Principle of induction

This article is about the term as it is used in the sciences. For mathematical induction, see Proof by induction

The principle of induction is a form of reasoning whereby general statements are derived from a collection of singular observations. It was once thought to be an accurate description of the scientific method, but this was thoroughly critiqued by Karl Popper. As such, although induction is commonly accepte4d as playing a part in the scientific method, specifically in the theory formation stage, the testing stage is actually a deductive process.

When you get out of bed in the morning, how do you know your bedroom floor will not collapse under your weight? When you watch the sun set, how do you know it will rise again tomorrow?

The PI states that if something x has happened in certain particular circumstances n times in the past, we are justified in believing that the same circumstances will produce x on the (n + 1)th occasion.

If something seems to happen repeatedly, such as an apple falling to the ground when it leaves the tree, you can use this prior behavior to predict what will happen next. It is commonly accepted that scientific theories are formulated through the Principle of Induction, but importantly, they are not testing through this procedure. Whilst the above examples may appear logical, simply because the sun has risen on every day throughout human existence it does not actually follow that it will do so tomorrow, or any other day yet to come. The expectation that it will is a psychological process, leading to a belief, not a logical process leading to a fact. Nor, as is commonly thought, does the probability that something will happen in future simply because it has happened in the past increase as the number of supporting observations increases. Again, this is simply a perception and has no basis in logical reasoning.

An example of the use of the Principle of Induction is the concept of numbers which are too big for any existing or foreseeable computers to calculate. This is known as Bremermann’s limit.

See also

• Proof by induction