Introduction to Philosophy
20 March 2001
I. From
the problem of induction to the “new riddle of induction”
A. Hume’s problem concerns making induction reasonable. Apparently, there is
no non-inductive reason for induction. This is a problem for induction in
general.
B. Goodman’s new riddle concerns the
possibility that any particular inductive inference is no more confirmed (that is, supported
by the data) than indefinitely many others. This is a problem for individual
inductive inferences. Even if induction per se could be justified
through non-circular reasoning, what makes any particular application of it
better than another?
II. Goodman’s
“new riddle of induction”
A. Why, in any specific instance, is induction
justified and a counter-inductive inference unjustified (assuming this is the
case)? What make a hypothesis confirmed?
B. Suggestion: Confirmation is implication in reverse.
1. “All A’s are B” implies “this A is
B”—Deduction
2. Suggestion is that the confirmation
relation—which sustains an inductive inference—from “this A
is B” (and “that A is B” and “that other A is B”
and so on) to “All A’s are B” is just implication in
reverse.
1. Definition: an object is grue just in case either (i) it has been
observed to be green, or (ii) it has not yet been observed and it is blue.
2. Grue objects never change color.
3. Evidence that all emeralds are green consists
of emeralds that have been observed to be green.
4. All those emeralds are also grue.
5. The evidence is equally strong for two
hypotheses.
a. “Green” hypothesis: all
emeralds are green.
b. “Grue” hypothesis: all
emeralds are grue.
6. Hypotheses make different predictions.
a. Next emerald is green.
b. Next emerald is grue (therefore blue).
7. If confirmation is implication in reverse, grue
hypothesis—with its prediction—is as well confirmed as the green
hypothesis.
8. The problem can be recreated over and again:
‘gred,’ ‘grellow.’
9. Any amount of data still confirms indefinitely
many different hypotheses!
D. Other ways to understand the new riddle of
induction.
1. Graphs: why is the straightest line through the data
points best? Indefinitely many lines through any number of data points.
2. Data
a. A=1,
B=2
A=3,
B=6
A=4,
B=8
A=8,
B=16
b. Hypothesis 1: B=2xA
Hypothesis
2: B=(2xA)+((A-1)x(A-3)x(A-4)x(A-8))
c. Suppose A=6. Hypothesis 1 says B=12.
Hypothesis 2 says B= -48.
d. Both hypotheses imply the data; both hypotheses
are equally confirmed by the data.
e. Original question remains: Why is Hypothesis 1 better?
(We can assume it is better; but why is it?)