philosophy paper 3

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Three Notions of Evidence

• Classificatory (qualitative) evidence: We ask whether a body of

information confirms (is evidence for or supports) a given

hypothesis.

• E.g., is the fact that the moon’s surface appears blotchy through

the telescope evidence that there are craters on the moon (as

Galileo claimed in 1610)?

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• Quantitative evidence: We assess the degree to which a body

of information confirms or supports a hypothesis.

• E.g., to what extent is Galileo’s hypothesis about the lunar

surface supported by his telescopic observations.

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• Comparative (relational) evidence: We ask whether a body of

information confirms a certain hypothesis more than some

body of information supports a competing hypothesis.

• E.g., does the fact that the moon’s surface appears blotchy

through the telescope support the hypothesis that the moon

contains craters more than it supports the hypothesis that the

telescope distorts the light coming from the moon (as

Galileo’s critics insisted).

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Classificatory Evidence: E confirms H

Quantitative Evidence: the degree of confirmation of H on E is U

Comparative Evidence: E confirms H more than E confirms H*

Question: When does a body of information provide classificatory

evidence for a general claim?

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Instance Condition

Examples of generalizations:

– All emeralds are green.

– Whenever the price of gasoline falls, its consumption rises.

– Everyone I have spoken to this morning thinks that the Democrats will

win the next election.

– All AIDS victims have such-and-such a chromosome.

• IC is also called “Nicod‘s criterion“

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IC. A generalization is confirmed by any of its instances

• The Instance Condition says that your evidence for a generalization is

stronger the more instances of it your total body of knowledge contains –

provided that it contains no counterinstances.

• According to the Instance Condition, any instance makes a positive

contribution, however slight, and however liable to be outweighted by

other factors, towards constituting classificatory and quantitative evidence.

• According to the Instance Condition, a single instance confirms but it may

not settle the matter. A single instance may not show that it is rational to

believe the generalization.

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IC. A generalization is confirmed by any of its instances

• When a generalization has the form

All As are Bs

An instance of it is any proposition of the form

This A is a B

• A counterinstances of a generalization “All As are Bs“ is a

proposition of the form

This A is not a B

• The opposition of confirmation is disconfirmation. An extreme

case of falsification. A generalization is falsified by any

counterinstance of it.

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Equivalence Condition

• Something can be known a priori if it can be known without appeal to

experience. Example: knowing that all bachelors are unmarried. (See

lecture 1.4, slide #2).

• Equivalence: if either hypothesis is true, so is the other, and if either one is

false, so is the other.

• If two propositions are connected by the phrase "if, and only if", they are

equivalent. (See lecture 10.1, slide #5)

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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.

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It is a priori knowable that any two of these three hypotheses are

equivalent:

R1 All ravens are black

R2 There are no ravens that are not black

R3 Everything non-black is a non-raven/

All non-black things are non-ravens

If R1 is true, so is R2. Also if R1 is true, any non-black thing is not a raven,

or, as R3 puts it, is a non-raven. So if R1 is true, so is R3. Suppose R1 is

false. Then some ravens are not black, contrary to R2. It also means that

some things that are not black are not ravens, so R3 is false too. R1, R2

and R3 are equivalent.

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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.

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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.

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Alternative formulation of the raven paradox:

1)The theses:

– R1 All ravens are black

– R3 All non-black things are non-ravens

2)If two hypotheses are equivalent, then any datum that confirms

the one must also confirm the other – and will do so to the same

extent.

3)A black raven will confirm R1 and analogously a non-black non-

raven (such as a brown shoe) will similarly confirm R3.

4)But intuitively a brown shoe does not confirm R1.

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• The problem is that a brown shoe should confirm R3 to the

same extend as it confirms R1.

• What‘s the best way to find support for R3? Looking at things

which are not black will not get you very far, since they are so

numerous and varied.

• The best way to confirm R3 (and hence R1) is to look for

ravens and see what color they have, since there are far

fewer ravens than non-ravens.

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Possible Solutions to Confirmation

Paradox

• Denial of the Equivalence Condition

• Acceptance of the apparently unacceptable conclusion

(Hempel‘s solution)

• Denial of the Instance Condition

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