Practice question · Match the pairs
Match each accessibility constraint to the principle it validates.
- Reflexive
- Transitive
- Symmetric
- No constraint at all
- Whatever is true is necessarily possible
- Only the minimal distribution principle holds
- Whatever is necessary is actually true
- Whatever is necessary is necessarily necessary
Hints
- Each structural property of the relation licenses one modal principle.
- The weakest system imposes no constraint and validates least.
Show the answer
- Reflexive → Whatever is necessary is actually true
- Transitive → Whatever is necessary is necessarily necessary
- Symmetric → Whatever is true is necessarily possible
- No constraint at all → Only the minimal distribution principle holds
Why
The correspondence between relational properties and modal axioms is exact and was one of the great results of twentieth-century logic, it turned choosing a modal system into a question about the structure of accessibility.
Practise Modal Logic: Necessity and Possibility
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More questions on Modal Logic: Necessity and Possibility
- Why must deontic logic reject the principle that whatever is necessary is actually true?
- The possibility operator means that a sentence is probably true.
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- Modal logic models necessity across possible worlds rather than degrees of belief. What follows from treating…
- Sort each claim by whether it concerns necessity or possibility.