# Infinities

## Two complementary distinctions:

###
- 1.Extendibility versus Divisibility
- 2.Actual versus Potential

##

| EXTENDIBILITY | DIVISIBILITY |

POTENTIAL | Time [for Aristotle] | Finite Intervals [for Aristotle] |

ACTUAL | Void [for the Atomists] | Finite Intervals [Zeno according to
Aristotle] |

###
Finite Intervals that are
actually infinitely divisible would lead to continua composed from points.
Aristotle rejected point-like continua on the grounds that such structures
were incoherent.

For another example of the difference between potential
and actual infinities, consider the natural numbers: 1, 2, 3, . . .. We
can construe them as being potentially infinite or actually infinite.

As
Potentially Infinite:For any number n, we can go on to a larger number n+1.
The process is un-ending.

As Actually Infinite:Consider the collection
as a whole. We represent collections by using curly brackets: {1, 2, 3, .
. .}. How BIG is this collection? That is, how many elements does it
contain? The collection contains an INFINITE NUMBER of elements. The
problem for making sense of this notion is to make sense of the idea that
an INFINITE NUMBER is really a NUMBER!

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