Lesson 1 · What Is an Argument?

Why stating a belief confidently doesn't establish it.

Estimated study time: 35–45 minutes · Stage I: Foundations of Reasoning

Before we begin

You don't need to become an atheist to take this course. You don't even need to be uncertain about Christianity. You do, however, need to agree that your confidence in a conclusion and your ability to justify that conclusion are different matters.

Imagine two Christians arguing for the existence of God. One says, "I know God exists because I feel his presence." The other gives a sequence of premises intended to support a conclusion. The first has described an experience; the second has offered an argument. The experience might matter to the person reporting it, but it doesn't automatically transfer their conviction to a sceptical listener.

Our working rule: whenever you offer an argument, your listener may ask whether the premises are true and whether the conclusion follows. Those are different questions.

1. Assertions, reasons and conclusions

An assertion is a claim. An argument is a set of claims offered as reasons for accepting another claim. The supporting claims are the premises; the claim they support is the conclusion.

Premise 1: All mammals are warm-blooded.

Premise 2: Whales are mammals.

Conclusion: Therefore, whales are warm-blooded.

Here the conclusion follows from the premises. The word therefore announces an inference, but writing "therefore" doesn't create one.

Consider: "The universe is enormous; therefore God loves me." The two statements could both be true. Yet the first offers no logical route to the second without further assumptions. A valid argument needs a connection, not merely neighbouring sentences.

In debates, the premises are often concealed. "The beauty of a sunset proves God exists" might rely on something like: (1) extraordinary beauty can exist only if it was intentionally produced; (2) sunsets are extraordinarily beautiful; (3) therefore sunsets were intentionally produced. That still doesn't identify the producer, and the first premise is highly contestable. Making assumptions visible allows them to be examined.

2. Deductive validity is about structure

A deductively valid argument is one in which it's impossible for every premise to be true while the conclusion is false. Validity concerns the logical relationship among propositions, not whether the propositions happen to be true.

Premise 1: All cats are philosophers.

Premise 2: Aisha is a cat.

Conclusion: Aisha is a philosopher.

The argument is valid. Its first premise is plainly false. This example demonstrates why "valid" does not mean "correct", "scientifically established" or "persuasive".

Try the form:

If P, then Q.

P.

Therefore Q.

This is modus ponens, a valid inference pattern. By contrast:

If P, then Q.

Q.

Therefore P.

This is affirming the consequent, an invalid inference. "If it rains, the pavement gets wet. The pavement is wet. Therefore it rained" overlooks sprinklers, hoses and other explanations. The same error appears when somebody argues: "If God created the universe, it might exhibit order. The universe exhibits order. Therefore God created it." Additional evidence would be needed to distinguish that hypothesis from alternatives.

3. Soundness: validity plus true premises

A sound deductive argument is valid and has true premises. Soundness is therefore stronger than validity.

Consider a deliberately simple argument:

All humans are mortal.

Socrates is human.

Therefore Socrates is mortal.

This is both valid and sound, given the ordinary understanding of those premises. Contrast it with the philosophers-and-cats argument. A valid argument with a false premise cannot be sound.

This gives you two distinct questions whenever someone presents a deductive proof for God: Does the conclusion follow? And are the premises true? Answering the first doesn't settle the second.

Equally, exposing a bad argument doesn't establish that its conclusion is false. If somebody makes a dreadful argument for God's existence, you've shown the argument fails, not demonstrated God's nonexistence. Critics of religion should learn that distinction too.

4. Necessary and sufficient conditions

If being a square guarantees being a rectangle, squareness is a sufficient condition for rectangularity. Being a rectangle is a necessary condition for being a square, but it's not sufficient: some rectangles aren't squares.

Mixing these relationships produces familiar apologetic errors. "If God exists, objective morality exists; objective morality exists; therefore God exists" is invalid as stated. Even if God's existence were sufficient for objective morality, that wouldn't establish it as a necessary condition. The missing premise is that objective morality is impossible without God, and that premise needs an argument of its own.

5. Inductive and abductive reasoning

Not every respectable argument attempts deductive certainty.

Inductive reasoning draws a probable generalisation from evidence. A large, well-selected sample may support a claim, without making contrary outcomes logically impossible.

Abductive reasoning, often called inference to the best explanation, compares hypotheses and asks which best accounts for the relevant evidence. Historical arguments for the Resurrection often take this form: proponents argue that a resurrection better explains certain historical claims than competing hypotheses. Critics can challenge the evidence, the alternatives considered, or the standards for comparing explanations. Neither side is entitled to declare victory merely because it has named a possible explanation.

For non-deductive arguments, ask whether the evidence makes the conclusion sufficiently likely, how alternatives compare, and whether important evidence has been excluded. Don't call a probabilistic argument "invalid" merely because its conclusion isn't certain; you may be using the wrong standard.

6. The scope of a conclusion

Here's a particularly important rule for the remainder of the course: a conclusion cannot carry more than the argument establishes.

Suppose, for the sake of discussion, that a cosmological argument establishes a cause of the universe. This doesn't, by itself, establish a personal, omniscient or morally perfect cause; still less does it establish the Incarnation, the Trinity or the Resurrection. Additional propositions and supporting arguments are required.

Conversely, some sophisticated defenders of cosmological arguments do offer supplementary arguments for divine attributes. A competent critic must engage with those arguments rather than claim nobody has attempted the move. An honest course teaches both sides that obligation.

Worked argument clinic

Original post: "Everything has to have a creator. The universe is a thing. So the universe has a creator. That creator is the God of Christianity."

Step 1: Extract the premises. The first three sentences resemble an argument from a universal causal principle. But "everything has a creator" is different from "everything that begins to exist has a cause". Neither wording should be silently substituted for the other.

Step 2: Test the structure. If all things have creators and the universe is a thing, it follows that the universe has a creator. This part can be made valid. But the claim that the creator is the Christian God has not been derived from those premises.

Step 3: Test the premises. Why assume all things have creators? What does "thing" cover? Does "creator" necessarily imply an agent? Are we discussing a beginning of time, a cause within time, or an explanation for existence? These questions can't be settled by emphasis or capital letters.

Step 4: Repair the argument. A well-prepared apologist might present a precise cosmological argument, separately defend its premises and then make explicit the further arguments proposed for a personal divine cause. This is a genuine improvement even if the listener remains unconvinced.

Practice exercises

1. Classify each as a claim, an argument or a report of experience: "God exists"; "I felt God's presence"; "The cosmos began to exist and whatever begins to exist has a cause, so the cosmos has a cause."
2. Is the following valid? "If the Resurrection occurred, Christianity is true. Christianity is true. Therefore the Resurrection occurred." Explain your answer without debating whether Christianity is true.
3. Construct one valid argument with an obviously false premise.
4. Take an apologetic claim from social media and rewrite it as numbered premises and a conclusion. Highlight every premise the author merely assumes.

Lesson summary

• Arguments consist of premises offered to support conclusions.
• Deductive validity concerns logical form; soundness additionally requires true premises.
• Inductive and abductive arguments call for assessment of evidential strength, not deductive certainty.
• A defective argument doesn't establish that its conclusion is false.
• Don't quietly smuggle Christian attributes into a conclusion that supports only a generic cause or explanation.

Further reading: OpenStax, Introduction to Philosophy, chapter 5 and Stanford Encyclopedia of Philosophy, Classical Logic. These are links to independent resources, not reproduced textbook material.