Infinite regresses (e.g., event3 caused event2,
event2 caused event1, ad infinitum;
statement3 justifies statement2,
statement2 justifies statement1, ad infinitum)
have been used as premises in arguments on a great variety of topics in
both Eastern and Western philosophy since ancient times. They are part
of a philosopher's tool kit of argumentation. But how sharp or strong is
this tool? How effectively is it used? The typical presentation of
infinite regress arguments throughout history is so succinct and has so
many gaps that it is often unclear how an infinite regress is derived,
and why an infinite regress is logically problematic, and as a result,
it is often difficult to evaluate infinite regress arguments. These
prevalent consequences indicate that there is a need for a theory to
re-orient our practice. After well over two thousand years of using
infinite regresses as premises, one would have expected that at least
some theory of infinite regress arguments would have emerged. None
exists. There have been only a few articles on infinite regress
arguments, but they are based on the examination of only a small number
of examples, discuss only a few logical or rhetorical aspects of
infinite regress arguments, and so they help to meet the need for a
theory in only a limited way.
Given the situation, I examined many infinite regress arguments to
clarify the various aspects of the derivation of infinite regresses, and
explain the different ways in which certain infinite regresses are
unacceptable. My general approach consisted of collecting and evaluating
as many infinite regress arguments as possible, comparing and
contrasting many of the formal and non-formal properties, looking for
recurring patterns, and identifying the properties that appeared
essential to those patterns. The six chapters of this book gradually
emerged from this approach. Two very general questions guided this work:
(1) How are infinite regresses generated in infinite regress arguments?
(2) How do infinite regresses logically function in an argument? In
answering these questions I avoided as much as possible addressing the
philosophical content and historical background of the arguments
examined. Due to the already extensive work done on causal regresses and
regresses of justification, only a few references are made to them.
However, the focus is on other issues that have been neglected, and that
do contribute to a general theory of infinite regress arguments: I
clarify the notion of an infinite regress; identify different logical
forms of infinite regresses; describe different kinds of infinite
regress arguments; distinguish the rhetoric from the logic in infinite
regress arguments; and discuss the function of infinite regresses in
arguments. The unexamined derivation of infinite regresses is worth
deriving - to discover what we have kept hidden from ourselves, improve
our ways of constructing and evaluating these arguments, and sharpen and
strengthen one of our argumentative tools. This work is one example of
empirical logic applied to infinite regress arguments: "the attempt to
formulate, to test, to clarify, and to systematize concepts and
principles for the interpretation, the evaluation, and the sound
practice of reasoning" (Finocchiaro, M. Arguments about Arguments,
Systematic, Critical and Historical Essays in Logical Theory. P48).
