Deck 16: Inductive Logic

Question 1

General Theory
-If $q$ deductively follows from $p$ , then it follows from $p \cdot r$ no matter what $r$ happens to be. But if $q$ inductively follows from $p$ , then does it follow from $p \cdot r$ no matter what $r$ happens to be? (Explain and give examples.)

Answer 1

No, since $r$ could affect the strength of the argument.

Question 2

General Theory
-Critically evaluate (giving original examples): "Induction goes from the less general to the more general".

Answer 2

There are cases of inductive arguments that go from the more general to the less general, or from particular cases to other particular cases.

Question 3

General Theory
-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?

Answer 3

Not Answered

Question 4

True and False

-If the premises of a valid inductive argument are true, then so is its conclusion.

Question 5

True and False

-An argument may be inductively valid, even though deductively invalid, provided its premises present evidence that constitutes good grounds for accepting its conclusion.

Question 6

True and False

-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.

Question 7

True and False

-Adding relevant premises to an inductive argument will generally alter either its conclusion or the probability of its conclusion.

Question 8

True and False

-Valid inductive arguments should include all known relevant information.

Question 9

True and False

-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.

Question 10

True and False

-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.

Question 11

True and False

-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).

Question 12

True and False

-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.

Question 13

Probability
-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?

Question 14

Probability

-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 $\textbf{ same }$ suit) when drawing five cards?
d. at least one spade in a five-card draw, given that the first card is a club?