Back to the on-screen lesson ·
An argument that does not quite work usually has a sentence missing rather than a sentence wrong.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will take an argument that states one reason for a conclusion, find the sentence it needs in order to get from one to the other, and write that sentence down at the weakest strength that still does the job. You will also say what happens to the argument, and to its conclusion, when the sentence you have written turns out to be false.
You can find a conclusion and say which sentences are offered for it. This lesson is about the sentences that are not offered and are being relied on anyway — which is where most real arguments are actually decided.
| Term | What it means |
|---|---|
| Hidden premise | An unstated claim used to connect the offered reasons to the conclusion. |
| Bridge conditional | An if-then claim running from the stated reason to the proposed conclusion. |
| Begging the question | Offering support whose acceptance already depends on accepting the disputed conclusion. |
| Independent support | A reason that can be assessed without first assuming the conclusion it is meant to establish. |
An argument can leave a connecting premise unstated. Write its stated reason and conclusion separately, then ask what additional claim would connect them. This reveals a possible reconstruction of the reasoning; it does not establish that the missing claim is true or that the author intended only that reconstruction.
Here is the whole method. Take Mira has a season ticket, so Mira swims every week.
The reason is about a ticket. The conclusion is about swimming. Nothing on the page joins those two things, so a sentence joining them is being relied on: anybody who buys a season ticket uses it every week.
Write it at the weakest strength that still does the job. Everybody with a ticket swims every single day would also close the gap and is a much wilder claim than the argument needs — and knocking that down would not touch the argument, because the arguer never needed it.
Another way: picture
Two stepping stones with a gap between them. One stone has the reason written on it and the other has the conclusion. The hidden premise is the stone that has to be in the gap for anybody to get across, and the argument is asking you to assume it is there without looking.
Another way: steps
Four steps, every time:
Three things get offered instead of the missing premise, and each is a different mistake.
| What it is | Example, for Mira has a season ticket, so Mira swims weekly |
|---|---|
| The conclusion again | Mira gets in the water every week. |
| A true but idle fact | The pool is open seven days a week. |
| A stretched version | Everybody with a ticket swims every day. |
The first is not a premise at all: an argument that assumes its conclusion has not gone anywhere. The second is true and would not help if you doubted the conclusion. The third is the dangerous one, because it looks like finding the assumption and is really building a worse argument to knock down — which is a whole lesson of its own later in this course.
Finding an assumption starts with a contrast between what the passage explicitly gives and what it asks you to accept. Suppose a notice says, 'Nia's bicycle is outside, so Nia is in the workshop.' The stated evidence concerns a bicycle's location. The conclusion concerns a person's location. The missing connection is not another fact about the bicycle's color or price. It is a link between the bicycle being there and Nia being there. A useful reconstruction is: if Nia's bicycle is outside, Nia is in the workshop.
That reconstruction makes the inference explicit, but it does not establish that the link is true. Nia might have left the bicycle and walked elsewhere. The argument might be intended as a likely inference rather than a guarantee. In that case, a more faithful reconstruction could be that Nia usually leaves the bicycle outside only while working inside. Preserve the intended strength: a probable conclusion does not require an exceptionless rule, while a claim of certainty requires more than a tendency. Do not silently turn every ordinary inference into a deductive proof.
There may also be more than one reasonable way to fill the gap. Perhaps the speaker knows that Nia never lends the bicycle and always takes it when leaving. Those two claims together could supply the connection. The short conditional compresses their combined role; it is not necessarily a sentence the speaker has consciously formulated. When asked to find a hidden premise, give a modest reconstruction supported by the passage and its context. If the context does not decide among several candidates, explain the alternatives instead of pretending to read the speaker's mind.
Compare three proposed additions. 'Nia owns a red bicycle' may be true but does not connect the evidence to the conclusion. 'Everyone whose vehicle is outside any building is inside that building' is vastly stronger than this argument needs. 'If Nia's bicycle is outside this workshop, Nia is inside' is local to the case. Its narrower scope makes the actual commitment easier to inspect. The aim is not to make the argument look as foolish as possible. It is to reveal the support the conclusion would need.
An assumption can concern a value or a goal as well as a factual pattern. 'The route through the park is shorter, so we should take it' relies on more than geography. It assumes that the relevant objective favors the shorter route and that other considerations do not outweigh the time saved. If the park route is inaccessible to someone in the group, shortest need not mean best. Reconstructing a recommendation therefore requires asking what the proposed action is supposed to achieve, rather than treating a factual comparison as an instruction by itself.
