Information Technology Reference
In-Depth Information
would probably not want to call them distinct paradoxes. Any paradox worth the
name, including SP, should obey this definition. Simplifying our reconstruction
of SP as a paradox in section 2.2, we provide a rough schema for SP with the
(optional) false premise marked by an asterisk, for the type 1 version of the
paradox.
(1) Sub-population 1 has a positive correlation between two variables.
(2) Sub-population 2 has a positive correlation between two variables.
(*3) If each sub-population in a partition of a larger population exhibits a posi-
tive correlation between two variables, then the population as a whole will
also exhibit that same positive correlation between the same two variables
(4) Overall population has a negative correlation between the same two vari-
ables.
If *3 is included, the set is inconsistent, since premise *3 is false. If *3 is not
included, the set seems to be inconsistent, but is not. Whether to analyze the
paradox one way or the other may depend on the example and the context. We
think that our definition is adequately general to include even the Liar paradox.
Call “this sentence is false” the liar sentence. The following provides a canonical
reconstruction of the Liar paradox with two premises and a conclusion.
(1) The liar sentence is true.
(2) The liar sentence is false.
(3) A sentence is either true or false, but not both.
In this section, among other issues, we both discussed and evaluated different
views on paradoxes. As a result, we are able to provide a general framework to
understand paradoxes while showing that both SP and the Liar paradox satisfy
it even though the former has an apparently contradictory conclusion while the
latter has a genuinely contradictory one.
8Conluon
Unraveling paradoxes is crucial to philosophers of logic as they challenge our
deeply held intuitions in a fundamental way. While addressing SP, we distin-
guished three types of questions. We showed that answering one does not nec-
essarily lead to the answers of the rest. Although, admittedly, the “what-to-do”
question is the most important insofar as the practical side of SP is concerned,
some causal theorists have overlooked the need to distinguish these three ques-
tions, thus failing to appreciate the first-level truth about the paradox. Even if
they recognize this first-level truth, the importance of the “what-to-do” question
drives them to assume that the causal calculus needed to address this question
is the correct way to unlock the riddle about the paradox. We, however, showed
that the truth about the paradoxical nature of SP and conditions for its emer-
gence need to be isolated from the “what-to-do” question. This failure on the
part of the causal theorists leads to their failure in appreciating the second-level
truth about the paradox. Pivoting on the question “why is SP paradoxical?”,
we provide a general framework for understanding any paradox. Our analysis of
