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Copy and pasted my own work from another wiki
An '''infinite regression''' is a proposed chain of causation in which each purported cause itself requires another event of exactly the same type to cause ''it.''
An '''infinite regression''' is a proposed chain of event causation of infinite length.
This raises the question of what set the original chain in motion—in short, what was the "first cause." Whether all things must have a "first cause" or not, is a subject of [[Debate:Is a first cause of a process necessary, always possible, or sometimes impossible?|debate]].
This raises the question of what set the original chain in motion – in short, what was the "first cause." Whether all things must have a "first cause" or not is a subject of [[Debate:Is a first cause of a process necessary, always possible, or sometimes impossible?|debate]].
==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 concludes that there exist no infinite numbers.
== An example ==
== An example ==