The '''Principle of induction''' is the fundamental precept of modern science. Without it, [[experiment]]s could not confirm a [[hypothesis]], and nothing in the physical universe could be predicted with any confidence. Thus there could be no natural laws or scientific truths.
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?
<blockquote>''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.'' <ref>“Everything and more, a compact history of infinity” by David Foster Wallace (Weidenfeld, 2003)</ref> </blockquote>
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. All scientific [[theory|theories]] are based on the Principle of Induction.
However, there is no way of truly knowing for certain that something will happen again in the future. The more often something behaves as predicted, the less likely it becomes that it will ever behave differently, but extreme unlikelihood is not the same as impossibility. If an apple suddenly fell upward from a tree, the whole of [[science]] would have to be reinvestigated and changed to accommodate the new information. Until then the theory that works remains the one that is used to predict future events. All science does is to try and predict what will happen in certain circumstances based on prior behavior.
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. <ref> http://www.kisekaeworld.com/Intractable/intractable.html?issue9.html </ref>
==References==
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[[category:mathematics]]
