Practice question · Put in order
Arrange the steps of an indirect proof in order.
- Reach a contradiction
- Discharge the assumption
- Assume the negation of the goal
- Derive consequences from that assumption together with the premises
- Conclude the original goal
Hints
- The assumption is the negation of what you want, not the goal itself.
- The goal is asserted only once the assumption has been discharged.
Show the answer
- Assume the negation of the goal
- Derive consequences from that assumption together with the premises
- Reach a contradiction
- Discharge the assumption
- Conclude the original goal
Why
Assume the denial, derive an absurdity, and conclude the original. Since the assumption led to contradiction it cannot hold, so its negation, the goal, must. Discharge comes before the conclusion is asserted.
Practise Proof Strategy
The app has 5 more questions on this lesson, and keeps your place in the course. Philosophy I is free to start.
More questions on Proof Strategy
- Modus tollens, hypothetical syllogism, disjunctive syllogism and contraposition are all derived rules. How…
- Derived rules add no logical power to a system, yet proof construction relies on them extensively. What…
- The most productive strategy is to apply rules forwards from the premises until the conclusion appears.
- Why is indirect proof available whatever the shape of the goal?
- Sort each move by whether it is a legitimate step in a natural deduction proof.