Lesson 4.1 — Premises and Conclusions

An argument is a collection of sentences arranged to convince you of something.

The Setup

Up until now we've worked with individual sentences and tested their truth. Now we're moving to arguments — collections of sentences arranged to convince someone of something.

An argument has two parts:

• Premises — the starting sentences (the "givens").
• Conclusion — the sentence the argument tries to convince you of.

The premises are supposed to lead to the conclusion.

A Simple Example

This is the most famous argument in the history of logic. Two premises, one conclusion. If you accept both premises, the conclusion follows.

How to Spot the Conclusion

In writing or conversation, conclusions are usually signaled by words like:

• "Therefore..."
• "So..."
• "Hence..."
• "Which means..."
• "This proves..."
• "That's why..."

These signal words mark the conclusion. What came before them was the premises.

"It's been raining all day, AND the gutters are clogged. So the basement is probably flooded."

Two premises ("raining all day," "gutters clogged"), then a conclusion ("basement is probably flooded").

Try It

Read each argument and pick the conclusion.

Implicit Premises

Sometimes arguments leave premises unstated, assuming you'll fill them in.

"Socrates is a human. Therefore, Socrates is mortal."

The unstated premise: "All humans are mortal." The argument doesn't say it, but you have to assume it for the conclusion to work.

When you're reading a tricky argument, ask: what premises is the author assuming that they didn't write down? Implicit premises are where bad reasoning hides.

What Premises Need to Do

For an argument to actually work, the premises need to:

1. Be true (otherwise we're starting from a falsehood).
2. Actually support the conclusion (otherwise we have unrelated facts).

Lesson 4.2 handles what "actually support" means — that's the difference between valid and true, and it's the most important distinction in logic.

Tricky Bits

1. Premises don't always come first. "The basement is flooded — it's been raining all day and the gutters are clogged." Same argument, conclusion first. Signal words like "because" and "since" mark backwards-pointing premises.

2. Sentences can be both premises and conclusions. A multi-step argument chains conclusions: "A. So B. And B AND C means D. So D." Here B is both a conclusion (from A) and a premise (for D).

Recap

• An argument has premises and a conclusion.
• Premises are the starting sentences; conclusion is what they're meant to support.
• Signal words mark conclusions: therefore, so, hence, which means, that's why.
• Watch for implicit premises — the author may be assuming something they didn't write.
• The conclusion only follows if the premises are both true AND actually support it.