(a) A rejection of Potts' proposed solution to the counterexamples. For while we accept that this solution may work for CE1-3, it will not work for CE4-5, and in fact makes the wrong predictions about expressive content in these cases.
It only takes one counterexample to disprove a theory, but in the case of simple network effects our counterexample cup "runneth over." Systematic research on online platforms by several authors, including one of us, shows considerable churn in leadership for online platforms over periods shorter than a decade.
Philosophers seem to intuit their way to a hierarchy of cases based on how important the instances are to a concept, theory, practice, etc., and how weighty a role they can serve qua counterexamples, i.e., as exception-carvers, circumscribers or delimiters, or falsifiers.
Counterexamples to [C.sup.[infinity]] well posedness for some hyperbolic operators with triple characteristics Enrico BERNARDI and Tatsuo NISHITANI Communicated by Masaki KASHIWARA, M.J.A.
Indeed, for any n there are examples of (n + 1) permutable varieties which are not n-permutable [8, 14, 16, 10], and by forgetting structure these counterexamples can be made to work here too.