Fallacy of extrapolation - Revision history

DavidE: /* See also */ added one

2020-02-17T15:31:17Z

‎See also: added one

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2019-04-09T12:03:49Z

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DavidB4-bot: /* Hubble constant */HTTP --> HTTPS [#1], replaced: http://www.youtube.com → https://www.youtube.com

2018-09-26T15:59:38Z

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2017-10-02T12:35:28Z

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2017-09-27T17:30:15Z

‎See also: adding See Also item

Conservative: /* Microevolution and Macroevolution */

2017-09-27T15:51:42Z

‎Microevolution and Macroevolution

DavidB4-bot: Spelling, grammar, and general fixes

2016-06-24T14:18:56Z

Spelling, grammar, and general fixes

DavidB4-bot: /* References */clean up

2016-06-23T20:48:02Z

‎References: clean up

AK: /* Hubble constant */ typo

2015-07-05T10:40:27Z

‎Hubble constant: typo

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2015-07-05T10:25:25Z

Wirkler, Hubble constant

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 *[[Generalization]]
 *[[Logic of possibility]]
 == References ==

@@ Line 11: / Line 11: @@
 |isbn=978-0-9790141-2-3
 |url=http://www.davidberlinski.org/deniable-darwin/about.php
-|quote=}}</ref> When attempting for an interpretation of research results, the scientist must be leery of extrapolating beyond the range of the data and conscious of the underlying assumptions to avoid drawing invalid conclusions.<ref>{{cite web |title=The fallacy of free extrapolation |author=Riegelman R. |publisher=Postgraduate medicine |date=September 1979 |issue=66(3)|pages=189–91, 194 |url=http://www.ncbi.nlm.nih.gov/pubmed/471851 |accessdate=October 31, 2013}}</ref>
+|quote=}}</ref> When attempting for an interpretation of research results, the scientist must be leery of extrapolating beyond the range of the data and conscious of the underlying assumptions to avoid drawing invalid conclusions.<ref>{{cite web |title=The fallacy of free extrapolation |author=Riegelman R. |publisher=Postgraduate medicine |date=September 1979 |issue=66(3)|pages=189–91, 194 |url=https://www.ncbi.nlm.nih.gov/pubmed/471851 |accessdate=October 31, 2013}}</ref>
 ==Valid vs. Fallacious Extrapolations==

@@ Line 36: / Line 36: @@
 |pages=0h:05min:00sec/1h:11min:39sec
 |accessdate=2012-10-14
-|url=http://www.youtube.com/watch?v=jWaOyy3WfWk
+|url=https://www.youtube.com/watch?v=jWaOyy3WfWk
 |quote=He also discovered that the universe is expanding. ... Some people think that Hubble is famous because here was a bunch of coffee stains at piece of graph paper and he was able to draw a straight line through it.}}</ref> Although Hubble hastily concluded, based on only 20 [[galaxy|galaxies]], that the [[redshift]] of the galaxies appears to be a [[linear function]] of their [[distance]], there is also a disturbing evidence that this linear relationship does not describe the facts entirely. Several authors made a point that Hubble's [[Scientific observation|observations]] suggested a quadratic rather than linear relation. After research of [[quasar]]s, it has been discovered that if one trends apparent brightness against the redshifts as for galaxies, the result is unexpected diagram with scattered points instead of smooth curve as it is the case of galaxies. This seems to indicate that the quasars do not follow the Hubble Law as do the most other objects. According to other authors including Capria, the value of [[Hubble constant]] depends on the cosmological model, and [[John Hartnett|J.Hartnett]] claims that the Hubble constant is not truly constant but it has shown up that there is an inherent scale dependence to its value. Consequently, new theories emerged such as [[Moshe Carmeli|M.Carmeli]]'s theory of [[Cosmological special relativity]] where the Hubble law is rewritten in a new invariant way.

