What an argument is, and how to find the missing step

A friend texts you on Sunday night: "Take the train tomorrow. The M6 is shut at junction 10." Two sentences, and you're already deciding whether to agree. That's an argument, and you just did something with it without noticing: you supplied a step your friend never wrote, something like "if the M6 is shut, driving will take much longer". If that step is wrong (the closure is northbound and you're going south), the advice is wrong, and your friend never said the thing that was wrong.

Almost every argument you meet works like this. Your manager, the advert, the voice in your own head: reasons offered for a claim, with one reason left out because it seemed too obvious to say. This lesson teaches you to see the shape of an argument, tell it apart from the things that only look like one, and write down the step that's missing. That last skill is the one that pays. When an argument has a weak step, the unstated one is a good place to look, because it's the step nobody checked.

The check you'll use for the whole course

Here is the method. You'll add to it lesson by lesson, and by lesson 3 you should be able to say it from memory.

1. Find the conclusion.
2. Find the premises.
3. Supply what's missing.
4. Test the link: does the conclusion follow from the premises?
5. Test the premises: are they acceptable?
6. Only now consult your opinion of the conclusion.

This lesson does steps 1 to 3. Step 6 is written last on purpose. Most people start there, decide whether they like the conclusion, and then go looking for reasons to have been right. The check makes you earn your opinion. It's also the order in which logic can help you: logic tests the link, and only the link. Whether the premises are true is a question for evidence, and that is a different course. I'll say that again in lesson 2, because it's the sentence people forget first.

What an argument is

An argument is a set of statements in which some of them, the premises, are offered as reasons for another, the conclusion. Not a quarrel. Just reasons offered for a claim, however calmly.

The definition is old. Aristotle, in the fourth century BC, wrote that a syllogism, his word for a deduction, is "discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so" (Prior Analytics I.1).⁶ Read it slowly: certain things stated (premises), something other (the conclusion), follows from their being so (the link). Nearly twenty-four centuries later that's still the shape. Aristotle's "of necessity" describes one kind of link, the deductive kind; there are also arguments whose premises are meant only to make the conclusion likely, and lesson 5 covers those.² The three parts are the same in both.

Your friend's text, laid out:

1. The M6 is shut at junction 10.
2. [If the M6 is shut, driving to work tomorrow will take much longer.]
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C: You should take the train tomorrow.

That's standard form, and every argument in this course gets written the same way: numbered premises, a line, then "C:" for the conclusion. Anything the arguer left unsaid goes in square brackets. No symbols, just the sentences in the order that shows what supports what.

One small thing you'll have noticed: your friend wrote "take the train", a command, and the standard form says "you should take the train", a claim. That's deliberate. A command can't be true or false, and a claim can, so a command gets rewritten as the claim behind it before it goes on the page. Every line in standard form is something you can ask "is that true?" of, including the conclusion.³

Standard form is a tool, not a ritual. Its point is that once the argument is laid out, you can see each premise on its own and ask two separate questions of it: is it true, and does it help? Buried in a paragraph, the premises lean on each other and on the tone of voice, and neither question gets asked.

Step 1: find the conclusion

The conclusion is whatever the passage is trying to get you to accept. That's the whole test, and it's more reliable than any word list.

Word lists exist, and they're useful as long as you don't trust them. Words that often mark a conclusion: so, therefore, hence, thus, consequently, it follows that, implies that. Words that often mark a premise: because, since, for, given that, as, seeing that. Matthew Van Cleave, whose free textbook is the best treatment of this lesson's material, gives both lists in section 1.2 and then warns that they are "not failsafe".¹

Two problems. First, most real arguments use none of these words. "Nobody's used the new system. The rollout should wait. Training takes two weeks." No indicator anywhere, and the conclusion is in the middle. Second, the words have other jobs. Van Cleave's examples: "I have been running competitively since 1999" has "since" as a date, and "I am so happy to have finally finished that class" has "so" as an intensifier. His quick test is to swap the word for a different indicator from the same list. "I have been running competitively because 1999" is nonsense, so that "since" wasn't marking a premise.¹ The swap has a limit, though. When a sentence has a causal reading, "because" slots in fine and the test tells you nothing: "since the road reopened, traffic has doubled" survives the swap and still isn't offering you a reason to believe anything. So the swap is a hint, and the question below is the test.

