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
Famous quotes containing the words mixed and/or inferences:
“Remember that the wit, humour, and jokes of most mixed companies are local. They thrive in that particular soil, but will not often bear transplanting.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.”
—Nelson Goodman (b. 1906)