philosophy discussion

8/28/2015

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Accepting the Conclusion

• Why not say that a brown shoe (i.e., a non-black non-raven) does

confirm the hypothesis that all ravens are black?

• Suppose that you are on an ornithological field trip. You have seen

several black ravens in the trees and formulate the hypothesis that

all ravens are black. You then catch sight of something brown in the

topmost branch. For a moment you tremble for the hypothesis,

fearing a counterinstance -- fearing that you have found a brown

raven. A closer look reveals that it is a shoe. In this situation you are

likely to agree that a brown shoe confirms the hypothesis.

• But this would mean that indoor ornithology is possible!

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• Hempel thinks that “the impression of a paradoxical situation is not

objectively founded; it is a psychological illusion.” He claims that the air

of paradox vanishes once we realize that the hypothesis “All ravens are

black” is not merely about ravens. For, anyone who holds this

hypothesis also holds the view that every object is such that it is either a

raven or not black, or, equivalently, that nothing is a non-black raven.

• The air of paradox disappears when the number of objects under

consideration is small.

• “All ravens are black” is supported by observation of any object that is

not a non-black non-raven. General moral: if evidence doesn't

contradict a hypothesis, then it supports the hypothesis.

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Three Problems with Accepting the

Conclusion

• 1) It’s not clear that some fact which just raises the probability of a

hypothesis thereby constitutes positive evidence for it.

• Counterexample: The publication of Kant’s Critique of Pure Reason

(1781) increased the probability that it will be turned into a

blockbuster film starring Jennifer Aniston. After all, if the Critique of

Pure Reason had never been published, the chances of its being

made into a film would be even smaller than they are. But surely the

actual publication of this book is not positive evidence for the

hypothesis that this book will be turned into a blockbuster film.

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• 2) We may require that E is positive evidence for H only if E

makes H’s probability sufficiently high, say above 0.5. So let’s

say:

E is confirming evidence for H if and only if Prob(H/E) ≥ 0.5

• Counterexample: H is the hypothesis that Tom is not

pregnant, while E is the statement that Tom smokes. Since

the probability of H is extremely high, the probability of H

given E (H/E) is also extremely high -- above 0.5. Yet

intuitively E is no evidence for H.

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8/28/2015

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• 3) My brown shoe not only confirms the hypothesis “All

ravens are black“ but also the hypothesis “All ravens are

white.“ For my brown shoe is a non-white non-raven. But

one and the same observation cannot confirm two mutually

exclusive hypotheses!

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Denial of Instance Condition

• Counterexample: Consider the hypothesis “All ravens live outside

Orange County”. According to IC, any raven found outside of Orange

County confirms the hypothesis. But the sighting of ravens outside of

Orange County, particularly in adjoining counties with similar climate

and environs, actually disconfirms the hypothesis. Unless we find some

special reason for excluding them from Orange County, the more

pervasive their presence in surrounding areas the less likely they are to

be absent from Orange County.

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IC. A generalization is confirmed by any of its instances

Another counterexample to IC:

• Three people leave a party each wearing one of the three

hats they arrived with. The hypothesis “Each person is

wearing someone else’s hat” is disconfirmed (even

falsified) by the two confirming instances “person A is

wearing person B’s hat” and “person B is wearing person

A’s hat”.

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Replacing the Instance Condition

• The problem of IC is that it takes no account of the role of

background information in inductive reasoning. Confirmation is not

simply the accumulation of confirming instances.

• We need to take into account background knowledge. In the case of

ravens‘ color, this background knowledge will include the fact that

birds‘ plumage serves to protect their species by camouflaging

them. So it‘s more important to look for ravens in different

environments – temperate, tropical, snowy – than to accumulate

more evidence about ravens in our own environment.

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8/28/2015

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What is the correct principle determining what makes a body of data

confirm a hypothesis? Reformulation of IC:

• Example: “A” stands for lobsters, “B” stands for being red, and “H”

stands for being boiled. Having observed lots of red lobsters does

not confirm the hypothesis that all lobsters are red if all the observed

ones have been boiled and if one knows that lobsters become red

when they are boiled.

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IC*: A hypothesis “All As are Bs” is confirmed by its instances if and

only if the data do not say, of some property H that the As in the data

are H, and if they had not been H they would not have been Bs.