philosophy

Deduction vs. Induction

Deductive arguments intend to establish the certainty of the conclusion on the basis of the premises.

Inductive arguments intend only to supply evidence (support) that the conclusion is probably true. The

probability of the conclusion of a valid deductive argument given that the premises are true is 1. The

probability that the conclusion of an inductive argument is true given the truth of its premises is less

than 1. The lower this probability figure, the weaker the inductive argument. By their nature, all

inductive arguments are deductively invalid – because all inductive arguments are ampliative.* Some

inductions are good (strong), so not every deductively invalid argument is worthless. Whether an

inductive argument is strong or weak (and hence whether an invalid argument taken as an induction is

good or bad) depends on the evidentiary relationship between the premises and the conclusion.

Deductive arguments are evaluated as being either valid or invalid (perfect or imperfect). Inductive

arguments are evaluated on a continuum from strong at one end to weak at the other. “Stronger” and

“weaker” are good terms to use.

Examples of inductive arguments follow. Notice how all are deductively invalid; all the arguments are

ampliative).

1. John was absent the first day of class. John was absent the second day of class. Therefore, John will be

absent the next class. [a weak induction.]

2. John was absent the first day of class. John was absent the second day of class. John was absent the

third day of class. John was absent the fourth day of class. John was absent the fifth day of class.

Therefore, John will never show up (maybe he dropped the class or died). [This might be a strong

inductive argument; it is certainly stronger than the first example.] This is "enumerative induction."

2a. Note that this argument is deductively valid: 1. John was absent on day 1. 2. John was absent on day 2. 3. John was

absent on day 3. … N. John was absent on day N. N+1. There are only N days in this class. Therefore, John was never in class.

3. [An argument I made up a few years ago.] The Phillies have the best four-pitcher rotation in the major

leagues. Howard, Utley, Victorino, Rollins, and Ruiz are all healthy and starting to hit well. The Phillies

have overall the best defense in both leagues (they commit the fewest number of errors). Therefore, the

Phils will (probably) win the World Series this year. [You would count this as a strong induction if you

would be willing to bet even money on the conclusion.]

4. John has been absent from class half the semester. He’s not dead (so says his mother). He’s not in the

hospital (there’s only one in our town, and he’s not there). The registrar says he has not dropped the

class. The police say he’s not in jail – his fingerprints are not in the system. What could explain his

absences? He has a demanding job? A demanding GF? He’s not really absent, but silent and invisible?

*Ampliative: an argument is ampliative if there is more information in the conclusion than in the

premises. All inductions are ampliative. Valid deductions are nonampliative: the information in the

conclusion is equal to or less than the information in the premises.