Arguments: claims, assumptions and conditions

Separate reasons from the conclusion

An argument gives reasons for accepting a conclusion. The premises are the reasons offered; the conclusion is what they are intended to support. Words such as 'because' and 'therefore' can help identify those roles, but an argument need not contain either word. First restate the reasoning in short sentences. Then ask whether the stated premises are enough. A conclusion may be factually true yet unsupported by the particular argument, and a valid form can still start from a false premise.

Worked example: apply a conditional in one direction

Use this fictional rule: 'Every applicant with an approved booking receives a confirmation code.' Liza has an approved booking, so she receives a confirmation code. The conclusion follows from the rule and the fact about Liza. Now suppose only that Ramon received a code. Can you conclude his booking was approved? No. The rule does not state that approved bookings are the only source of codes. Treating 'if approved, then code' as 'if code, then approved' reverses the conditional without justification.

Necessary and sufficient conditions

Under the fictional rule, having an approved booking is sufficient for receiving a code: it guarantees a code within the model. Receiving a code is necessary for an approved booking: if no code is received, the booking cannot be approved under the stated rule. This is the contrapositive. These conclusions assume the rule is universal and the facts are known correctly. Real registration systems may have delays or errors; a reasoning exercise's stipulated rule should not be mistaken for a description of any actual institution.

A shared trait does not prove a shared cause

Suppose a club says, 'Members who attend optional review meetings earn higher scores, so the meetings alone caused their higher scores.' Attendance and scores may be associated, but the conclusion ignores other explanations. Members who attend might already study more or have stronger prior preparation. Evidence that similar participants were randomly assigned to attend or not attend would address some alternative explanations better than the observed association alone. Even then, the scope, measurement and implementation of the study would matter.

Strengthen or weaken the link that matters

A strengthening statement should make the conclusion more supported by the premises, while a weakening statement should create doubt about that link. Irrelevant facts can be impressive without doing either. If the claim concerns attendance causing scores, information about the colour of the meeting room is usually irrelevant unless a plausible connection is established. An assumption is a needed bridge that the argument takes for granted. Identifying it requires understanding the claim, not merely finding a statement that sounds agreeable.

• For deductive questions, temporarily accept the supplied premises even if the scenario is fictional.
• Do not convert 'some' into 'all' or reverse 'all A are B' into 'all B are A.'
• A counterexample can disprove a universal claim, but one example cannot establish every case.

Sources & further reading