For any passage: what is this trying to get me to accept? Often the answer is the sentence you'd push back on if you disagreed. Premises tend to be things the writer expects you to grant; the conclusion is the thing they're working to earn.

One more thing people assume: the conclusion comes last. It comes last in textbook examples. In real writing it's often first: people state the claim and then defend it. A careful reader gets used to finding the conclusion first, in the middle, or split across two sentences.

Step 2: find the premises, and notice what isn't an argument

Once you have the conclusion, the premises are the statements offered to support it. Everything else in the passage (background, colour, a joke, a repetition) can be left out of the standard form.

But before you list premises, check that you have an argument at all. Several kinds of passage look like arguments and aren't. The one that fools nearly everyone is the explanation.

The test is direction. An argument runs from what's offered to what's claimed: here are reasons, therefore accept this. An explanation runs the other way: this is accepted, here is why it happened. Van Cleave puts it as the difference between establishing that something is true and explaining why it's true; in an explanation, "we assume that what we are trying to explain (i.e., the conclusion) is true" (section 1.3).¹

So the question to ask is: is the thing after "because" being used to convince me of the thing before it, or is the thing before it already agreed and the "because" telling me how it came about? Go back to (a): "the train was late because a tree came down." If you'd never believe the train was late unless told about the tree, it would be an argument. Nobody's in that position. It's an explanation.

Three more look-alikes, quicker:

A report. "The city council's report says the bridge needs repairs within two years." That tells you what a document claims. It gives no reason to believe the claim and takes no position on it. A report can contain an argument ("the council argues that, because the piers are corroding, the bridge needs repairs"), in which case you can lay out the council's argument. But the reporting sentence itself argues for nothing.

A bare assertion. "The bridge needs repairs, and that's all there is to it." A conclusion with no premises. People assert things all day, and the confident tone can make an assertion feel argued for. It isn't. You can't check a link that isn't there; you can only ask for one.

A conditional on its own. "If the bridge isn't repaired by June, it'll have to close." This says what follows from a condition. It doesn't claim the condition holds, so it doesn't conclude anything. Add "and it won't be repaired by June" and you have an argument. Lesson 3 is about conditionals, and a great deal of confused arguing comes from treating "if P then Q" as though it had asserted P.

Step 3: supply what's missing

Now the part that matters most: nearly every argument you'll meet outside a logic textbook leaves something out. The old name for an argument with an unstated premise (or, sometimes, an unstated conclusion) is an enthymeme. Van Cleave makes the same observation without the name: "quite often, an argument will not explicitly state a premise that we can see is needed in order for the argument to be valid".¹ The name doesn't matter. Why the premise is missing does.

It's missing because the arguer thought it too obvious to say. Most of the time they were right: the unstated step is shared background, and writing it down changes nothing. But "too obvious to say" is also exactly the description of a claim nobody checked. When someone writes a premise down, they look at it, and a reader looks at it. When they leave it out, neither does. So some unstated steps are harmless and some are the weak point of the whole argument, and from the outside the two look identical. The only way to tell which you have is to write it down. That's why you always do.

That gives you the rule for what to write in the brackets. Not the premise that makes the argument work. The premise the arguer is actually relying on, in the form they'd accept if you read it back to them. Sometimes that premise makes the argument work. Sometimes, once it's written down, it plainly doesn't, and then you've found the problem, and you've found it in the arguer's own words rather than in a version you invented.

