Does divine ancestry require an infinite regress?

Yes. Bullock’s notes of the June 1844 sermon report Joseph applying the father-and-son analogy to the Father of Jesus.

You start with the historical evidence. The June sermon discusses ancestry. The April King Follett sermon discusses the Father living on an earth.

The Church teaches very little about this today, so there is no evidence Joseph discussed it.

The current limits on what is taught are a separate question. A contemporary record of the June sermon directly reports the ancestry argument.

One predecessor settles the whole genealogy. There can’t be a first member.

The premise establishes a predecessor for one member. An endless line requires the rule to apply to every member, with no cycle.

The rule would have to apply to every predecessor, without the line ever circling back. Pratt explicitly defended that stronger model.

You distinguish one link from a rule covering the whole chain. Pratt’s published view is evidence that a Latter-day Saint leader did defend the endless version.

If every member only passes along power received from another, that’s a serious question. We still need to show that this genealogy requires that kind of dependence.

Aquinas distinguishes successive parents from a series of causes needed together for an effect. A question about the existence of the whole chain can still be raised separately.

Infinite sequences are possible in math, so any infinite causal explanation works.

An infinite sequence of numbers does not establish that a series of wholly dependent causes explains an effect. Identify the type of causal relation and why the regress would or would not explain it.

Since Pratt was an apostle, his entire explanation is the Church’s current doctrine.

The source establishes his published view. The current essay quotes Snow’s couplet and says little has been revealed about its first half.

The Church affirms exaltation and continuing worship of the Father. Its essay says little has been revealed about God’s prior history. I would attribute the detailed genealogy to the sources that taught it.

You acknowledge the historical teaching and explain the scope of the Church’s current statement.