The Problem of the Affirmation of an Infinite Series and the Affirmation of a Natural Terminus to the Infinite Series with Atheism.

Atheists may posit an infinite series of causes to account for the existence of any single contingent substance. An infinite series of causes implies that the nature of cause and effect in an infinite number of creatures is to be both a caused effect, and a cause of an effect. Or again, an infinite series implies it is natural for creatures to be both effects of creatures and causes of creatures in the same respect. And again, if there is an infinite series (at least according to regress), it is natural for each member of the series to be dependent upon an infinite number of creatures, and also cause the being of a great many creatures. Yet the infinite series is also posited to be finite, for the series has a terminus in the existence of the creature at the end of the series. The series is then in some manner naturally infinite, but also naturally ordered towards a natural end, and therefore has both a natural infinitude and natural finitude.

Yet so, if the series has a natural finitude, then the series must account for how an infinite series ends at one creature rather than any other creature. Indeed, if the series is infinite, then if any member can be the terminus of the series, then the infinitude of the series must also be accounted for. For if any member of the series can be the natural terminus of the series, then it is natural for the infinite series to never begin.

For each member of the series may be the natural term of a series. So then, if each member of the series may or may not be the natural term of the series, yet the series is infinite according to regress, but finite at the natural term, then the series must exist in which each member is naturally not the term of the series, except for one member of the series.

Consequently, the series is composed of an infinite number of members, each of which have a nature that is unlike the nature of the final creature. Yet all of the creatures within the series are posited to exist to cause the nature of the one creature. Therefore, the infinite series is composed of an infinite number of creatures which have a fundamental difference of nature to that of the final creature. But if all the members of a set are different to one member of the same set, that one different member within the set is not accounted for. For the nature of a cause is to produce a likeness of the cause in the effect. If then a series of causes produces many effects that are the same, except for one, then those causes are not the cause of the diverse effect.

For a diverse effect is only accounted through a diverse cause. And a diverse cause is not found within the infinite series. Therefore, a series of infinite regress with a natural term in one creature is against the nature of cause and effect. Therefore, such a series does not account for the existence of the one creature. Consequently, the atheist cannot account for the existence of a creature through infinite regress.