You can make the bridge visible with a simple notation. Let B mean the stated reason and C mean the conclusion. Write B → C for 'if B, then C'. In the workshop example, B means the bicycle is outside and C means Nia is inside. The arrow runs from the evidence being used to the claim it is supposed to establish. C → B runs the other way: it says where the bicycle is when Nia is inside, which does not by itself tell us where Nia is whenever the bicycle is outside.
A special problem arises when the proposed support simply assumes what the argument is supposed to establish. Consider 'The club's rule is fair because it treats everyone fairly.' Unless the second phrase adds an independently supported criterion or fact, it restates the original claim. A reader who doubts that the rule is fair has been given no new reason to change their mind. This is a straightforward form of begging the question, also called circular reasoning. Here that name concerns a failure to supply independent support, not a request to ask another question.
Circularity can hide behind different vocabulary. 'The witness is trustworthy because everything the witness says is reliable' changes the words but leaves the same issue unresolved. It can also involve a longer chain: a newsletter is reliable because a committee approves it, and the committee is reliable because the newsletter says so. Drawing arrows makes the loop visible. If the disputed claim is the only eventual support for itself, following the chain has not produced an independent starting point.
This does not mean that every argument whose conclusion follows from its premises is circular. In a sound deductive argument, the premises can provide an independently acceptable route to something the reader had not yet recognized. 'All the boxes in this shipment were checked; this is one of those boxes; therefore it was checked' may convey new information about a particular box. The problem with begging the question is that acceptance of the offered support already depends on accepting the disputed conclusion in the relevant discussion.
To test a suspected circle, imagine a reasonable reader who has suspended judgment about the conclusion. Could that reader accept the proposed premise for a reason that does not already require the conclusion? A dated inspection record might give independent grounds for believing a box was checked. 'It was checked because it belongs among checked boxes', with no separate grounds for membership, does not. The question is about the source of support, not merely whether the same noun occurs twice.
A better repair adds evidence instead of a more impressive synonym. Replace 'the rule is fair because it is equitable' with the actual criterion being applied and information about the rule. For example, the club might give every member the same booking limit and a way to appeal an error. Those facts do not settle every possible question about fairness, but they give the discussion something to examine. A critic can now ask whether equal limits are appropriate or whether appeals are genuinely available.
Hidden assumptions and circular premises therefore require different responses. For a genuine bridge, write the link and test its truth or suitability. For a disguised repetition, ask for an independent reason. In neither case should you conclude automatically that the original claim is false. A poorly supported fair-rule claim might concern a rule that really is fair. Your analysis identifies what this argument has failed to establish. It does not give permission to reverse the conclusion without evidence of your own.
A fictional sports club sold 120 tickets at 5 credits each last spring, taking 600 credits. A volunteer writes, 'We took 600 last spring, so we can put 600 in this spring's ticket-income budget.' The stated reason is about last year's receipts. The conclusion is a forecast about this year's receipts. Naming the two quantities is the first step; simply repeating 600 does not explain why the years should match.
One possible bridge is that this year's ticket quantity and price will match last year's. If the price stays at 5 and the number sold stays at 120, the calculation remains 120 × 5 = 600. The inference also assumes the budget is comparing the same kind of income: gross ticket receipts in both years, rather than gross receipts in one year and profit after costs in the other. Writing the bridge exposes exactly which details need checking.
Suppose the hall is smaller and has only 100 seats this year. At the same ticket price, selling every seat produces 100 × 5 = 500 credits. The smaller capacity undermines the particular bridge from last year's receipts to this year's forecast. It does not prove that 600 is impossible under every plan: raising the price to 6 or adding another session would change the calculation. Those would be new premises, not facts supplied by the original note.
The committee can therefore respond constructively: 'The 600 forecast assumes the same ticket quantity and price. Our available seats have changed, so please state the new quantity and price before we use that forecast.' The criticism targets the actual reasoning, supplies a checkable issue, and avoids accusing the volunteer of dishonesty or rejecting the whole event.
*Treating assumption as an accusation.* Every argument you have ever made has had assumptions in it. Naming one is the beginning of the conversation, not the end of it.
Writing the assumption stronger than it needs to be. Anybody with a ticket uses it weekly is what the argument needs; everybody swims daily is a different and much easier target.
Thinking a false assumption makes the conclusion false. It does not. It takes the support away and leaves the conclusion exactly where it was: possibly true, and now unsupported by this argument.
Write the stated observation.
B: Nia's bicycle is outside the workshop.
This is the evidence actually given in the passage.
Write the conclusion separately.
