Countable Infinities

Many people seem to be familiar with the basic concept of infinity--a thing or set of things that continues onward forever.  Calling an infinity countable, though, may raise eyebrows.  Despite the fact that the phrase might initially strike some as being contradictory, the concept is not.  In statistics, countable infinities would fall into the category of discrete variables, which can be counted exactly (the number of ice cubes in a cup or the number of texts sent in a day), as opposed to continuous variables, which can only be measured approximately because a more precise measurement is always possible (the amount of water in a cup).

A countable infinity is a set of things which goes on forever, but any particular value/quantity within the set can be counted to (even if it would take a vast amount of time).  For instance, I could count to 6,740,211, but I could also continue counting onward past that number, infinitely, since there is no boundary point at which the number line stops.  Some people might think "countable infinity" is an oxymoron, but counting to any a specific place does not mean that the set of things does not persist onward infinitely.  There is no contradiction conveyed by the phrasing.

Past infinities (like there being an infinite number of past moments) exist only as abstract logical/numerical concepts and are not possible in actuality [1].  Future infinities, contrarily, are entirely possible [2]; they have a fixed beginning point from which any point in the future infinity can be reached.  For instance, there cannot be an infinite past, as then the present could not be reached, yet it is possible for there to be an infinite number of future moments.

A countable infinity represent one of many concepts in mathematics that logicians and philosophers can explore, and it is relevant to issues like the nature of the past, which is itself related to whether or not an uncaused cause exists.  The nature of reality is such that many disciplines, concepts, and pursuits inevitably bump into each other; they overlap with each other, and this can enable us to properly examine and understand things more holistically--though, of course, to understand the whole one must understand the parts.  Countable infinities are thus not irrelevant to philosophical matters of great importance.


[1].  https://thechristianrationalist.blogspot.com/2017/04/the-uncaused-cause.html

[2].  https://thechristianrationalist.blogspot.com/2017/08/an-eternal-future.html