From infinite chains to a foundational reality

A brief analysis of Billon's case for explanatorily complete infinite chains

Alexandre Billon presents a super insightful analysis of infinite chains in his article, “A Recipe for Complete, Non-Wellfounded Explanations.” I’m interested in how Billon’s analysis bears on the prospect of an infinite bottomless regress of explanations without any foundational reality. Billon concludes by suggesting that there may be no need for a foundational reality: “Those who want a complete explanation of the world need not restrict their attention to foundationalist explanations starting with a self-explanatory or autonomous item."

However, I wish to note that nothing in Billon’s analysis implies that there can be a world without a foundational reality. On the contrary, the examples of infinite chains involving stick adjusters, wheel turners, and laws all include items that themselves are not included in the proposed series of explained items.

In fact, one could argue for a foundational item from the results of the paper. Take the the series of all grounded items. Per the examples, this series is itself only explanatorily complete if its total explanation is in terms of at least some item not included among those same items. The only item that is not included among all grounded items is an item that is not grounded—i.e., a foundational item. Therefore, rather than point away from the reality of a foundational item, it appears to me that Billon’s analysis may actually clarify a path to a foundational item.