@@ Line 23: / Line 23: @@
 :<math>x^4 + y^4 + z^4 = w^4</math>
-For two hundred years nobody could disprove this claim despite years of computer sifting. Lack of a [[counter-example]] was interpreted as strong evidence in favor of a theory until Naom Elkies of Harvard University discovered the solution in 1988.<ref>{{cite book |title=The True Marvel of Numbers: And How Fermat Proved His Last Theorem! |author=David Searle |publisher=AuthorHouse |year=2009 |pages=71 |url=http://books.google.sk/books?id=PQC8AQiFCSsC&pg=PA71&lpg=PA71&dq=Naom+Elkies+of+Harvard+University+1988&source=bl&ots=vtJbAgMJdI&sig=rGHNn8o_kiBJ9Vx9o5XpP41Ep2k&hl=en&sa=X&ei=8OBzUuPcLKi24ATAjYGwCw&ved=0CFYQ6AEwBQ#v=onepage&q=Naom%20Elkies%20of%20Harvard%20University%201988&f=false |isbn=978-1-4389-4530-9}}</ref> Despite all the evidence, Euler's conjecture turned out to be false at the end. Extrapolating a theory to cover an infinity of numbers based on insufficient and limited amount of [[scientific evidence|evidence]] without absolute proof has shown to be an unacceptable gamble. The moral is that it is not possible to use evidence from first local set of million numbers to prove the theory or rather conjecture about global set of all numbers.<ref>{{cite book |title=Fermat's Last Theorem |author=Simon Singh |publisher=Fourth Estate |place=London |year=1997 |pages= 177–178|url=http://books.google.no/books?id=Ncrnn9hCn_kC&dq=simon+singh&hl=en&sa=X&ei=29NyUrXWEIGv4ASqzIDoAQ&redir_esc=y |isbn=1-85702-521-0}}</ref>
+For two hundred years nobody could disprove this claim despite years of computer sifting. Lack of a [[counter-example]] was interpreted as strong evidence in favor of a theory until Naom Elkies of [[Harvard University]] discovered the solution in 1988.<ref>{{cite book |title=The True Marvel of Numbers: And How Fermat Proved His Last Theorem! |author=David Searle |publisher=AuthorHouse |year=2009 |pages=71 |url=http://books.google.sk/books?id=PQC8AQiFCSsC&pg=PA71&lpg=PA71&dq=Naom+Elkies+of+Harvard+University+1988&source=bl&ots=vtJbAgMJdI&sig=rGHNn8o_kiBJ9Vx9o5XpP41Ep2k&hl=en&sa=X&ei=8OBzUuPcLKi24ATAjYGwCw&ved=0CFYQ6AEwBQ#v=onepage&q=Naom%20Elkies%20of%20Harvard%20University%201988&f=false |isbn=978-1-4389-4530-9}}</ref> Despite all the evidence, Euler's conjecture turned out to be false at the end. Extrapolating a theory to cover an infinity of numbers based on insufficient and limited amount of [[scientific evidence|evidence]] without absolute proof has shown to be an unacceptable gamble. The moral is that it is not possible to use evidence from first local set of million numbers to prove the theory or rather conjecture about global set of all numbers.<ref>{{cite book |title=Fermat's Last Theorem |author=Simon Singh |publisher=Fourth Estate |place=London |year=1997 |pages= 177–178|url=http://books.google.no/books?id=Ncrnn9hCn_kC&dq=simon+singh&hl=en&sa=X&ei=29NyUrXWEIGv4ASqzIDoAQ&redir_esc=y |isbn=1-85702-521-0}}</ref>
 ===[[Microevolution]] and [[Macroevolution]]===
-In the 1980 University of Chicago conference entitled "Evolution", scientists were  trying to address the question whether the mechanisms underlying microevolution can be extrapolated to explain the phenomena of macroevolution. Despite the risk of doing violence to the positions of some of the people at the meeting, the answer given was a clear "No".<ref>{{cite web |title=Evolutionary theory under fire: A historic conference in Chicago challenges the four-decade long dominance of the Modern Synthesis|author= |publisher=Science |date=November 21, 1980
