Practice question · Numerical answer
An argument has premises that are inconsistent. How many valid conclusions can be drawn from them?
Hints
- Think about how many sentences follow from an inconsistent set.
- Every sentence follows, so the count is unbounded, enter -1 to indicate "all of them".
Show the answer
-1
Why
Every sentence follows, so the count is unbounded, recorded here as for "all of them". That total collapse of discrimination is the principle of explosion, and it is why inconsistency is a catastrophe rather than a gap.
Practise Tautology, Entailment and Consistency
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 Tautology, Entailment and Consistency
- Why does an inconsistent set of premises entail every sentence?
- Which statements about entailment are correct?
- A tautology carries no information about how the world is.
- An argument with premises Γ and conclusion φ is shown to be valid. What follows if we now combine Γ with the…
- Sort each sentence by its semantic status.