philosophy discussion
Valerielee
13.2SolutionstoConfirmationParadoxI.pdf
8/28/2015
1
Phil 2: Puzzles and Paradoxes
Prof. Sven Bernecker
University of California, Irvine
Lecture 13.2
Solutions to the
Confirmation Paradox I
Two Assumptions of the Ravens
Paradox
2
EC. If two hypotheses can be known a priori to be equivalent, then
any data that confirm (disconfirm) one hypothesis also confirm
(disconfirm) the other.
IC. A generalization is confirmed by any of its instances
Paradox of the Ravens
1) A brown shoe confirms the hypothesis that all non-black things are non-ravens. (IC)
2) The hypothesis that all non-black things are non-ravens is equivalent to the hypothesis that all ravens are black. (EC)
C) Therefore, a brown shoe confirms the hypothesis that all ravens
are black.
3
The conclusion seems absurd. Data relevant to whether or not all ravens are black must be data about ravens. The color of shoes can have no bearing whatsoever on the matter. Thus IC and EC – apparently acceptable principles – lead to an apparently unacceptable conclusion.
Solutions to Confirmation Paradox
• Denial of the Equivalence Condition
• Acceptance of the apparently unacceptable conclusion
(Hempel‘s solution)
• Denial of the Instance Condition
4
8/28/2015
2
Denial of Equivalence Condition
• One might respond to the raven paradox by denying EC, and saying
that generalizations are never confirmed by the instances of logically
equivalent generalizations.
• Implausible: If we are wondering whether everyone who has a disease
was exposed to chemical X, it seems as though we could provide
support for this claim by showing that everyone not exposed to
chemical X does not have the disease.
5
EC. If two hypotheses can be known a priori to be equivalent, then
any data that confirm (disconfirm) one hypothesis also confirm
(disconfirm) the other.
Putative counterexample to EC:
• Consider the following piece of evidence:
(C) The card which is facedown on the table is a face card.
This seems to confirm:
(H1) The card on the table is a red jack.
But does not seem to confirm:
(H2) The card on the table is red.
• But (H2) is a logical consequence of (H1) - so why, if (C) confirms (H1),
does (C) not also confirm every other theory that must be true if (H1) is?
More to the point: if evidence can confirm a theory without confirming
logical consequences of that theory, there seems no reason why EC
could not be false.
6
• What’s going on with the example of the card? There are 52
possibilities for what the random card in a deck can be and hence,
before learning (C), one regards the probability of (H1) being true
as 1 in 52. Upon learning (C), the relevant possibilities are reduced
to the 12 face cards, which makes the probability of (H1) being true
1 in 12 - hence (C) confirms (H1), because it makes it more likely
that - is evidence that - (H1) is true.
• Before learning (C), there is a 26/52 chance - i.e., ½ - that (H2) is
true. After (C) narrows the relevant possibilities to the 12 face
cards, there is a 6/12 chance - still ½ - that (H2) is true. So (C)
does not confirm (H2).
7
• What this shows is that sometimes evidence can eliminate possibilities
in such a way that it makes one hypothesis A significantly more likely
to be true but does not do this for a second hypothesis B, even though
every possibility in which A is true is also one in which B is true.
• This is possible if hypothesis B is true in some possibilities in
which hypothesis A is not, and the possibilities eliminated by the
evidence eliminate a greater proportion of those in which A is
false than those in which B is false.
• Conclusion: the card example is no challenge to the Equivalence
Condition.
8
