What is Inductive Reasoning?
Inductive reasoning is a form of logical argument where premises provide some degree of support for the conclusion, but not total support. This is different from deductive reasoning, where all premises provide total support for the conclusion reached, so long as the premises are both valid and true. Inductive reasoning is also known as bottom-up logic since it works from a range of partially supportive premises, the bottom, to reach a conclusion, the top. Inductive reasoning is sometimes framed as using specific evidence to reach a general conclusion, and while this is a form of inductive reasoning there are many other forms of induction in logic.
The inductive generalization is the most common form of inductive reasoning. Inductive generalizations take a sample size of a community, sometimes as few as one subject, looks at a trait of those subjects, and reasons this trait must be common in the rest of the community. This can be written out as:
- Sample A from Population C has Trait B
- Population C has Trait B
Here are a few examples of inductive generalizations:
- A toy factory makes crates of toys.
- Half the toys in one crate are rubber balls.
- Half the toys in all the crates are rubber balls.
- There are forty student groups on campus
- Five student groups are 50% men and 50% women
- All student groups are 50% men and 50% women
Statistical syllogisms are another common form of inductive reasoning based on a non-deductive syllogism. In syllogisms two premises are combined to reach a conclusion, statistical syllogisms simply use statistics or probabilities as premises. The formula for this argument is:
- X portion of population A is C
- B is part of population A
- B is C
The following are samples of statistical syllogisms:
- Almost all sixteen year olds are high school students
- Brian is sixteen years old
- Brian is most likely a high school student
- Only 10% of people are left handed
- Hannah is a person
- Hannah is most likely not left handed
Another, more complicated form of inductive argument is the argument from analogy. This argument involves listing the similar traits of two subjects, then inferring they share another trait because of this. The argument can be described as:
- A and B have properties 1, 2, and 3
- A also has property 4
- Therefore, B might also have property 4
Here are a few examples of arguments from analogy:
- Magpies and crows are both birds with black feathers who can mimic other animals
- Magpies also like shiny objects
- Therefore, crows might also like shiny objects
- Spiders and scorpions are arachnids who hunt other animals for food and are venomous
- Spiders bite their prey
- Therefore, scorpions might bite their prey
Since inductive reasoning relies on drawing possible conclusions from generalizations, it is easy for induction to draw the wrong conclusion even with correct evidence. If, for instance, Example University accepts 75% of all applicants and Bob Generic applies as a student, it is likely that he will be accepted. It is not certain, however, since there is still a 25% chance he will not be accepted. Other potential problems for inductive reasoning are biases in data or hasty generalizations that are not supported by facts.