Sharp cutoffs must exist!
Reader Paul Beke emailed me an excellent question about the short article that I linked to in my previous post on the emergence of species. In the article, I argue that a sharp cutoff ‒ sharp to within a single generation ‒ must exist between one species and any new species that arises from it.
Paul asked: If we assume that species membership comes in degrees, does my argument still work? I address a version of this question on pp. 10-12 of the article, but Paul’s question is more general and deserves a more general answer. The more general answer is that a sharp cutoff must exist between any two nonempty, mutually exclusive categories. If Homo erectus gave rise to our species, Homo sapiens, and nothing can belong to both species, then a sharp cutoff must exist between them.
Making species membership a matter of degree doesn’t avoid the need for sharp cutoffs. Suppose we say that an organism or a population belongs to Homo sapiens only when the organism or population has some feature F to at least degree x. A sharp cutoff must still exist between the first organism or population to have F to at least degree x and all earlier organisms and populations.
The ancient sorites paradox tells us that without sharp cutoffs we get contradictions. It doesn’t, however, tell us that we should expect to know where those cutoffs occur. A great many sharp cutoffs remain unknown, even unknowable. Still, they must exist.
The only way to avoid sharp cutoffs is to reject classical logic or embrace a semantic theory that gives illogical results, such as allowing that “P or Q” can be true when neither P nor Q could be true. In an earlier post, I showed one disastrous consequence of rejecting classical logic. On pp. 10-20 of my book, I explain how we can keep classical logic by accepting the existence of sharp cutoffs even if we often can’t know their precise locations.
