Taxonomy is the science of classification. 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 the 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 do not change over time. With the discovery that fossils came from dead organisms, it became clear that some of his species had changed over time.
The solution to this problem was to reclassify organisms both living and dead in a new 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 hypothesis was soon adopted: species are temporary population groupings with universal common ancestry. If all species are temporary, there is only one fixed class: the class of all species. Others hypothesize there are multiple classes of species that are fixed and have separate ancestries, which supports design or special creation.
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 species on the earth over all the history of life on earth. Hypothesis H1 states that there are multiple classes of species that span the history of life on earth, each class with separate ancestry. Hypothesis H2 states that there is only one class of species that span the history of life on earth, all with common ancestry.
Sober notes that Darwin routinely inferred common ancestry if there was some similarity between species. Sober calls this modus Darwin. It is better to have an overall metric of distance between species than rely on a few similarities. However, there is no generally accepted distance metric for species. In its absence, we can still make some inferences.
If there are many similarities between two species, that evidence is more likely given hypothesis H2 (common ancestry), though there is some likelihood given hypothesis H1. If there are discontinuities between two species, even if there are some similarities, that evidence is more likely given hypothesis H1 (separate ancestry).
Note that if someone proposes a possible sequence of events that explains a discontinuity given hypothesis H2, it is merely a possibility and lacks likelihood. But since hypothesis H1 includes partial common ancestry, it is likely with evidence of similarities as well as differences. Note that universal common ancestry (H2) must have higher likelihood in all cases, which is unlikely. The conclusion from this exercise is that separate ancestry is the superior hypothesis.
A problem arises when proponents of common ancestry insist there must first be an explanation of how these separate lines of ancestry originated. The best answer is that, just as abiogenesis is not part of the common ancestry hypothesis, so the origin of the separate classes of species is not part of the separate ancestry hypothesis.