Finitude

Finitude in Mathematics

In mathematics, a set of numbers is a “finite set” if the number of elements can be counted and the total represented as a natural number (e.g., a positive integer). A finite set cannot be put into a one-to-one correspondence with a subset of itself (e.g., a set of the numbers 1 through 10 cannot be matched with a set of the numbers 2 through 8). This is contrasted with an infinite set (e.g., a set consisting of all multiples of 2, an infinite set, could be matched in a one-to-one correspondence with a subset consisting of all multiples of 10, since neither the set nor the subset come to an end).

A “finite decimal” refers to a number that comes to an end, such as 1.543. This is contrasted with a “repeating decimal,” in which the same digits are repeated infinitely, represented in the format 2.714714714…

Finite Resources

The second law of thermodynamics states that energy cannot be used indefinitely, and that available usable energy is a finite resource. In this sense, the word finite is often applied to the supply of the world's natural resources, as in “finite resources” [Page 525](also called “nonrenewable resources”). Finite resources, such as oil, coal, and natural gas, are produced at a slower rate than they are consumed, and thus will eventually run out.

Finitude in Humans

The finitude of the human lifespan has been a source of many questions and arguments in theology and philosophy. Pascal, using the finitude of human life as an argument for theism, stated that without God, a person's life would be meaningless because he or she would eventually die. It has also been used as an argument for atheism, encouraging people to make the most of their time on Earth, rather than preparing for an afterlife. In his essays, Albert Camus raised many questions about the mortality, and therefore meaninglessness, of human existence, without arguing for or against any particular way of thinking.

Martin Heidegger wrote that when a human being accepts his or her eventual death is the point when the essence (a human's knowledge of his or her own existence) is brought into focus. This finitude gives human beings a drive to live a productive life and accomplish things before their time is up.

Finitude has also been used to refer to the limits of human knowledge and potential: Unlike the God of the Judeo-Christian tradition, who is infinite and omniscient, human beings cannot objectively know reality and truth. This is reflected in the bible verse I Corinthians 1:25, in which the apostle Paul writes, “God's foolishness is wiser than human wisdom.”