N: Nia is inside the workshop.
The conclusion concerns a person rather than the bicycle.
Locate the unstated connection.
The bicycle's presence is being treated as sufficient for Nia's presence.
Without such a connection the observation does not guarantee the conclusion.
State the local bridge.
B → N: if the bicycle is outside, Nia is inside.
The arrow must run from the offered evidence to the inferred claim.
Check whether the bridge is independently plausible.
Nia might have left the bicycle and walked away.
That possibility challenges the bridge without denying the observed bicycle.
Record the stated rule.
The shop is closed on Sundays.
The rule describes opening rather than delivery arrangements.
Record the intended conclusion.
No delivery came yesterday.
This concerns a particular day and a different activity.
Supply the calendar fact.
Yesterday was Sunday.
The weekly rule cannot apply to yesterday without identifying its day.
Supply the operational connection.
Deliveries occur only while the shop is open.
A closed shop could otherwise receive an unattended or back-door delivery.
State what must be checked.
Check both the calendar and the delivery rule.
One true assumption is not enough when the inference also needs a second one.
State last year's evidence.
Last spring: 120 tickets × 5 credits = 600 credits.
This calculation establishes past gross receipts, not future receipts.
State this year's proposed conclusion.
This spring will bring 600 credits in ticket receipts.
The year changes, so a connection between the two cases is required.
Write a sufficient numerical bridge.
This spring also sells 120 tickets at 5 credits each.
The unchanged quantity and price reproduce the same gross receipt calculation.
Check a known change.
Only 100 seats are available; at 5 credits, maximum one-session receipts are 500.
The reduced capacity undermines the unchanged-quantity assumption.
Reject a disguised repetition as a repair.
'The forecast is right because 600 is the correct forecast' supplies no independent evidence.
Restating the disputed forecast begs the question rather than supporting it.
Identify a repair that adds new information.
A 6-credit price with 100 sales would produce 600 credits.
A revised forecast can be supported only by stating and checking the changed plan.
Separate the two claims.
R: Bel was in the room. B: Bel touched the box.
Presence alone does not state what Bel handled.
Write the first missing bridge.
R → B.
The bridge says that being in this room led Bel to touch this box.
Identify another unstated link before inferring prints.
Four arguments, each with one sentence missing. Match each argument to the sentence it needs and does not say.
| Rain is worth carrying a coat for. | Everybody who was in the room touched the box. | Yesterday was a Sunday. | Scoring twice is enough to be picked. | |
|---|---|---|---|---|
| Rain is forecast, so take a coat. | ||||
| Bel was in the room, so Bel touched the box. | ||||
| The shop is shut on Sundays, so the delivery did not come yesterday. | ||||
| Kofi scored twice, so Kofi will be picked on Saturday. |
Nia's bicycle is outside, so Nia is inside. B means the bicycle is outside; N means Nia is inside. Complete the local bridge.
Name the observation.
Observation letter: reason.
The bicycle's position is the fact the speaker supplies.
Name the inferred claim.
Conclusion letter: conclusion.
Nia's location is the claim to which the speaker moves.
Choose the direction of the bridge.
Write start -> N.
The conditional must start with the stated evidence, not with the conclusion.
The argument is: *There is a damp patch on the ceiling under the bathroom.* Therefore *The bath is leaking.* Which sentence does it need and never say?
The shed light is on, so somebody is inside. Write a local if-then premise that would connect the stated reason to the conclusion. L means the shed light is on; O means somebody is inside. Use -> for if-then.
Answer:
Kai did not sign the register, so Kai was not in the building. S means Kai signed; B means Kai was in the building. Write the local bridge from the stated reason to the conclusion, using ~ for not and -> for if-then.
Answer:
A club says: last spring's ticket receipts were 600 credits, so this spring's receipts will be 600 credits. L means last spring brought 600; C means this spring will bring 600. Construct the local conditional bridge this inference leaves unstated. This asks for its structure, not whether the forecast is sensible.
Answer:
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Jo reserved a workshop place, so Jo will attend. R means Jo reserved a place; A means Jo will attend. Write the missing local if-then premise that connects the reason to the conclusion.
Answer:
You can name the unstated premise an argument is resting on, and say why writing it stronger than the argument needs is a mistake rather than a bonus. Tell somebody why showing an assumption is false does not show the conclusion is false. Next: checking whether the argument really needs it.
13. From being present to leaving prints, step 3
Touching the box would leave identifiable prints on it.
Even touching does not guarantee detectable prints, so a careful reconstruction exposes this further assumption.