+In the 1980 [[University of Chicago]] conference entitled "Evolution", scientists were  trying to address the question whether the mechanisms underlying [[microevolution]] can be extrapolated to explain the phenomena of [[macroevolution]]. Despite the risk of doing violence to the positions of some of the people at the meeting, the answer given was a clear "No".<ref>{{cite web |title=Evolutionary theory under fire: A historic conference in Chicago challenges the four-decade long dominance of the Modern Synthesis|author= |publisher=Science |date=November 21, 1980
 |volume=210 |number=4472 |pages=883–887 |url=http://www.sciencemag.org/content/210/4472/883.extract |doi= 10.1126/science.610799|quote=The central question of the Chicago conference was whether the mechanisms underlying microevolution can be extrapolated to explain the phenomena of macroevolution. At the risk of doing violence to the positions of some of the people at the meeting, the answer can be given as a clear, No.}}</ref>
@@ Line 37: / Line 37: @@
 |accessdate=2012-10-14
 |url=http://www.youtube.com/watch?v=jWaOyy3WfWk
-|quote=He also discovered that the universe is expanding. ... Some people think that Hubble is famous because here was a bunch of coffee stains at piece of graph paper and he was able to draw a straight line through it.}}</ref> Although Hubble hastily concluded, based on only 20 [[galaxy|galaxies]], that the redshift of the galaxies appears to be a linear function of their distance, there is also a disturbing evidence that this linear relationship does not describe the facts entirely. Several authors made a point that Hubble's observations suggested a quadratic rather than linear relation. After research of [[quasar]]s, it has been discovered that if one trends apparent brightness against the redshifts as for galaxies, the result is unexpected diagram with scattered points instead of smooth curve as it is the case of galaxies. This seems to indicate that the quasars do not follow the Hubble Law as do the most other objects. According to other authors including Capria, the value of Hubble constant depends on the cosmological model, and [[John Hartnett|J.Hartnett]] claims that the Hubble constant is not truly constant but it has shown up that there is an inherent scale dependence to its value. Consequently, new theories emerged such as [[Moshe Carmeli|M.Carmeli]]'s theory of [[Cosmological special relativity]] where the Hubble law is rewritten in a new invariant way.
+|quote=He also discovered that the universe is expanding. ... Some people think that Hubble is famous because here was a bunch of coffee stains at piece of graph paper and he was able to draw a straight line through it.}}</ref> Although Hubble hastily concluded, based on only 20 [[galaxy|galaxies]], that the [[redshift]] of the galaxies appears to be a [[linear function]] of their [[distance]], there is also a disturbing evidence that this linear relationship does not describe the facts entirely. Several authors made a point that Hubble's [[Scientific observation|observations]] suggested a quadratic rather than linear relation. After research of [[quasar]]s, it has been discovered that if one trends apparent brightness against the redshifts as for galaxies, the result is unexpected diagram with scattered points instead of smooth curve as it is the case of galaxies. This seems to indicate that the quasars do not follow the Hubble Law as do the most other objects. According to other authors including Capria, the value of [[Hubble constant]] depends on the cosmological model, and [[John Hartnett|J.Hartnett]] claims that the Hubble constant is not truly constant but it has shown up that there is an inherent scale dependence to its value. Consequently, new theories emerged such as [[Moshe Carmeli|M.Carmeli]]'s theory of [[Cosmological special relativity]] where the Hubble law is rewritten in a new invariant way.
 == See also ==

