1.1.x. Exercise questions

1.

Some of the following references to arguments refer to the same argument in different ways (remember that changing the order of premises or the number of times a given premise is referred to does not change the argument being referred to). If Γ stands for the sentences φ, χ, θ, what are the different arguments referred to below? Identify each by listing the sentences making up its premises and conclusion, and tell which of the following refer that argument:

  a. φ, ψ, χ / θ f. φ, θ, ψ, θ / χ
  b. θ, φ, ψ / χ g. Γ, φ / ψ
  c. χ, φ, ψ / θ h. Γ / θ
  d. Γ / ψ i. χ, θ, φ / ψ
  e. Γ, ζ / ψ h. Γ, ψ / χ
2. The basis for testing a scientific hypothesis can often be presented as an argument whose conclusion is a prediction about the result of the test and whose premises consist of the hypothesis being tested together with certain assumptions about the test (e.g., about the operation of any apparatus being used to perform the test).
hypothesis to be tested:   hypothesis ⎫

assumptions about the test:
 ⎧
⎨
⎩ 		assumption
⋮
assumption 		⎬
⎪
⎭ 		premises
   
   
prediction of the test result:   prediction   conclusion
Suppose that the prediction is entailed by the hypothesis together with the assumptions about the test (i.e., suppose that the argument shown above is valid) and answer the following questions:
  a. Can you conclude that the hypothesis is true on the basis of a successful test (i.e., one for which the prediction is true)? Why or why not?
  b. Can you conclude that the hypothesis is false on the basis of an unsuccessful test (i.e., one for which the prediction is false)? Why or why not?
Glen Helman 15 Aug 2006