Practice question · Match the pairs
Match each proof technique to the shape of reasoning it formalises.
- Conditional introduction
- Negation introduction
- Disjunction elimination
- Conjunction introduction
- Both hold, so their conjunction holds
- Either way, the same conclusion follows
- Suppose it, and derive an absurdity
- Suppose it, and see what follows
Hints
- Each formal rule corresponds to a familiar move in ordinary argument.
- One of them is reasoning by cases.
Show the answer
- Conditional introduction → Suppose it, and see what follows
- Negation introduction → Suppose it, and derive an absurdity
- Disjunction elimination → Either way, the same conclusion follows
- Conjunction introduction → Both hold, so their conjunction holds
Why
Each rule formalises something people already do. Disjunction elimination is argument by cases; negation introduction is reductio. The rules were designed to look like natural reasoning, which is where the name comes from.
Practise Natural Deduction: The Rules
The app has 3 more questions on this lesson, and keeps your place in the course. Philosophy I is free to start.
More questions on Natural Deduction: The Rules
- Arrange the steps of a conditional introduction proof in order.
- Why may a line from a closed subproof not be used later in the proof?
- A proof of "if P then Q" by conditional introduction requires how many assumptions to be made and then…
- Which statements about natural deduction are correct?
- Truth tables establish validity by surveying every valuation, whereas natural deduction constructs a…
- Natural deduction is strictly weaker than truth tables: some valid arguments cannot be proved in it.
- Sort each rule by whether it introduces or eliminates a connective.