You should know that most textbooks state the rule from the other side. Van Cleave, in section 1.9, tells you to supply the most plausible premise that makes the argument valid or strong, and calls that charity.¹ In practice the two rules agree, because "most plausible" and "the one they'd accept" almost always pick out the same sentence, and where they differ the arguer's own version wins: a premise they'd reject isn't charity, it's a substitution. Lesson 7 comes back to charity properly. For now, hold both halves: the premise must be one the arguer would sign, and among those, take the strongest.

Worked example 1: the icy roads

"The roads are icy. Leave ten minutes early."

Step 1, the conclusion: what's this trying to get me to do? Leave ten minutes early, which as a claim is "you should leave ten minutes early". Step 2, the premise: the roads are icy. Now step 3. Something links icy roads to leaving early, and it isn't stated.

1. The roads are icy.
2. [Icy roads make the drive slower.]
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C: You should leave ten minutes early.

Now the same words doing a different job: "We left early because the roads were icy." Is that an argument? Run the test. Is anyone trying to convince you that we left early? No, that's granted. The sentence says why. It's an explanation, and there's nothing to put in standard form.

Worked example 2: Harry, and the exception that appears when you write the rule down

This example is from Stephen Toulmin's The Uses of Argument, published in 1958, and nearly every textbook on argument since has borrowed it.⁴⁵

"Harry was born in Bermuda, so Harry is a British subject."

1. Harry was born in Bermuda.
2. [A man born in Bermuda will generally be a British subject.]
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C: Harry is a British subject.

That was the law as Toulmin described it in 1958. British nationality law has been rewritten since, so the rule itself has gone out of date, which is worth a moment: a bracketed premise like this is a claim about the world, and claims about the world can stop being true.⁷

Here's the wrinkle. Look at premise 2. The moment it's written down, that "generally" is sitting there in plain view, and a reader immediately asks: generally, except when? Toulmin supplies two exceptions and a trailing ellipsis for the rest: unless both his parents were aliens (the legal term, then and now, for citizens of another state), or unless he has since become a naturalised American.⁴ Those exceptions were invisible in the one-line version. Nobody reading "born in Bermuda, so British" pauses to think about Harry's parents. Reading "a man born in Bermuda will generally be a British subject", everyone does.

That is what step 3 is for. Writing the missing premise down shows you how far the argument reaches. A general rule has exceptions, the exceptions are the counter-cases to the argument, and you only find them by looking at the rule. Toulmin built a whole layout around this. He calls the rule the warrant and the exceptions the rebuttal, and he draws the argument like this:

Look at the warrant: its own box, drawn dashed, sitting outside the step rather than beside the data as a second premise. It's the rule that licenses that step, and it's the thing nobody said. The rebuttal hangs off the claim, and it only exists because the warrant says "generally". Lesson 7 gives you the full layout, with the two slots this drawing leaves out. For now, the habit is enough: write the rule the arguer relies on, then ask what it doesn't cover.

Notice too that the argument for Harry is a perfectly good one. The exceptions don't sink it; they qualify it. "Harry is presumably a British subject, unless one of those things applies" is what the argument actually earns, and an honest arguer would say so. Most of the time, finding the missing premise doesn't destroy an argument. It tells you how much weight it can bear.

Worked example 3: no indicator words, conclusion first

Here's a passage of the kind you might get in an email from a friend who's house-hunting. (It's made up; the point is the shape.)

"Don't offer on the Elm Street house. The survey found damp in two rooms. Damp like that costs thousands to put right. And the seller has already dropped the price once, which tells you something."

No "so", no "therefore", no "because". Do steps 1 and 2 yourself before opening the answer. What is this trying to get you to accept, and what's offered in support? Then try step 3: there are two things this argument leans on and never states. What are they?

1. The survey found damp in two rooms.
2. Damp like that costs thousands to put right.
3. The seller has already dropped the price once.
4. [A price drop means other buyers have looked and walked away.]
5. [You shouldn't offer on a house with faults that cost thousands, unless the price already reflects them.]
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C: You shouldn't offer on the Elm Street house.

