1. Hypothetical Syllogism for subjunctive conditionals is the inference form:

   p []→ q
   q []→ r
   ————
   ∴ p []→ r.
   

   Prove that hypothetical syllogism for subjunctive conditionals is not a valid inference form on

   1. Stalnaker's semantics,

   2. Lewis's semantics.

2. Prove that hypothetical syllogism for indicative conditionals is a reasonable inference form on the following revised version of Stalnaker's definition of reasonable inference, given his pragmatic condition on apropriateness for indicative conditionals (as well as the general pragmatic condition on appropiateness given in the appendix).

   Revised Definition (for a two premise argument): The inference from ordered premises A₁, A₂, to conclusion C is a reasonable inference just in case, in any context k in which the sequence s=A₁,A₂,C is appropriate, the conclusion C is entailed by the context set S(k''), where k''=g(A₂,g(A₁,k)).

   Remember that for a sequence s=A₁,...,A_n to be appropriate in a context k₁, is for A₁ to be appropriate in k₁, A₂ to be appropiate in k₂=g(A₁,k₁), and in general for A_(i+1) to be appropiate in k_(i+1)=g(A_i,k_i). So the crucial difference between the above definition of reasonable inference and Stalnaker's definition is that we may assume C to be appropriate in k''.

3. Modus Tollens for subjunctive conditionals is the inference form:

   p []→ q
   ¬q
   ————
   ∴ ¬p.
   

   Prove that Modus Tollens for subjunctive conditionals is a vaid inference form on

   1. Stalnaker's semantics

   2. Lewis's semantics

4. (Extra Credit)

   Contraposition for indicative conditionals is the inference form:

   p ⊃ q
   ————
   ∴ ¬q ⊃ ¬p.
   

   1. Is contraposition for indicative conditionals a reasonable inference on Stalnaker's semantics?

      (You may assume either Stalnaker's official definition, or the revised version given above. Make sure to state which definition you're using)

   2. Are there any plausible pragmatic conditions on appropriateness for indicative conditionals that could be added to Stalnaker's account in order to render contraposition a reasonable inference according to any definition on which you found it not to be reasonable?

   (For both parts of this problem you should assume Stalnaker's pragmatic condition on appropriateness for indicatives, as well as the general appropriateness condition given the appendix.)

Due Date for Exercises: Tuesday, 19 April 05.

This page created by Delia Graff
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