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Principle of induction (view source)
Revision as of 03:50, October 31, 2009
, 03:50, October 31, 2009Took out Bremermann's limit--it has nothing to do with this topic, though it is interesting. Can anyone think of a better home for it?
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 [[theory|theories]] are formulated through the Principle of Induction, but importantly, they are not tested 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.
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 [[theory|theories]] are formulated through the Principle of Induction, but importantly, they are not tested 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. <ref> http://www.kisekaeworld.com/Intractable/intractable.html?issue9.html </ref>
<!-- This statement and reference are interesting, but they have nothing to do with the topic of this page. If someone can find some other page (something in computer science?) to move it to, please do so.
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> -->
==See also==
==See also==
*[[Proof by induction]]
*[[Proof by induction]]