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Cosmological argument: Difference between revisions
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====Premise 2==== | ====Premise 2==== | ||
The crucial premise of the argument. | The crucial premise of the argument. Before the Big bang theory was theorized in the 20th century, scientists generally thought that the universe was eternal. The implicit question of premise 2 is, can an actually infinite collection actually exist? Can there actually be an infinity of past events for an eternal past of matter? | ||
* | * An actual infinite is a collection that has an actually infinite number of members. The number of its member is greater than any other natural number (0,1,2,3 etc). It is not growing toward infinity, it is infinite. There literally exists an actually infinite number of things in the collection. This is irrational because, you could subtract a number from the infinite collection and that will lead to self-contradictory results. Within the math of an actually infinite number of members you subtract identical quantities from identical quantities, but this is why in [[mathematics]] subtraction from identical quantities is prohibited, it is self-contradictory. <ref>[http://www.rfmedia.org/RF_audio_video/Defender_podcast/20040509CosmologicalArgumentPart2.mp3 Cosmological Argument Part 2] By William Lane Craig</ref> | ||
* Potential infinite - Collection is at every point finite, but always growing to infinity as a limit. It is indefinite, finite in any point in time, but is always growing toward infinity but never reaching it. Potential infinite, is seen as a limit. Christians would accept this view. | * Potential infinite - Collection is at every point finite, but always growing to infinity as a limit. It is indefinite, finite in any point in time, but is always growing toward infinity but never reaching it. Potential infinite, is seen as a limit. Christians would accept this view of whether or not there could be an infinite number of past events. | ||
=====Modern mathematical set-theory objection===== | =====Modern mathematical set-theory objection===== | ||
