called a syllogism:

1. Everyone who practices gets better.
2. Emma practices guitar every day.
3. So Emma gets better at guitar.

Two words help you judge any argument:

• An argument is valid when the conclusion really follows from the premises.
• An argument is sound when it is valid and its premises are true.

A good argument is sound. Validity alone isn’t enough. (All fish can fly. A trout is a fish. So a trout can fly. The logic works, but the first premise is false.)

Watch out for arguments that only look valid. “All cats are animals, so all animals are cats” sounds like logic, but it flips the claim around. The conclusion doesn’t follow.

4. The Kinds of Reasoning

Deduction [reasoning where the conclusion must be true if the premises are] gives certainty, if the premises are true. (All phones need batteries. My iPhone is a phone. So my iPhone needs a battery.)

Induction [expecting unobserved cases to resemble observed ones] gives likelihood, not certainty. (My dog has barked at the mail carrier every day this week, so he’ll probably bark tomorrow.) Most of what people claim is inductive. It rests on patterns and evidence, so it deals in likelihood, too.

Abduction [reasoning to the best explanation] proposes what might explain what we see. (The grass is wet this morning. The best explanation is that it rained overnight, unless the sprinklers ran.)

Analogy [reasoning by resemblance] helps us see connections, but only suggests. (The brain is like a computer: both process information and both make errors.)

Deduction demonstrates, induction discovers, abduction explains, and analogy suggests. Each has its place.

Induction is the everyday method of science: we watch what happens again and again, then expect it to keep happening. Science also leans on deduction to work out what a theory implies, and on bold guesses to explain what we see.

That points to something important. Very little can be known with certainty. Try it: think of something you’re sure of, and ask whether it could be doubted. Did yesterday really happen? What if the world were created this morning, complete with memories? You can’t rule it out. Most of what we call facts are really high probabilities. Many are very high, but all of them are open to correction.

5. Practicing Logic Every Day

Logic isn’t a school subject. It’s a habit of mind.

1. Ask what you mean. “That’s unfair.” What do I mean by unfair?
2. Ask how you know. If something feels true, pause and ask why.
3. Separate facts from judgments. “He’s mean” is a judgment. The fact may be “He interrupted me.”
4. Try to prove yourself wrong. Ideas that are true survive testing.
5. Listen generously, think independently. Listening isn’t agreeing. It’s respect.
6. Correct your errors without shame. Every mistake you fix is progress.

6. The Rational Mind and Its Enemies

A rational mind isn’t cold. It is clear, and its strength comes from seeking truth, not from being certain. It has a few traits:

• Clarity: prefers understanding to agreement.
• Humility: believes neither everything nor nothing.
• Patience: waits for evidence, because quick judgments often fail.
• Integrity: loves truth more than comfort or pride. Admitting you were wrong is one of the highest acts of reason.
• Courage: thinks independently, even against the crowd.
• Wonder: takes joy in discovering how the world works.

Its enemies live inside us, not outside:

• Emotion [feeling before seeing]: Feelings help us act. Make sure you act on truth.
• Pride [the love of being right]: The proud want to win, not to learn.
• Bias [unexamined habits of belief]: We see the world through filters. Know yours.
• Haste [judging before understanding]: Truth rarely rushes.
• Conformity [agreeing in order to belong]: Truth isn’t decided by counting votes.

Reason isn’t the absence of feeling. It’s the mastery of it.

Closing Letter

Dear Children,

These pages can’t make you wise, but they can show you the path. Wisdom comes from walking it.

Reasoning well won’t always bring comfort. You’ll notice errors others miss, and that can feel lonely. Find people who also want to live in truth, and walk with them.

Be patient with those who don’t see what you see. Use your reason to love yourself and others well. That won’t always be easy, because sometimes love means disagreeing.

Logic isn’t about winning arguments. It’s about living in harmony with reality: seeing the world as it is, thinking clearly about it, and acting 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