Inductive Arguments: Enumerative and Causal

Question 1

Strong Inductive argument

Answer 1

An inductive argument in which if the premises are true, the the conclusion is probably true.

Question 2

Cogent Inductive argument

Answer 2

An inductive argument that is strong and has true premises.

Question 3

Enumerative Inductive Arguments

Answer 3

Argument patterns in which we reason from premises about individual members of a group to conclusions about the group as a whole.

Form: X percent of the observed members of a group A have property P.
Therefore, probably Y percent of all members of group A have property P.

Ex: Most peace activists I know are kind-hearted. So, probably most peace activists are kind-hearted.

Question 4

Target Population of Inductive Generalization

Answer 4

The target group or the group as a whole.
Ex: Most Christians I know go to church. So, probably all Christians go to church.
Target Population: All Christians.

Question 5

Sample Population of Inductive Generalization

Answer 5

The observed members of the target group.
Ex: Most Christians I know go to church. So, probably all Christians go to church.
Sample Population: Most Christians

Question 6

Relevant property of Inductive Generalization

Answer 6

The property we are interested in.
Ex: Most Christians I know go to church. So, probably all Christians go to church.
Relevant Property: Go to church

Question 7

Causal Claim

Answer 7

A causal claim is a statement about the cause(s) of a thing.

Question 8

Sufficient Causal Condition

Answer 8

Condition C is a sufficient causal condition for event E just in case if C occurs, then E occurs.

Question 9

Necessary Causal condition

Answer 9

Condition C is a Necessary Causal condition for event E just in case if C does not occur, then E does not occur.

Question 10

Necessary and Sufficient causal condition

Answer 10

Condition C is a Necessary and Sufficient causal condition for event E just in case C occurs if and only if E occurs.

Question 11

Causal Argument

Answer 11

An inductive argument whose conclusion is a causal statement.

Question 12

Method of Agreement

Answer 12

Look for factors that each instance has in common: if two or more occurrences of a phenomenon have only one relevant factor in common, that factor is probably the cause.

Schematic form: 
Case 1: a, b, c > E
Case 2: a, d, f > E
Case 3: a, g, h, > E
Therefore: a probably caused E.

Question 13

Negative use of Method of Agreement

Answer 13

Shows that E does not occur in one of the cases in which a is present.

Schematic form: 
Case 1: a, b, c > -E
Case 2: a, d, f > -E 
Case 3: a, g, h > -E 
Therefore: a probably does not cause E.

Question 14

Method of Difference

Answer 14

Look for factors that are points of difference among the instances: the relevant factor present when a phenomenon occurs and absent when the phenomenon does not occur is probably the cause.

Schematic form:
Case 1: a, b, c > E
Case 2: -, b, c > -E
Therefore, a is probably the cause of E

Question 15

Negative use of the Method of Difference

Answer 15

Shows that E occurs when a is absent

Schematic form:
Case 1: a, b, c > E
Case 2: -, b, c > E
Therefore, a is probably not the cause of E

Question 16

Joint Method of Agreement and Difference

Answer 16

Look both for factors in common and points in difference among the cases: the cause is likely the factor isolated when (i) identify the relevant factors common to occurrences of the phenomena (The Method of Agreement), and (ii) discard any of these that are present even when there are no occurrences of the phenomena(The Method of Difference).

Question 17

Schematic form for the Joint Method of Agreement and Difference

Answer 17

Case 1: a, b, c > E
Case 2: -, b, c > -E 
Case 3 : a, d, f > E
Case 4: -, d, f > -E 
Case 5: a, g, h > E
Case 6: -, g, h > -E
Therefore a is probably the cause of E.
Notice cases 1, 3, and 5 are Method of Agreement, while (1 and 2), (3 and 4), (5 and 6) are Method of Difference.

Question 18

Method of Concomitant Variation

Answer 18

If quantitative changes in the effect are associated with quantitative changes in a given factor (i.e. they vary concomitantly), then the factor is probably causally related to the effect.

Schematic Form: 
Case 1: Factors a-, b, c >E-
Case 2: Factors a, b, c > E
Case 3: Factors a+, b, c > E+ 
Therefore, a is causally connected with E.

Ex: Smoking is often followed by lung cancer. Indeed, researchers have found that the more you smoke the more likely you are to get lung cancer, the less you smoke the less likely you are to get lung cancer. Therefore, smoking probably causes lung cancer.

Limitations: does not tell us whether a is a necessary or sufficient cause of E.

Question 19

Negative Use for Concomitant Variation

Answer 19

quantitative changes in a do not vary concomitantly with quantitative changes in E. Thus, a is not causally related to E.

Question 20

Method of Residues

Answer 20

If in a given case where E occurs, the factors other than a only explain a part of E, then a probably is the cause of the remainder of E.

No Schematic form: We begin with the knowledge that E occurs in the presence of a, b, and c, and with the knowledge that b and c are only causally responsible for part of the effect. From this information we infer that a be responsible for the reminder of E.
Ex: John weighs 160 pounds. When he stands on the scale with his doe, the scale reads 180 pounds. So the dog must weigh 20 pounds.