Taxonomy is the science of classification. Once multiple classes are determined, it is possible to determine the classes of classes and so on. At some point this process will end, either with a single class or multiple classes with too many differences to be reasonably classified together.
Taxonomy applied to biology is a systematic approach to classifying organisms. It can be applied to all organisms at a particular time, throughout time, or within any context. Once a classification is determined, other questions arise such as whether there is an independent reason that organisms are in a same class together.
The basic question in all classifications is whether the objects to be classified fit within a class or belong to another class. The goal of a classification is to minimize the within-class differences and maximize the between-class differences. This is often done by defining a distance metric that quantifies the differences.
Carl Linnaeus is known as the father of modern taxonomy who formalized the binomial nomenclature and called the lowest classes species and genus (no doubt after Aristotle’s method of defining with species and genera). His original expectation was that these biological species were natural kinds that persist through time. With the discovery that fossils were from dead organisms, it became clear that his species changed over time.
The solution to this problem is to classify organisms both living and dead in one classification system. But this was easier said than done since it took years for fossils to be examined. Meanwhile, people were anxious to know how all the diversity of species arose. Charles Darwin‘s answer was quickly adopted: species are temporary population groupings rather than natural kinds that persist over time.
Without persistence over time there is only one permanent class: the class of all organisms.
Others reject Darwin’s answer and assert there are multiple classes of organisms that persist over time. This is implicit in arguments that infer design or special creation, in which there are discontinuities between classes. How can this dispute be resolved? Elliott Sober compares these two hypotheses in his book Evidence and Evolution.
Sober argues for a likelihood approach to determining the better of two hypotheses. The law of likelihood states that evidence E favors hypothesis H1 over H2 if and only if the probability of E given H1 is greater than the probability of E given H2, or in symbols, P(E | H1) > P(E | H2). Note that this is a comparative approach; it only works when comparing two specific hypotheses.
In this case, the context is all organisms on the earth over all the history of life on earth. Hypothesis H1 states that there are multiple classes of organisms that span the history of life on earth (because there is separate ancestry). Hypothesis H2 states that there is only one class of organisms that span the history of life on earth (because there is common ancestry).
Sober notes that Darwin routinely inferred common ancestry if there was some similarity between organisms or species. Sober calls this modus Darwin. But it is better to have an overall metric of distance between organisms or species than rely on a few similarities. However, there is no such generally accepted distance metric. In its absence, we can still make general inferences.
If there are many similarities between two organisms or species, that evidence is more likely given hypothesis H2 (common ancestry). But if there are fewer similarities and some great differences between two organisms or species, that evidence is more likely given hypothesis H1 (separate ancestry). Since hypothesis H1 includes partial common ancestry, it can explain similarities as well as differences. The conclusion from this exercise is that separate ancestry is the superior hypothesis.
A problem arises when proponents of common ancestry insist on an explanation of how these separate lines of ancestry arose in time. The best answer is that, just as biogenesis is not part of the common ancestry hypothesis, so the ultimate origin of the separate classes is not part of the separate ancestry hypothesis.