← Older revision		Revision as of 17:30, September 27, 2017
Line 40:		Line 40:

	== See also ==		== See also ==
		+	*[[Generalization]]
	*[[Logic of possibility]]		*[[Logic of possibility]]

@@ Line 1: / Line 1: @@
 ''Alternative names: Hasty Generalization, Hasty Conclusion, Overgeneralization or Unwarranted Extrapolation, Free Extrapolation.''
-'''The fallacy of extrapolation''' (more precisely: '''fallacy of unwarranted extrapolation'''), occurs when a [[phenomenon]] responsible for a number of trivial local effects is read into the great global phenomena, or when a generalized rule is concluded based on too few cases.<ref name="Virkler">{{cite book |author= Henry A. Virkler|title= A Christian's Guide to Critical Thinking |accessdate=5 July 2015 |year= 2005 |publisher= Wipf and Stock Publishers |location= Eugene, OR|isbn= 1-59752-661-4|page=224-225 |pages= |chapter= 9 |url=http://books.google.no/books?id=rUgqAAAACAAJ|quote= }}</ref>  . For example, [[Darwin]]'s theory of [[evolution]] makes use of a fantastic extrapolation in which the mechanisms of random variation and [[natural selection]] are declared to account for the development of such complex structures as the [[mammal|mammalian]] eye or the [[immunology|immuno-defense]] system.<ref name="DeniableDarwin">{{cite book
+'''The fallacy of extrapolation''' (more precisely: '''fallacy of unwarranted extrapolation'''), occurs when a [[phenomenon]] responsible for a number of trivial local effects is read into the great global phenomena, or when a generalized rule is concluded based on too few cases.<ref name="Virkler">{{cite book |author= Henry A. Virkler|title= A Christian's Guide to Critical Thinking |accessdate=5 July 2015 |year= 2005 |publisher= Wipf and Stock Publishers |location= Eugene, OR|isbn= 1-59752-661-4|pages=224–225 |chapter= 9 |url=http://books.google.no/books?id=rUgqAAAACAAJ|quote= }}</ref> For example, [[Darwin]]'s theory of [[evolution]] makes use of a fantastic extrapolation in which the mechanisms of random variation and [[natural selection]] are declared to account for the development of such complex structures as the [[mammal]]ian eye or the [[immunology|immuno-defense]] system.<ref name="DeniableDarwin">{{cite book
 |author=David Berlinski
 |title=The Deniable Darwin
@@ Line 11: / Line 11: @@
 |isbn=978-0-9790141-2-3
 |url=http://www.davidberlinski.org/deniable-darwin/about.php
-|quote=}}</ref> When attempting for an interpretation of research results, the scientist must be leery of extrapolating beyond the range of the data and conscious of the underlying assumptions to avoid drawing invalid conclusions.<ref>{{cite web |title=The fallacy of free extrapolation |author=Riegelman R. |publisher=Postgraduate medicine |date=September 1979 |issue=66(3)|pages=189-91, 194 |url=http://www.ncbi.nlm.nih.gov/pubmed/471851 |accessdate=October 31, 2013}}</ref>
+|quote=}}</ref> When attempting for an interpretation of research results, the scientist must be leery of extrapolating beyond the range of the data and conscious of the underlying assumptions to avoid drawing invalid conclusions.<ref>{{cite web |title=The fallacy of free extrapolation |author=Riegelman R. |publisher=Postgraduate medicine |date=September 1979 |issue=66(3)|pages=189–91, 194 |url=http://www.ncbi.nlm.nih.gov/pubmed/471851 |accessdate=October 31, 2013}}</ref>
 ==Valid vs. Fallacious Extrapolations==
-In general, extrapolation is a legitimate scientific tool. There are at least two aspects that help to distinguish between valid and fallacious extrapolation<ref name="Virkler"/>:
+In general, extrapolation is a legitimate scientific tool. There are at least two aspects that help to distinguish between valid and fallacious extrapolation:<ref name="Virkler"/>
 #The likelihood of erroneous extrapolation is higher when insufficient data points were obtained for its construction.
 #In science, the research is used to confirm or disprove the predictions of hypothesis. Reporting an extrapolation before testing it is unwise.
@@ Line 23: / Line 23: @@
 :<math>x^4 + y^4 + z^4 = w^4</math>
-For two hundred years nobody could disprove this claim despite years of computer sifting. Lack of a [[counter-example]] was interpreted as strong evidence in favor of a theory until Naom Elkies of Harvard University discovered the solution in 1988.<ref>{{cite book |title=The True Marvel of Numbers: And How Fermat Proved His Last Theorem! |author=David Searle |publisher=AuthorHouse |year=2009 |pages=71 |url=http://books.google.sk/books?id=PQC8AQiFCSsC&pg=PA71&lpg=PA71&dq=Naom+Elkies+of+Harvard+University+1988&source=bl&ots=vtJbAgMJdI&sig=rGHNn8o_kiBJ9Vx9o5XpP41Ep2k&hl=en&sa=X&ei=8OBzUuPcLKi24ATAjYGwCw&ved=0CFYQ6AEwBQ#v=onepage&q=Naom%20Elkies%20of%20Harvard%20University%201988&f=false |isbn=978-1-4389-4530-9}}</ref> Despite all the evidence, Euler's conjecture turned out to be false at the end. Extrapolating a theory to cover an infinity of numbers based on insufficient and limited amount of [[scientific evidence|evidence]] without absolute proof has shown to be an unacceptable gamble. The moral is that it is not possible to use evidence from first local set of million numbers to prove the theory or rather conjecture about global set of all numbers.<ref>{{cite book |title=Fermat's Last Theorem |author=Simon Singh |publisher=Fourth Estate |place=London |year=1997 |pages= 177-178|url=http://books.google.no/books?id=Ncrnn9hCn_kC&dq=simon+singh&hl=en&sa=X&ei=29NyUrXWEIGv4ASqzIDoAQ&redir_esc=y |isbn=1-85702-521-0}}</ref>