Now look at premises 4 and 5, the ones the friend never said. Would they accept them? Roughly, yes. Are they true? Premise 5 carries its own exception in its last four words: if the price has already dropped by more than the damp costs to fix, the argument points the other way. And premise 4 is one reading of "which tells you something"; the other reading is that a seller who has dropped the price once is a seller in a hurry, which makes the house a bargain, not a warning. The friend's argument was persuasive in the email and looks much thinner in standard form, and nothing was added or removed; it was only written down.

What people get wrong

"An argument is a quarrel." In everyday English it can be. In this course it never is. An argument is reasons offered for a claim, and two people can argue, in this sense, while agreeing about nearly everything and liking each other throughout. If you find yourself thinking "I don't want to argue", check whether you mean "I don't want to fight" or "I don't want to give reasons". The second is the one to worry about.

"If there's a 'because', it's an argument." "Because" introduces explanations as readily as premises. The cafe shut because the lease ran out. The pipe burst because the water froze. Neither of those is trying to convince you of anything. The test is never the word. The test is whether the thing before "because" is being established or taken for granted.

"The conclusion is the last sentence." It's the last sentence in textbook examples, which is where the habit comes from. In real writing it's often first, sometimes in the middle, and sometimes unstated (a passage can list reasons and let you draw the conclusion yourself, which is a rhetorical move you should notice). Find it by asking what the passage wants from you.

"The missing premise is whatever makes the argument work, whether or not they'd accept it." This one feels like generosity, and it isn't. If you add a premise the arguer wouldn't accept, you're no longer evaluating their argument; you're evaluating one you built. Add the strongest premise they'd sign. If that premise makes the argument work, good. If it doesn't, you've found the gap, and you can show it to them in their own terms, which is the version they can't wave away.

"Finding a missing premise means the argument is bad." Almost every real argument has one. Finding it is the beginning of evaluation, not the end. Harry's argument has a missing premise and is a good argument; it just reaches a little less far than its one-line version claimed.

Practice

Five passages. For each, decide whether it's an argument, an explanation, a report, or something else that isn't an argument. For the arguments, write the standard form with any missing premise in brackets. Do all five on paper before you open the answers.

(A) "The forecast says thunderstorms from three. Move the barbecue to Sunday."

(B) "The match was abandoned because lightning was seen within five miles of the stadium."

(C) "According to the club's statement, the pitch will be relaid over the summer."

(D) "He's never once returned a book on time. I wouldn't lend him that one."

(E) "If the river rises another foot, the footpath will be under water."

Connections

You now have steps 1 to 3 of the six-step check. Lesson 2 fills in step 4 for arguments that claim certainty: what it means for a conclusion to follow, how to show that it doesn't, and why your opinion of the conclusion gets in the way of judging the link. Lesson 3 gives you the four conditional shapes worth memorising and the two that fool almost everyone. Lesson 5 fills in step 4 for arguments that claim only likelihood, which is most of them.

The missing premise comes back in lesson 7 under Toulmin's name for it, the warrant, with the full layout for finding it in longer passages and a proper treatment of charity. And the checkpoint above, about a bad argument telling you nothing about its conclusion, becomes the fallacy fallacy in lesson 8.

If you took How to Learn Anything first, you'll recognise what the practice section just asked of you. Writing the standard form from a passage, with the passage closed, is retrieval practice on this lesson's skill. Reading my answers and nodding is not.

Go deeper

• Van Cleave, Introduction to Logic and Critical Thinking, 2nd ed., chapter 1 (free, CC BY, on LibreTexts). Sections 1.2, 1.3 and 1.9 are this lesson: indicator words, arguments versus explanations, and missing premises, with exercises.
• Toulmin, The Uses of Argument (1958; updated edition 2003), chapter 3, "The Layout of Arguments". The Harry example in its original setting (pages 92 to 98 of the 2003 edition), and the full layout that lesson 7 teaches. Dense but short. No free full text; a library copy is the way in.
• Aristotle, Prior Analytics, Book I, chapter 1 (free, MIT Classics, Jenkinson's translation). Two pages. Worth reading once to see how little the core idea has changed.

