  The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables
has been well studied. The present work comprehensively revisits this problem
using a combination of philosophical reflections, causal considerations, and
probability theory. The first contribution is to provide a schematic analysis
of SP in $2\times 2$ contingency tables and present new results, detailed
proofs of previous results and a unifying view of the important examples of SP
that have been reported in the literature. The second contribution of the paper
suggests a new perspective on the surprise element of SP, raises some critical
questions regarding the influential causal analyses of SP and provides a broad
perspective on logic, probability, and statistics with SP at its center. The
upshot of this research is that we need both causal concepts and statistical
tools coupled with philosophical analyses to sort out issues regarding SP.
