Hull, Rainbows in Retrospect 
533 
trees are always possible, and to make matters worse, given any one tree, several 
alternative ways can be found to classify the groups that make it up. 
These worries about phylogeny are genuine, but certainly no more genuine than 
worries about discerning overall similarity (or affinity) and reflecting it in a general- 
purpose classification. If anything, reconstructing phylogeny is more operational than 
determining overall similarity. As Johnson (1968; 24) put this point: 
We may not know the details of phylogeny but (unless we reject biological 
evolution) we must accept that they exist uniquely in space and time, and 
therefore form a concrete basis for concepts of phylogenetic relationship, 
however defined. In contrast, the notioir of 'affinity' is subject to unlimited 
variation and any claim for a firm basis for it must be metaphysical. 
To be sure, reconstructing phytogenies is extremely difficult, but at least the goal is 
clear. In the case of overall similarity, we do not even know what it is we are 
attempting to approximate, even if it does flit like a ghost before the mind's eye. 
Looking back over thirty years at Johnson's critique of overall similarity and general- 
purpose classifications, I find his objections to be as well taken now as they were then. 
Although some numerical taxonomists came to see problems with these notions quite 
early, Sokal (1985:5, 16; 1986:423) and Sneath (1995:284) continue to view overall 
similarity and general-purpose classifications as part of the fundamentals of numerical 
taxonomy, albeit in a somewhat modified form. As Sneath (1995: 284) observes: 
The power of overall similarity measures to construct taxonomic groups, to 
determine evolutionary relationships, and for identification has been amply 
borne out, even if somewhat different forms of similarity may be needed for different 
purposes (emphasis added; see also Sneath & Sokal 1973: 28, 107, 109). 
From the preceding quotation, one might conclude that Sneath has abandoned the 
notion of a single measure of overall similarity for numerous special-purpose 
measures of similarity, a position in keeping with an abandonment of the notion of 
a general-purpose classification for numerous special-purpose classifications (Ehrlich 
& Ehrlich 1967). 
Vicious circles and reciprocal illumination 
As Johnson (1968:11) points out, any scientific inquiry must either begin from 
unsubstantiated first principles or be led into an infinite regress. The whole point of 
axiomatization is to formulate first principles by which all the rest of the system can 
be derived, and these first principles receive no substantiation within this system. If 
they are to be justified at all, these justifications must come from the outside. But 
this insoluble problem arises in the context of the rational reconstruction of science. 
Scientific practice is quite a different matter. Johnson agrees with Popper and Hennig 
that there is no one place where all scientists can and must begin. Scientists begin 
wherever they happen to find themselves and then proceed in a sort of feedback 
process in which improvements in one area lead to improvements in another area, 
and another area, and so on until this process reflects back on the original contribution, 
leading to an improvement in it. 
Eor example, systematists working on a particular group may have extensive data on 
Recent species but little fossil evidence. Some of these systematists may decide to 
delve into the fossil record to see if they can find anything to supplement their 
knowledge of present-day species. Others might try out different computer programs 
to see what happens. Several different programs may focus on the same problem; e.g.. 
