Principle of induction - Revision history

SamHB: Take out "says concerning".

2019-09-04T02:24:18Z

Take out "says concerning".

Conservative at 19:42, September 3, 2019

2019-09-03T19:42:54Z

Conservative at 19:41, September 3, 2019

2019-09-03T19:41:52Z

AK: intlink

2017-09-28T09:28:06Z

intlink

Aschlafly: Reverted edits by Rogerramsey34 (talk) to last revision by PatrickD

2012-04-17T04:46:21Z

Reverted edits by Rogerramsey34 (talk) to last revision by PatrickD

PatrickD: Low-class theories get refuted all the time.

2009-11-07T04:05:08Z

Low-class theories get refuted all the time.

PatrickD: Huge rewrite. Stepping closer to controversial topics than is usual for me!

2009-11-07T03:58:56Z

Huge rewrite. Stepping closer to controversial topics than is usual for me!

PatrickD: Took 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?

2009-10-31T03:50:56Z

Took 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?

PatrickD: Put super-quick example into the intro.

2009-10-31T02:03:37Z

Put super-quick example into the intro.

DWiggins: cleared up some misconceptions

2009-10-30T14:27:13Z

cleared up some misconceptions

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 <blockquote>''The Principle of Induction 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>
-The Internet Encyclopedia of Philosophy says concerning inductive reasoning:
+The Internet Encyclopedia of Philosophy puts it this way:
 {{Cquote|Here is a mildly strong inductive argument:

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 Every time I've walked by that dog, it hasn't tried to bite me. So, the next time I walk by that dog it won't try to bite me.
-An inductive argument is an argument that is intended by the arguer to be strong enough that, if the premises were to be true, then it would be unlikely that the conclusion is false. So, an inductive argument's success or strength is a matter of degree, unlike with deductive arguments. There is no standard term for a successful inductive argument, but this article uses the term "strong." Inductive arguments that are not strong are said to be weak; there is no sharp line between strong and weak. The argument about the dog biting me would be stronger if we couldn't think of any relevant conditions for why the next time will be different than previous times. The argument also will be stronger the more times there were when I did walk by the dog. The argument will be weaker the fewer times I have walked by the dog. It will be weaker if relevant conditions about the past time will be different next time, such as that in the past the dog has been behind a closed gate, but next time the gate will be open.
+An inductive argument is an argument that is intended by the arguer to be strong enough that, if the premises were to be true, then it would be unlikely that the conclusion is false. So, an inductive argument's success or strength is a matter of degree, unlike with [[deduction|deductive]] arguments. There is no standard term for a successful inductive argument, but this article uses the term "strong." Inductive arguments that are not strong are said to be weak; there is no sharp line between strong and weak. The argument about the dog biting me would be stronger if we couldn't think of any relevant conditions for why the next time will be different than previous times. The argument also will be stronger the more times there were when I did walk by the dog. The argument will be weaker the fewer times I have walked by the dog. It will be weaker if relevant conditions about the past time will be different next time, such as that in the past the dog has been behind a closed gate, but next time the gate will be open.
 An inductive argument can be affected by acquiring new premises (evidence), but a deductive argument cannot be. For example, this is a reasonably strong inductive argument:

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 David Foster Wallace stated it this way:
 <blockquote>''The Principle of Induction 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>
 ==Induction, and Deduction, in Natural Science==

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 <small>''This article is about the term as it is used in the sciences.  For mathematical induction, see [[Proof by induction]]''</small>
-The '''principle of induction''' is perhaps most succinctly described as the reason that we believe that the Sun will rise tomorrow.  It is a form of reasoning whereby general statements are derived from a collection of singular observations.
+The '''principle of induction''' is perhaps most succinctly described as the reason that we believe that the Sun will rise tomorrow.  It is a form of reasoning whereby [[Generalization|general statements]] are derived from a collection of singular observations.
 If something seems to happen repeatedly, such as an apple falling to the ground when it leaves the tree, one can use this prior behavior to predict what will happen next.  The reason we believe that the Sun will rise tomorrow is that it has done so, without exception, countless times in the past.

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 But they are not actual theorems, and they could be "falsified" by observations that are inconsistent with the predictions.  When such inconsistencies arise, they are generally fairly minor:  If we were to observe apples falling upward tomorrow, it would upset our world view in a catastrophic manner.  The universe ''really does'' appear to behave consistently; that's what make scientific induction work in the first place.  But, in the end, it's a matter of human belief.
-Observations that falsify scientific theories are generally fairly minor, and often lead to extensions of the theories.  Quantum mechanics has overthrown our interpretation of F&nbsp;=&nbsp;ma, but that formula is still accepted as extremely important and very nearly true.
+Observations that falsify well-established scientific theories are generally fairly minor, and often lead to extensions of the theories.  Quantum mechanics has overthrown our interpretation of F&nbsp;=&nbsp;ma, but that formula is still accepted as extremely important and very nearly true.
 ==Falsifiability==
-An important aspect of a scientific theory is the notion of "falsifiability", made famous by philosopher [[Karl Popper]].  Simply put, a theory is falsifiable if one could imagine circumstances under which it wouldn't be true.  If one can't, then the theory may not be scientifically acceptable.  For example, gravity might have been an inverse-cube law.  Observations were performed that led Isaac Newton to conclude that it was an inverse-square law.  An inverse-cube law would have led to different observations.  A theory that says, for example, "blue is a triangular color", is unfalsifiable.  One couldn't conceive of an experiment to test it.  Unfalsifiable "scientific theories" are generally met with great skepicism.
+An important aspect of a scientific theory is the notion of "falsifiability", made famous by philosopher [[Karl Popper]].  Simply put, a theory is falsifiable if one could imagine circumstances under which it wouldn't be true.  If one can't, then the theory may not be scientifically acceptable.  For example, gravity might have been an inverse-cube law.  Observations were performed that led Isaac Newton to conclude that it was an inverse-square law.  An inverse-cube law would have led to different observations.  A theory that says, for example, "blue is a triangular color", is unfalsifiable.  One couldn't conceive of an experiment to test it.  Unfalsifiable "scientific theories" are generally met with great skepticism.
 <!-- 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.

← Older revision	Revision as of 04:46, April 17, 2012
(No difference)

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 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==
 *[[Proof by induction]]

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 <small>''This article is about the term as it is used in the sciences.  For mathematical induction, see [[Proof by induction]]''</small>
-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.
+The '''principle of induction''' is perhaps most succinctly described as the reason that we believe that the Sun will rise tomorrow.  It 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 accepted 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 reason we believe that the Sun will rise tomorrow is that it has done so, without exception, countless times in the past.
 <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. It is commonly accepted that scientific [[theory|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.
+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>
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 [[category:mathematics]]