Inductive Logic

Inductive Arguments

  • The premises are intended to make the conclusion probable
  • Inductive arguments are
    • strong or weak
    • cogent or uncogent

Strong or Weak

  • An inductive argument is strong if it is probable (but not necessary) that, if the premises are true, then the conclusion is true.
  • An inductive argument is weak if it is not probable that, if the premises are true, then the conclusion is true.

Cogent or Uncogent

  • An inductive argument is cogent if it is strong with all true premises.
  • An inductive argument is uncogent if it is either weak or strong with at least one false premise.

Example

1.
Most Texans love football.
2.
Chris is a Texan.
∴ 3.
Chris loves football.

Common Inductive Forms

Statistical Syllogism

 

Form

1.
Over 50% of \(A\)s are \(B\).
2.
\(x\) is an \(A\)
∴ 3.
\(x\) is \(B\)

Example

1.
98% of Star Wars fans hate Jar Jar Binks.
2.
Joe is a Star Wars fan.
∴ 3.
Joe hates Jar Jar Binks.

Enumerative Induction

 

Form

1.
\(X\%\) of the observed members of group \(A\) have property \(P\).
∴ 2.
\(X\%\) of all members of group \(A\) have property \(P\).

Example

1.
82% of a randomly chosen sample of 600 American college students are sleep-deprived.
∴ 2.
Approximately 82% of American college students are sleep-deprived.

Analogical Induction

Form

1.
\(X\) has properties \(P_1\), \(P_2\), \(P_3\), plus property \(P_4\)
2.
\(Y\) has properties \(P_1\), \(P_2\), \(P_3\)
∴ 3.
\(Y\) probably has property \(P_4\)

Example

1.
Humans can walk upright, use simple tools, learn new skills, and devise inductive arguments.
2.
Chimpanzees can walk upright, use simple tools, and learn new skills.
∴ 3.
Chimpanzees can probably devise inductive arguments.

Argument from Authority

 

Form

1.
Authority \(A\) claims that \(P\)
∴ 2.
\(P\)

Example

1.
Neal deGrasse Tyson claims that Pluto is not a planet.
∴ 2.
Pluto is not a planet.

Abduction

Abduction

AKA Inference to the best explanation

Form

1.
Phenomenon \(X\) (or \(X\), \(Y\), \(Z\))
2.
Explanation \(E\) provides the best explanation for \(X\) (or \(X\), \(Y\), \(Z\))
∴ 3.
It is probable that \(E\) is true.

Abduction

AKA Inference to the best explanation

Example

1.
Anna told you she failed her physics midterm.
2.
Anna hasn’t been in physics class since your teacher graded the exams.
3.
Anna has been in sociology class, which meets right after physics.
∴ 4.
Anna probably dropped physics.

Sources

Crash Course. 2016. “How to Argue: Induction and Abduction.” Crash Course. February 22, 2016. https://thecrashcourse.com/courses/how-to-argue-induction-abduction-crash-course-philosophy-3/.
Howard-Snyder, Frances, Daniel Howard-Snyder, and Ryan Wasserman. 2013. The Power of Logic. New York: McGraw-Hill.
Pojman, Louis P., and Lewis Vaughn, eds. 2017. Philosophy: The Quest for Truth. 10th ed. New York: Oxford University Press.