Lesson 4.2 — Valid vs True

The most important distinction in logic. Get this one, and most reasoning starts to come into focus.

Two Different Questions

When evaluating an argument, there are TWO separate questions you can ask. They look similar but they're completely independent.

• A sentence is true when it matches reality.
• An argument is valid when its conclusion follows from its premises.

These are not the same. An argument can be valid with FALSE premises. An argument can have all TRUE sentences and still be INVALID. We'll walk through both.

Validity Is About the Connection

An argument is valid when: IF the premises were all true, the conclusion would HAVE to be true.

Notice the "if." Validity isn't about whether the premises ACTUALLY are true. It's about whether the LOGIC connecting them to the conclusion is good.

Premise 1 is FALSE. Premise 2 is FALSE. But the argument is VALID. If the premises were true, the conclusion would have to follow. The shape is right; the inputs are nonsense.

True Premises + True Conclusion ≠ Valid

All three statements are TRUE. But is the argument VALID? No. The premises don't support the conclusion at all. They're unrelated facts that happen to all be true.

Validity is about the connection, not the truth of individual sentences.

The Four Combinations

Mixing validity with truth gives four kinds of argument:

Only one box wins: SOUND = valid argument + true premises. That's the only one that lets you actually trust the conclusion. The others all fail in one way or another.

Classify These

Read each argument. Pick whether it's Sound, Valid-but-unsound, or Invalid.

Why This Distinction Matters

When you're evaluating someone's reasoning, you have TWO separate jobs:

1. Are the premises actually true?
2. Does the conclusion actually follow from the premises (is the argument valid)?

A bad argument can fail either way. A good argument needs both.

Most everyday bad reasoning fails on validity — people stack true facts and reach an unrelated conclusion. Spotting that failure is the practical payoff of this lesson.

Tricky Bits

1. A valid argument can have a false conclusion. If the premises are false, the conclusion can be false too, even with valid logic. Garbage in, garbage out.

2. An invalid argument can have a true conclusion. "Apples are red. Fire trucks are red. So apples are red." The conclusion is true, but the argument is bad — the second premise is irrelevant.

3. Validity is a property of the shape. Same argument shape with different content stays valid (or invalid). Modus Ponens is valid; "affirming the consequent" is invalid. Lessons 4.3 and beyond name the common shapes.

Recap

• TRUE is about sentences matching reality.
• VALID is about conclusions following from premises.
• A valid argument can have false premises. An invalid argument can have all true sentences.
• SOUND = valid AND with true premises. That's the only kind you can fully trust.