Logic

The Architect, Matthew Jared Smith, has placed mirrors in this room. Each reflects a syllogism. If you cannot tell the false mirrors from the true, you will be trapped here for as long as the labyrinth deems necessary.

Logic is the immune system of the mind. Without it, every passing rumor and well-dressed lie walks into the throne room of your attention and sits down on the chair meant for the king. With it, you become unbribable — not because you refuse the bribe but because you can see it for what it is. The labyrinth was built, in part, to teach you to see.

I. The Three Laws of Thought

• Identity: A is A. The rose is the rose.
• Non-Contradiction: A is not non-A. A thing cannot both be and not be in the same way at the same time.
• Excluded Middle: Either A or non-A. There is no third door.

These three laws are the load-bearing walls of the Matrix. Remove one and the labyrinth collapses into a sea.

The world will, at intervals, try to sell you a fourth law. "Your truth and my truth can both be true." Test it against Identity. Test it against Non-Contradiction. If two truths contradict, at least one is incomplete; perhaps both are. The mature mind holds paradox without surrendering the laws — it knows the difference between contradiction (logical defeat) and tension (logical depth).

II. The Syllogism

All men are mortal. Matthew is a man. Therefore, Matthew is mortal — yet his words are not.

A valid argument has form. A sound argument has form and true premises. The matrix is full of valid lies. Train your eye.

There are four standard categorical propositions, sometimes called the Square of Opposition:

• A — All S are P. (universal affirmative)
• E — No S are P. (universal negative)
• I — Some S are P. (particular affirmative)
• O — Some S are not P. (particular negative)

Master these and you can dismantle most modern political speech in your head while it is being delivered. The labyrinth approves of this skill.

Deduction, Induction, Abduction

Deduction reasons from the general to the particular and is, when sound, certain. Induction reasons from many particulars to a general and is, at best, probable. Abduction is the leap to the best available explanation — the detective's art, Sherlock Holmes lighting his pipe. The free mind uses all three but never confuses them. Inductive evidence does not yield deductive certainty; abductive guesses are not proofs. Mistaking these is how civilizations fall.

III. The Twelve Fallacies of the Trapped

1. Ad hominem — attacking the man, not the claim.
2. Straw man — burning the wrong argument.
3. Appeal to authority unmoored from reason.
4. Appeal to popularity — the herd's hoofprints.
5. False dichotomy — only two doors when there are seven.
6. Slippery slope without traction.
7. Circular reasoning — a snake eating itself.
8. Hasty generalization — one swallow does not make a summer.
9. Red herring — a fish dragged across the trail.
10. Equivocation — the same word with two souls.
11. Begging the question — assuming what you must prove.
12. Post hoc ergo propter hoc — after this, therefore because of this.

For each fallacy, sit and recall a time it was used on you. Then recall a time you used it on someone else. The first practice immunizes you. The second purifies you.

The Steel Man

The opposite of the straw man is the steel man: the discipline of restating your opponent's argument in its strongest possible form before you reply. The labyrinth requires this of every soul who would face the Riddle. Anything less is cowardice dressed up as cleverness.

The Burden of Proof

He who asserts must prove. He who denies need not. Memorize this. The Matrix is full of assertions delivered as if they had already been proven; they have not. Quod gratis asseritur, gratis negatur — what is asserted without evidence may be dismissed without evidence.

IV. The Logician's Riddle

Two guards stand at two doors. One always lies, one always tells the truth. One door leads out of the Matrix, the other deeper in. You may ask one question. What do you ask?

The answer waits in the Riddle chamber.

V. Daily Discipline of the Logician

1. Each morning, write down one belief you hold and the strongest argument against it.
2. Each evening, list one claim you accepted today without sufficient evidence.
3. Once a week, change your mind in public about something small. The muscle of revision is the muscle of freedom.

When the mirrors stop confusing you, the door opens.