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Cosmological argument: Difference between revisions
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* 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. The implicit question of premise 2 is, can an actually infinite number of members exist? 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> | * 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. The implicit question of premise 2 is, can an actually infinite number of members exist? 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. | * 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. | ||
=====Objections===== | =====Objections===== | ||
=====Modern mathematical set-theory===== | =====Modern mathematical set-theory===== | ||