+For two hundred years nobody could disprove this claim despite years of computer sifting. Lack of a [[counter-example]] was interpreted as strong evidence in favor of a theory until Naom Elkies of Harvard University discovered the solution in 1988.<ref>{{cite book |title=The True Marvel of Numbers: And How Fermat Proved His Last Theorem! |author=David Searle |publisher=AuthorHouse |year=2009 |pages=71 |url=http://books.google.sk/books?id=PQC8AQiFCSsC&pg=PA71&lpg=PA71&dq=Naom+Elkies+of+Harvard+University+1988&source=bl&ots=vtJbAgMJdI&sig=rGHNn8o_kiBJ9Vx9o5XpP41Ep2k&hl=en&sa=X&ei=8OBzUuPcLKi24ATAjYGwCw&ved=0CFYQ6AEwBQ#v=onepage&q=Naom%20Elkies%20of%20Harvard%20University%201988&f=false |isbn=978-1-4389-4530-9}}</ref> Despite all the evidence, Euler's conjecture turned out to be false at the end. Extrapolating a theory to cover an infinity of numbers based on insufficient and limited amount of [[scientific evidence|evidence]] without absolute proof has shown to be an unacceptable gamble. The moral is that it is not possible to use evidence from first local set of million numbers to prove the theory or rather conjecture about global set of all numbers.<ref>{{cite book |title=Fermat's Last Theorem |author=Simon Singh |publisher=Fourth Estate |place=London |year=1997 |pages= 177–178|url=http://books.google.no/books?id=Ncrnn9hCn_kC&dq=simon+singh&hl=en&sa=X&ei=29NyUrXWEIGv4ASqzIDoAQ&redir_esc=y |isbn=1-85702-521-0}}</ref>
 ===[[Microevolution]] and [[Macroevolution]]===
 In 1980 the scientists at the Chicago conference were  trying to address the question whether the mechanisms underlying microevolution can be extrapolated to explain the phenomena of macroevolution. Despite the risk of doing violence to the positions of some of the people at the meeting, the answer given was a clear "No".<ref>{{cite web |title=Evolutionary theory under fire: A historic conference in Chicago challenges the four-decade long dominance of the Modern Synthesis|author= |publisher=Science |date=November 21, 1980
-|volume=210 |number=4472 |pages=883-887 |url=http://www.sciencemag.org/content/210/4472/883.extract |doi= 10.1126/science.610799|quote=The central question of the Chicago conference was whether the mechanisms underlying microevolution can be extrapolated to explain the phenomena of macroevolution. At the risk of doing violence to the positions of some of the people at the meeting, the answer can be given as a clear, No.}}</ref>
+|volume=210 |number=4472 |pages=883–887 |url=http://www.sciencemag.org/content/210/4472/883.extract |doi= 10.1126/science.610799|quote=The central question of the Chicago conference was whether the mechanisms underlying microevolution can be extrapolated to explain the phenomena of macroevolution. At the risk of doing violence to the positions of some of the people at the meeting, the answer can be given as a clear, No.}}</ref>
 ===[[Hubble constant]]===
@@ Line 39: / Line 39: @@
 |quote=He also discovered that the universe is expanding. ... Some people think that Hubble is famous because here was a bunch of coffee stains at piece of graph paper and he was able to draw a straight line through it.}}</ref> Although Hubble hastily concluded, based on only 20 [[galaxy|galaxies]], that the redshift of the galaxies appears to be a linear function of their distance, there is also a disturbing evidence that this linear relationship does not describe the facts entirely. Several authors made a point that Hubble's observations suggested a quadratic rather than linear relation. After research of [[quasar]]s, it has been discovered that if one trends apparent brightness against the redshifts as for galaxies, the result is unexpected diagram with scattered points instead of smooth curve as it is the case of galaxies. This seems to indicate that the quasars do not follow the Hubble Law as do the most other objects. According to other authors including Capria, the value of Hubble constant depends on the cosmological model, and [[John Hartnett|J.Hartnett]] claims that the Hubble constant is not truly constant but it has shown up that there is an inherent scale dependence to its value. Consequently, new theories emerged such as [[Moshe Carmeli|M.Carmeli]]'s theory of [[Cosmological special relativity]] where the Hubble law is rewritten in a new invariant way.
-== See Also ==
+== See also ==
 *[[Logic of possibility]]

@@ Line 44: / Line 44: @@
 == References ==
 {{Reflist}}
-[[category:Logical Fallacies]]
+[[Category:Logical Fallacies]]
 [[Category:Methodology of Science]]
 [[Category:Rhetoric]]