1. IN DEFENSE OF IMPERATIVE INFERENCE Peter B. M. Vranas University of Wisconsin-Madison Warsaw, 18 May 2012

2. INTRODUCTION l Driving instructor tells you first “If there is a stop sign, stop” and then “There is a stop sign, so stop”. This is apparently an example of an imperative inference: Imperative premise: If there is a stop sign, stop Declarative premise: There is a stop sign Imperative conclusion: Stop l But several philosophers are skeptical about imperative inferences: Williams 1963, Wedeking 1970, Harrison 1991, Hansen 2008.

3. ARGUMENTS VS INFERENCES l An imperative argument is a pair consisting of (1) a nonempty set of imperative or declarative sentences (the premises) and (2) an imperative sentence (the conclusion). l An imperative inference is a process of reason- ing which starts by endorsing certain sentences and ends by endorsing an imperative sentence. l To endorse a sentence is to believe that it is [if declarative] true or [if imperative] binding (i.e., supported by a reason).

4. OVERVIEW Part 1 WILLIAMS’S ARGUMENT Part 2 ARE IMPERATIVE INFERENCES USELESS?

5. WILLIAMS’S ARGUMENT [W]e see an objection to construing the schema [ “ do x or do y; do not do x; so do y ” ] as anything that could be called a pattern of inference. For the first premiss presupposes permission to do x, and permission to do y; but the second premiss, ‘ do not do x ’, obviously has the force of denying permission to do x. Thus the speaker implicitly gives or admits something with his first utterance, which he withdraws with his second; and this can be construed only as the speaker changing his mind, or going back on what he first said. This destroys any resemblance of this sequence of commands to an inference; it is essential to the idea of an inference of q from a set of premises P that in reaching q, the speaker should not go back on or change his mind about any of the members of P  the form of an inference is ‘ given P, q ’ (Williams 1963: 32)

6. RECONSTRUCTING WILLIAMS’S ARGUMENT (W1) Utterances of imperative sentences have conflicting permissive presuppositions. So: (L1) No one can utter (nonequivalent) imper- ative sentences without changing her mind. So: (L2) No one can utter the premises and the conclusion of a (nontrivial) imperative argument without changing her mind. (W2) An inference can exist only if someone can utter its premises and its conclusion without changing her mind. So: (C) No imperative inference can exist.

7. OBJECTION 1 TO WILLIAMS: L1 IS FALSE l The objection: An examiner who says “Answer exactly two out of the three questions. But don’t answer both questions 1 and 3” need not change her mind. l Williams might respond: The examiner in effect utters a single sentence. l I reply: This response renders invalid the move from L1 to L2: anyone who expresses an argu- ment can be understood as uttering a single sentence (“do x or y, but don’t do x, so do y”).

8. OBJECTION 2 TO WILLIAMS: W2 IS FALSE l An examiner says: “Answer exactly two out of the three questions  any two questions, at your choice.” l A minute later, the examiner says: “I changed my mind. Don’t answer both questions 1 and 3. So answer either questions 1 and 2 or questions 2 and 3, at your choice.” l Although the examiner must have changed her mind, she can have inferred the last imperative sentence from the first two, so W2 is false.

9. OBJECTION 3 TO WILLIAMS: W1 IS FALSE l The imperative sentences “If the volcano erupts, flee” and “If you don’t flee, let it not be the case that the volcano erupts” are not equivalent but have the same permissive presuppositions: they forbid everything which entails that the volcano erupts and you don’t flee, and they permit everything else. l Similarly for “Don’t drink immoderately” and “If you drink, don’t drink immoderately”.

10. PART 2 Part 1 WILLIAMS’S ARGUMENT Part 2 ARE IMPERATIVE INFERENCES USELESS?

11. ARE IMPERATIVE INFERENCES INFREQUENT? l Recipes, instruction manuals, etc. suggest that imperative inferences are common. l Williams: No, the inferences are deontic. l But even if first-person imperative inferences are rare, second-person ones need not be. E.g.:  “Invite them either today or tomorrow. … Wait! Don’t invite them today: I forgot that we have guests. So invite them tomorrow.”  “Meet me at noon.” “I can meet you at noon only if I skip lunch.” “Then skip lunch.”

12. ARE IMPERATIVE INFERENCES DISPENSABLE? l The objection: Imperative inferences can always be replaced with declarative ones. l I reply: It does not follow that imperative inferences are useless. Analogy: geometric inferences can be replaced with algebraic ones. l Inference (1) is easier than (2)&(3): (1) Run (2) It rains (3) It rains and If it and you run you don’t run rains, run You run You don’t run