Mixed Inferences
The following is an example of a pure imperative inference:
- P1. Do both the following: wash the dishes and clean your room!
- C1. Therefore, clean your room!
In this case, all the sentences making up the argument are imperatives. Not all imperative inferences are of this kind. Consider again:
- P1. Take all the books off the table!
- P2. Foundations of Arithmetic is on the table.
- C1. Therefore, take Foundations of Arithmetic off the table!
Notice that this argument is composed of both imperatives and declaratives and has an imperative conclusion.
Mixed inferences are of special interest to logicians. For instance, Henri Poincaré held that no imperative conclusion can be validly drawn from a set of premises which does not contain at least one imperative. While R.M. Hare held that no declarative conclusion can be validly drawn from a set of premises which cannot validly be drawn from the declaratives among them alone. There is no consensus among logicians about the truth or falsity of these (or similar) claims and mixed imperative and declarative inference remains vexed.
Read more about this topic: Imperative Logic
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