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Cosmological argument: Difference between revisions
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The crucial premise of the argument. | The crucial premise of the argument. | ||
* 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. Accept this. | * 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. Accept this. | ||
=====Modern mathematical set-theory===== | |||
In set theory, the set of all natural number is said to be an infinite set, it contains an actually infinite number of members in the set. Not all mathematicians would agree on this however, some suggest that natural number sets are potentially infinite but is a minority view. Existence in the mathematical realm does not mean existence in the real world, because philosophical assumptions need to govern this realm but there isn't good reason to suggest that these assumptions are true. | |||
==Natural Theology== | ==Natural Theology== | ||
