LessonsThe Originator of the World: Necessary Existence, Infinite Regress and the Correspondence ProofQuiz

وإن لم يكن فقد وجد في الأولى ما لا يوجد بإزائه شيء في الثانية
If not, there will be a member in the first series with no corresponding member in the second.

On this second alternative, the shorter series has a terminal point. Since the longer series differs by only a finite number of terms, it too is said to terminate.

The reasoning is:
The shorter series is finite.
The longer exceeds it by one member.
Therefore the longer is also finite.

The classical argument uses this pair of alternatives to deny an actually unending series of dependent existents.

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Second alternative: correspondence stops

The Originator of the World: Necessary Existence, Infinite Regress and the Correspondence Proof

وإن لم يكن فقد وجد في الأولى ما لا يوجد بإزائه شيء في الثانية
If not, there will be a member in the first series with no corresponding member in the second.

On this second alternative, the shorter series has a terminal point. Since the longer series differs by only a finite number of terms, it too is said to terminate.

The reasoning is:
The shorter series is finite.
The longer exceeds it by one member.
Therefore the longer is also finite.

The classical argument uses this pair of alternatives to deny an actually unending series of dependent existents.