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). "
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