Infinite regress

[[File:Turtles_all_the_way_down.png|right|165px|thumb|This is what [[Creationists]] [[Argument_from_first_cause|actually believe]].]]
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{{Sources needed}}
{{cquote|Big fleas have little fleas,<BR>
Upon their backs to bite 'em,<BR>
And little fleas have lesser fleas,<BR>
and so, ad infinitum.|||The ''Siphonaptera'' poem by Augustus De Morgan<ref>''The Poetry of John Milton'' by Gordon Teskey (2015) Harvard University Press. p. 480. ISBN 0674416643.</ref>}}
An '''infinite regress''' or '''homunculus fallacy''' is when an [[argument]] relies on a series of never-ending propositions, where the validity of one proposition depends on the validity of the one which follows and/or precedes it.

The infinite regress is a close sibling of [[Circular_reasoning|circularity]], wherein the premises provide support for the conclusion, which in turn provides support for said premises to begin with, <small>which in turn…</small><ref>And so on, in a ''looping'' infinite regress.</ref>

==Why it's logically fallacious==
{{cquote|Neither can there be a separated infinite number: for number, or what has number, is countable, and so, if it is possible
to count what is countable, it would be possible to traverse the infinite.|||[[Aristotle]]}}
Aristotle posits an argument that shows an infinite regress to result in a contradiction. Formed using predicate logic, the [[proof]] reads like this:

#Nx⊃Cx
#Cx⊃Tx
#∴Nx⊃Tx (1, 2 hypothetical syllogism)
#Ix⊃~Tx
#| ∃x(Nx·Ix)
#| Na·Ia
#| Na (6, simplification)
#| Ta (3, 7 ''[[modus ponens]]'')
#| Ia (6, simplification)
#| ~Ta (4 , 9 ''modus ponens'')
#| Ta·~Ta (8, 10 conjunction)
#[[Quod erat demonstrandum|QED]] ∃x(Nx·Ix) results in a contradiction
#∴There does not exist a number that is infinite

Let's define the terms. Nx⊃Cx reads "if x is a number, then x is countable." Cx⊃Tx reads "if x is countable, then x is traversable." Ix⊃~Tx reads "if x is infinite, then x is not traversable." ∃x(Nx·Ix) reads "there exists an x such that x is a number and x is infinite," and is a supposition for the sake of argument. Now, 'countable' and 'traversable' need to be defined. Aristotle regarded numbers as made up of composite parts. If Aristotle had thought of the number [[42]], he would have thought that it was composed of 42 individual parts. This is what he means by 'countable'. 'Traversing' is the act of counting. So, if a number is countable, then counting the individual parts and finally reaching the number is traversing, which means the number is traversable. Aristotle says that if a number is truly infinite, it can't be traversed because the end of the number can't ever be reached. Given the definitions of the terms and the logical validity of the argument, Aristotle concluded that there exist no infinite numbers.

==Examples==
===Intelligent design===
One example of a viciously infinite regression arises in [[intelligent design]] [[creationism]], which states that there are problems in the theory of Darwinian [[evolution]] by [[natural selection]] which can only be resolved by invoking a ''designer'' or ''[[first cause]]'' without proposing a solution to the immediate question, "[[Irreducible complexity#So who designed God?|Who designed the designer?]]" Despite that, the response to this is an example of [[special pleading]]: [[creationists]] assert that every being needs a cause, but [[God]] is an eternal presence which did not need a cause. No evidence for this has ever been presented for [[peer review]], or critical analysis of any kind.

===Turtles===
The {{wpl|Turtles all the way down|"Turtles all the way down"}} anecdote illustrates a popular example of infinite regress:

{{cquote|A well-known scientist (some say it was [[Bertrand Russell]]) once gave a public lecture on [[astronomy]]. He described how the [[earth]] orbits around the [[sun]] and how the sun, in turn, orbits around the center of a vast collection of stars called [[Milky Way|our galaxy]]. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever", said the old lady. "But it's turtles all the way down!|||[[Stephen Hawking]], ''A Brief History of Time''}}

===Homunculi===
[[File:Preformation.GIF|thumb|right|165px|"Preformation" by N. Hartsoecker (1695). There's a man in my sperm!]]
The term "homunculus" first appeared in {{wpl|Paracelsus||'}} writing on [[alchemy]], ''De Natura Rerum'' (1537),<ref name=wp>{{wpa|Homunculus}}</ref> referring to what later became known as sperm after the invention of the microscope. In [[folklore]] and in [[literature]], the term "homunculus" often refers to a miniature fully-formed human.<ref name=wp/>

In the [[Eastern Bloc]], homunculus has referred to attempts to remold people to be "without sexual, high intellectual or high emotional 'centres'".<ref>''Literature in Post-Communist Russia and Eastern Europe: The Russian, Czech and Slovak Fiction of the Changes 1988-1998'' by Rajendra Anand Chitnis (2004) Routledge. ISBN 0415355575.</ref>{{rp|178}}<ref>Чапаев: Место рождение - Рига. In: ''Цыганский роман'' by Андрей Левкин (2000). Амфора.</ref> More recently, Daniel Kalder has used homunculus to refer primarily to the heads of [[puppet state]]s who felt compelled to follow [[Dogma|the party line]] while at the same time not showing any innovation from the party canon.<ref name=kalder>''The Infernal Library: On Dictators, the Books They Wrote, and Other Catastrophes of Literacy'' by Daniel Kalder (2018) Henry Holt and Co. ISBN 1627793429.</ref> [[Stalinist]] examples include {{wpl|Khorloogiin Choibalsan}} of [[Mongolia]], {{wpl|Georgi Dimitrov}} of [[Bulgaria]], {{wpl|Klement Gottwald}} of [[Czechoslovakia]], [[Enver Hoxha]] of [[Albania]], [[Kim Il Sung]] of [[North Korea]], and {{wpl|Konstantin Chernenko}} of the [[Soviet Union]].<ref name=kalder/>{{rp|212,216,242,252,279}}

===Motor homunculus===
[[File:Sensory Homunculus-en.svg|thumb|right|165px|The right side of the motor homunculus, this image is now known to be inaccurate since 2023<ref>[https://www.nature.com/articles/s41586-023-05964-2 A somato-cognitive action network alternates with effector regions in motor cortex] by Evan M. Gordon et al. (2023) ''Nature'' 617:351–359. doi:10.1038/s41586-023-05964-2. Page 357 has the updated map.</ref>]]
The motor homunculus or somatotopic homunculus, is a visualization tool used in neuroanatomy to illustrate which parts of the brain control which parts of the body.

==See also==
*''[[Argumentum ad nauseam]]''
*[[Circular reasoning]]
*[[Infinity]]

==External links==
*{{wpa|Infinite regress}}
*[http://www.logicallyfallacious.com/index.php/logical-fallacies/105-homunculus-fallacy HOMUNCULUS FALLACY], Logically Fallacious
*[http://michiganssa.blogspot.com/2013/09/the-fallacy-of-infinite-regress.html The "Fallacy" of Infinite Regress], Michigan Secular Students Alliance

==References==
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{{stub|Logic}}

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[[Category:Circular reasoning]]
[[Category:Informal fallacies]]
[[Category:Numbers]]

Categories: Circular reasoning, Informal fallacies, Numbers