Testing hypotheses (cont.)


test implications—are normally conditional (if-then) statements of the form,

          “If conditions C occur then event E will occur”


“conditions C”:

·       Conditions of some experiment

·       Observed conditions


auxiliary hypothesis—hypothesis other than the test hypothesis which is assumed to be true

and is needed to derive the test implication


            “If H (test hypothesis) and A (auxiliary hypothesis) are true, then I (test implication) is




                   If childbed fever is caused by infectious matter (H) and chlorinated lime

destroys infectious matter (A), then if persons attending the patients wash

 their hands in a chlorinated lime solution (C) deaths from childbed fever will

 be reduced (E).


Forms of reasoning involving auxiliary hypotheses


Case 1—the test implication is true:


                   If H and A are true, then I (if C then E) is true.

                   I is true. (observation or outcome of experiment)

                   Therefore, H is true.


Case 2—the test implication is false:


                    If H and A are true, then I (if C then E) is true.

                   I is false. (observation or outcome of experiment)

                   Therefore, either H or A (and possibly both) are false.


According to Hempel, in order for a statement to qualify as a scientific hypothesis, it must be

empirically testable in principle


[I.e., There must be some conceivable observation or experiment the results of which

 would determine the truth or falsity of the hypothesis’s test implication.]


pseudo-hypothesis—a statement that appears to be a scientific hypothesis but fails the

       condition of empirical testability in principle


crucial test—a test (experimental or observational) intended to determine which of two

    rival hypotheses is true and which is false



                   If H1 is true, then I1 (if C then E1) is true.

                   If H2 is true, then I2 (if C then E2) is true.

                             [E1 and E2 are incompatible.]

C and E1. [outcome of experiment]

Therefore, H1 is true and H2 is false.



the “tower experiment” to decide between the geocentric (earth-centered) and

heliocentric (sun-centered) theories of the solar system



According to Hempel, “strictly construed, a crucial experiment is impossible in science.”

(p. 28)—reasons:

1.    Because auxiliary hypotheses are almost always needed to derive test implications from test hypotheses, it is impossible to disprove either of two competing hypotheses.

2.    Test hypotheses cannot be “conclusively proved by any set of available data.” (pp. 27-28)


ad hoc hypothesis—an auxiliary hypothesis introduced for the sole purpose of saving a test

      hypothesis being threatened by adverse evidence


example—the phlogiston theory: phlogiston as having negative weight


According to Hempel—

1.    There is no precise criterion for ad hoc hypotheses.

2.    An ad hoc hypothesis is motivated by the desire to protect someone’s favored test hypothesis from refutation by the results of experiments.

3.    Generally speaking, an ad hoc hypothesis leads to no additional test implications.