Hull, Rainbows in Retrospect 
529 
like the huge literature on numerical cladistics to count as part of numerical taxonomy, 
but thus far they have not been very successful in this regard. 
Although many systematists objected to the 'numerical' aspect of numerical taxonomy 
just because it was numerical, Johnson did not. He raised objections to certain of 
these techniques but did not reject the basic goal of making systematics as quantitative 
as possible. He merely concluded that taxonomic evaluations could not be made 
entirely quantitative. In his own taxonomic work, Johnson used the comparative 
method but not in a formal, mathematically rigorous way. As he remarked in 1972, 
he himself had not used taximetric methods because the kind and quantity of data 
needed for such studies were not available. However, he hoped that 'within the next 
decade it will indeed be feasible to carry out taximetric analysis both by variable- 
strategy phenetic techniques and by the use of phyletic (cladistic and perhaps patristic) 
models' (Johnson 1972:12). 
Because Johnson clearly understood the quantitative techniques being devised, such 
numerical taxonomists as Sokal and Sneath took his criticisms seriously. Johnson was 
not a mathematical Luddite. In fact, Sokal and Sneath would have very much liked to 
persuade Johnson to join with them in their efforts to improve taxonomic principles. 
They failed. Johnson joined no 'school' of taxonomy but tended to his Eucalypts. 
Certainly one of the goals of numerical taxonomy was to make systematics as 
quantitative as possible, but this group of systematists also set out a basic philosophy 
that sounded quite hostile to what they termed 'a priori speculation.' As Sokal and 
Sneath (1963: 55) put this position: 
A basic (and very controversial) attitude of the proponents of numerical 
taxonomy is the strict separation of phylogenetic speculation from taxonomic 
procedure. Taxonomic relationships between taxa are to be evaluated purely 
on the basis of the resemblances existing noiu in the material at hand. The 
relationships are thus static ... or phenetic, as we now prefer to call them. 
At the time, Sokal and Sneath were interpreted as opposing a priori speculation 
entering into the classificatory process, at least in the early stages of classification. 
The unequal weighting of characters because of their presumed phylogenetic 
importance was their usual target (Sokal & Sneath 1963:16, 34, 50), but they also 
questioned 'speculation on phyletic relationships based on neontological evidence ... 
since there is no way of being certain which embryonic features do and which do 
not reflect that actual phylogeny' (Sokal & Sneath 1963: 24). 
Later Sneath and Sokal (1973: 6, 23) repeated their objections to a priori weighting 
but added that 'phenetic similarity can be based on equally or unequally weighted 
characters as long as the operation for obtaining the similarity has been defined 
explicitly by the investigator' (Sneath & Sokal 1973: 29). They did not object to 
weighting just so long as it was done in an explicit, testable, quantitative way. In a 
recent retrospective evaluation of numerical taxonomy, Sneath (1995: 285) finds it 
'perverse to to imply [thatj phonetics is theory free or that phylogeny requires no 
models of evolution (points that have regrettably been misunderstood by philosophers 
of science)' — including this one. 
I must plead guilty. 1 really did think that pheneticists objected to letting theoretical 
speculations about such things as the connection between ontogeny and phylogeny 
enter into classification, especially in the early steps. At least, I shared this 
misinterpretation with Johnson. When Johnson (1989: 96) returned to taxonomic 
philosophy, he remarked that the 'pure phenetic approach to taxonomy is now 
moribund, or indeed to many of us, quite dead.' If Sneath is right, phenetic taxonomy 
was never born in the first place. No one ever held any of the beliefs usually attributed 
