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.)

Accepted Answer

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".

Accepted Answer

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?

Accepted Answer

Mill's Methods, specifically the method of difference, can be used to help establish causation between low income and crime. This method involves comparing situations where the effect is present with situations where the effect is absent, and identifying the difference between the two.

In the case of low income and crime, we could use this method to compare areas with similar income levels but differing crime rates. If we find that there are areas with low income but low crime rates, or areas with high income but high crime rates, it would indicate that there are other factors at play besides income.

Further investigation could then be conducted to identify these other factors. This might involve looking at social and economic factors such as education levels, employment opportunities, access to resources, and community support systems. It could also involve considering psychological and behavioral factors such as individual resilience, coping mechanisms, and social support networks.

By using Mill's Methods as a starting point and then conducting more in-depth investigation, we can potentially uncover the complex web of factors that contribute to crime, and ultimately establish a more nuanced understanding of the causes of crime beyond just low income.

Question 4

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

Accepted Answer

The answer of True and False
-If the premises of a...

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.

Accepted Answer

The answer of True and False
-An argument may be inductively...

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.

Accepted Answer

The answer of True and False
-There is no more reason...

Question 7

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

Accepted Answer

The answer of True and False
-Adding relevant premises to an...

Question 8

True and False
-Valid inductive arguments should include all known relevant information.

Accepted Answer

The answer of True and False
-Valid inductive arguments should include...

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.

Accepted Answer

The answer of True and False
-In analogical reasoning, we often...

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.

Accepted Answer

The answer of True and False
-Mill's Methods are methods for...

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).

Accepted Answer

The answer of True and False
-It often is claimed that...

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.

Accepted Answer

The answer of True and False
-Analogical arguments are inferior to...

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?

Accepted Answer

The answer of Probability
-Suppose we use an honest (symmetrical) pair...

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?

Accepted Answer

The answer of Probability
-Suppose we randomly draw cards from a...

Quiz 16: Inductive Logic

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.)

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

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

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.

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.

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

True and False -Valid inductive arguments should include all known relevant information.

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.

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.

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).

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.

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?