Sources

1. Van Cleave, M., Introduction to Logic and Critical Thinking, 2nd ed. (Lansing Community College; CC BY 4.0), ch. 1, sections 1.2 "Identifying arguments", 1.3 "Arguments vs. explanations" and 1.9 "Arguments with missing premises", read on LibreTexts at draft time and re-checked at review. Premise and conclusion indicator lists; indicator words are "not failsafe"; the "running competitively since 1999" and "so happy" examples, quoted verbatim; the swap test; arguments establish that, explanations why; in an explanation "we assume that what we are trying to explain (i.e., the conclusion) is true"; "because" appears in both; missing premises supplied by the principle of charity as the most plausible statements that make the argument valid or strong.
2. Van Cleave, M., Introduction to Logic and Critical Thinking, 2nd ed. (Lansing Community College; CC BY 4.0), section 1.8 "Deductive vs. inductive arguments", read September 2026. "A deductive argument is an argument whose conclusion is supposed to follow from its premises with absolute certainty, thus leaving no possibility that the conclusion doesn't follow from the premises"; "an inductive argument is an argument whose conclusion is supposed to follow from its premises with a high level of probability, which means that although it is possible that the conclusion doesn't follow from the premises, it is unlikely that this is the case". Used for the deductive/inductive contrast beside Aristotle's "of necessity".
3. Magnus, P. D., Button, T., Thomas-Bolduc, A., Zach, R. et al., forall x: Calgary (CC BY 4.0), chapter 1, read from the PDF September 2026. On what counts as a sentence in the logical sense: questions "will not count as sentences, but answers will"; of an imperative, "the command is neither true nor false"; and "'You will respect my authority' is either true or false, either you will or you will not, and so it counts as a sentence in the logical sense". Used for rewriting a command as the claim behind it before it goes into standard form.
4. Toulmin, S., The Uses of Argument (Cambridge University Press, 1958; updated ed. 2003), ch. 3 "The Layout of Arguments", pp. 97 to 102 in the 1958 edition (page numbers via Hitchcock, source 6) and pp. 92 to 98 in the 2003 edition, from which the wording here is taken. The Harry example: claim "Harry is a British subject", data "Harry was born in Bermuda", warrant "A man born in Bermuda will generally be a British subject" (2003 ed. pp. 94, 97), qualifier "presumably", rebuttal "Both his parents were aliens / he has become a naturalised American / ..." (2003 ed. p. 97), which the lesson renders as two "unless" clauses. Backing and the two remaining slots of the layout are left to lesson 7.
5. Hitchcock, D., "Toulmin's Warrants", in van Eemeren, Blair, Willard & Snoeck Henkemans (eds.), Anyone Who Has a View: Theoretical Contributions to the Study of Argumentation (Kluwer, 2003), pp. 69 to 82. The 1958 page references for the Harry example, the reading of the warrant as an inference licence rather than a premise, and the remark that the example is by now "hackneyed and familiar", which is the basis for "nearly every textbook since has borrowed it".
6. Aristotle, Prior Analytics, Book I, ch. 1 (24b18 to 20), trans. A. J. Jenkinson, MIT Internet Classics Archive, re-checked at review: "A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so." Also the definition of a premiss as "a sentence affirming or denying one thing of another". Robin Smith's Stanford Encyclopedia entry "Aristotle's Logic" (rev. 2022) gives the alternative rendering "a deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so", and places the passage at I.2 by its chapter division; the Bekker number is the same.
7. British Nationality Act 1981 (in force from 1 January 1983), which replaced the framework of British subjecthood that Toulmin's 1958 example assumed. Cited only for the point that the rule in the warrant no longer describes the law.