# Infinity

Infinity refers to unboundedness or endlessness. Something is said to be infinite if it has no limit in extent or no end (or no beginning) in time. The phrase ad infinitum refers to repeating or continuing an action forever. Something which is not infinite is said to be finite. An infinite series of causes or of explanations is called an infinite regress.

Various apologetic and counter-apologetic arguments rely on notions of infinity. See:

## Concepts of infinities

There are several types of infinity with different definitions or mathematical foundations. They include:

A potential infinity is a process that can continue indefinitely or a set that can expand indefinitely and without limit. While the process may continue without limit, the number of steps that have actually occurred in the process is finite. The existence of potential infinities is generally accepted.

An actual infinite is a set (or group of entities) which has more members than any natural number i.e. it is very large. A set containing all whole numbers (natural numbers) arguably is an actual infinite which exists as a mathematical concept. The controversy of infinite regress often involves the question of the existence of actual infinities in physical reality.

The theory of transfinite cardinal numbers, proposed by Georg Cantor, allows for different types of infinities and their mathematical usage. The mathematics of infinity is notoriously tricky and sometimes counter intuitive.

## Are God's attributes actual infinities?

Apologists argue that actual infinities do not exist. But if actual infinities do not occur, God cannot have actually infinite attributes. William Lane Craig rebuts this argument by saying God's quantitative attributes are not an actual infinity at all:

"Really "infinity" is just a sort of umbrella term used to cover all of God's superlative attributes. If you abstract away all of those attributes, there really isn't any distinct attribute called "infinity" left over. But none of those attributes need involve an infinite number of things.[1]"

This is similar to the idea that God's attributes are "without limited" but not "actually infinite". He also claims that it is not a concept that can be addressed mathematically:

"But when people talk about the infinity of God, this is not a quantitative concept [...] rather it is a qualitative notion when one speaks of God's infinity [2]"

This is contrary to the type of God that apologetics typically attempts to demonstrate.

## References

1. William Lane Craig, Is God Actually Infinite?
2. William Lane Craig If an actual infinite doesn't exist, then how can God exist?, drcraigvideos, Youtube, Uploaded 15 Jan 2010