How to Make a Logical Argument: Premises, Conclusions and Validity

Premises and conclusions

In logic, an argument is a set of statements in which some, the premises, are offered as support for another, the conclusion. The classic example is: All humans are mortal (premise 1). Socrates is a human (premise 2). Therefore, Socrates is mortal (conclusion).

Words that signal a conclusion include “therefore”, “so”, “thus” and “hence”. Words that signal a premise include “because”, “since” and “given that”. Looking for these words is the quickest way to find the structure of someone else’s argument.

Watch: How to Argue: Philosophical Reasoning (Crash Course Philosophy #2) (CrashCourse). Premises, conclusions, validity and soundness in about ten minutes.

Valid, invalid, sound and unsound

These four terms are often confused. They describe different things.

Two common valid forms

Learning a few forms helps you spot good and bad reasoning quickly.

• Modus ponens: If P then Q. P. Therefore Q. Example: If it rains, the pitch will be wet. It is raining. So the pitch is wet.
• Modus tollens: If P then Q. Not Q. Therefore not P. Example: If it rained, the pitch would be wet. The pitch is dry. So it did not rain.

Two common invalid forms

These look valid but are not. They are formal fallacies.

• Affirming the consequent: If P then Q. Q. Therefore P. Example: If it rains, the pitch is wet. The pitch is wet. So it rained. (A sprinkler could have wet it.)
• Denying the antecedent: If P then Q. Not P. Therefore not Q. Example: If it rains, the pitch is wet. It did not rain. So the pitch is dry. (Again, a sprinkler.)

How to build a logical argument

Use this sequence when you need to build an argument from scratch.

1. Write your conclusion as a single, clear statement.
2. List the premises that, if true, would lead to it.
3. Check that the premises are linked: does the conclusion follow?
4. Fill gaps by adding the missing premise.
5. Check that each premise is true, or that you can support it.
6. Replace vague terms with precise ones, so the same word means the same thing throughout.

A worked example

Conclusion: Schools should teach media literacy. First draft premises: Students see a lot of misinformation online. Therefore, schools should teach media literacy. That is incomplete. A missing premise links the two: Schools should teach skills students need to function well in society.

Full argument: (1) Students encounter misinformation regularly online. (2) Misinformation harms individuals and society when it is believed. (3) Skills in evaluating sources reduce the chance of believing misinformation. (4) Schools should teach skills that protect students and society from serious harm. Therefore, (5) schools should teach media literacy.

Now each premise can be examined. An opponent might dispute (3) by asking whether media-literacy teaching actually works. That is a good debate, because it is about something specific.

Testing an argument

Apply three tests in order.

1. Structure: if the premises are true, does the conclusion follow? If not, what premise is missing?
2. Premises: is each one true? Which ones are open to doubt?
3. Hidden assumptions: what must also be true for the argument to work?

Watch: Critical Thinking: Fundamentals: Validity (Wireless Philosophy). What it means for an argument to be valid, with examples.

Ambiguity: the silent problem in logic

Many arguments that look valid fail because a key word changes meaning between premises. “Nothing is better than a good education. A cheese sandwich is better than nothing. So a cheese sandwich is better than a good education.” The word “nothing” is doing two different jobs, which is the fallacy of equivocation. Before you test structure, check that each term means the same thing every time it appears. In debate, define your key terms early and hold to them, and listen for the moment an opponent’s term drifts.

Strong arguments are not always valid ones

Most real arguments are not deductively valid. They are probabilistic: the premises make the conclusion likely, not certain. “The last five trains were late, so this one will probably be late” is a reasonable inductive argument. It can be strong or weak, depending on how many cases there are and how similar they are. See the guide on deductive and inductive reasoning for the difference.

Checklist

Before you present an argument, check these points.

• One conclusion, stated clearly.
• Premises that actually lead to it.
• No missing steps or hidden assumptions.
• Key terms used consistently.
• Premises you can support with evidence.
• A response ready for the most obvious objection.

Frequently asked questions

What is a logical argument?

It is a set of statements, called premises, offered as reasons for a conclusion. A good logical argument has premises that are true and a conclusion that follows from them.

What is the difference between valid and sound?

A valid argument has a conclusion that follows from its premises. A sound argument is valid and has true premises. A valid argument can be unsound if a premise is false.

What is a premise?

A premise is a statement offered as a reason to accept the conclusion. Premises are the building blocks of an argument.

How do you test an argument for logic?

Check whether the conclusion follows from the premises, whether each premise is true, and what hidden assumptions the argument depends on.

What is an example of a logical argument?

All humans are mortal. Socrates is a human. Therefore Socrates is mortal. It is valid and sound.

Sources and further reading

• Argument and Persuasion (Stanford Encyclopedia of Philosophy)
• Informal Logic (Stanford Encyclopedia of Philosophy)
• Logic in Argumentative Writing (Purdue Online Writing Lab)
• Deductive reasoning (Wikipedia)
• Argument (UNC Writing Center)