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XVI. CHAPTER SIXTEEN: INDUCTIVE LOGIC
A. General Theory
1. If q deductively follows from p, then it follows from p r no matter what r
happens to be. But if q inductively follows from p, then does it follow from p r
no matter what r happens to be? (Explain and give examples.)
2. Critically evaluate (giving original examples): “Induction goes from the less
general to the more general”.
3. Statistics indicate a rough inverse correlation between income and rate of crime:
the lower the income, the higher the rate of crime. Using one of Mill‘s Methods,
we might conclude that low income is the cause of crime. But could we somehow
use Mill’s Methods (plus more investigation) to prove that other factors “really”
are the cause of crime? How might this happen?
A. Answers (only partial, since these are meant to involve explanation and examples
given by the student)
B. True and False
1. If the premises of a valid inductive argument are true, then so is its conclusion.
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2. An argument may be inductively valid, even though deductively invalid, provided
its premises present evidence that constitutes good grounds for accepting its
conclusion.
3. There is no more reason to doubt the conclusion of a valid deductive argument
than there is to doubt its premises. Similarly there is no more reason to doubt the
conclusion of a valid inductive argument than there is to doubt its premises.
4. Adding relevant premises to an inductive argument will generally alter either its
conclusion or the probability of its conclusion.
5. Valid inductive arguments should include all known relevant information.
6. In analogical reasoning, we often reason from the more general to the less
general, which contradicts the old saw that inductive reasoning moves from the
less general to the more general.
7. Mill’s Methods are methods for finding cause effect relationships and hence are
not inductive, since once we find a causal connection we can reason with certainty
about it, but inductive reasoning is never certain.
8. It often is claimed that we don’t really need analogical arguments since all
conclusions drawn analogically can be drawn by means of other kinds of
inductive arguments (plus deductive arguments).
9. Analogical arguments are inferior to standard inductive generalizations in that the
conclusion of an analogical argument is less probable, given certain evidence,
than the conclusion of an inductive generalization based on the same evidence.
B. Answers
C. Probability
1. Suppose we use an honest (symmetrical) pair of dice, and toss them randomly.
a. What is the probability of getting a deuce (“snake eyes”) on a given toss?
b. A seven?
c. An eleven?
d. A twelve?
e. Suppose you toss a six. Is it more or less probable that you will get a seven
before tossing another six? Why?
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2. Suppose we randomly draw cards from a standard deck. What is the probability of
getting:
a. an ace on a given draw?
b. a spade?
c. a flush (five cards of the same suit) when drawing five cards?
d. at least one spade in a five card draw, given that the first card is a club?
C. Answers
1. a. 1/36