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Telopea Vol. 6(4): 1996 
In 'Rainbow's End' Johnson paid equal attention to both the numerical and the phenetic 
aspects of 'numerical phenetics/ In this paper 1 discuss only his philosophical objections. 
This decision on my part tends to work against the numerical taxonomists, making 
them look much less successful than they actually were, but I am a philosopher, not 
a mathematician. Any evaluations I might make of Johnson's mathematical criticisms 
of numerical taxonomy would be derivative at best. In his later comments, Johnson 
(1989) criticized both the particular computer programs devised by cladists and the 
philosophical stance known as pattern cladism. Once again, I am forced to limit myself 
to his philosophical criticisms. Although I went to IBM school in 1955, my computer 
skills are decidedly below those of the average teenager today. To complicate matters 
further, no one seems to have ever held the philosophical views that Johnson and I 
once criticized. Were we as confused as later authors claim? 
Overall similarity and general purpose classifications 
The main message of Johnson's presidential address was that there is no one correct 
classification of plants and animals — no crock of gold at the end of the rainbow — 
and the search for such a classification is futile and misguided. One of the chief errors 
made by early pheneticists was believing that something properly termed a 'general 
purpose' classification reflecting 'overall similarity' was possible. Johnson (1968:11) 
traces this belief to two philosophical views — operationism and British empiricism: 
The background to this way of thought is the 'operational' approach of logical 
positivism, a more far-reaching anti-metaphysical philosophy than empiricism 
but, like empiricism, of obvious appeal to the scientific mind. 
According to operationism all scientific terms, even the most theoretical, are to be 
defined totally and exclusively by the operations used in their application; e.g., the 
general concept of length in physics is to be defined in terms of meter sticks, light 
triangulation, etc. Empiricists want to ground all knowledge in observations. Not 
only must we begin all scientific investigations with observations and nothing but 
observations, but also all scientific knowledge must be justified in terms of observations 
and nothing but observations. The appeal of both of these tenets to scientists is clear. 
As Johnson sees it, scientists really do need explicitly stated ways of applying their 
concepts, and observations do play a necessary and important role in science. The 
issue is the 'nothing-but' interpretation of these tenets. 
Johnson zeroes in on the correlative notions of overall similarity and general-purpose 
classification as one of the weakest parts of phenetic taxonomy. He argues at great 
length and with considerable skill that both notions are 'metaphysical' in the sense 
that neither can be operationally defined in even the weakest sense. Nothing out 
there in nature answers to the name 'overall similarity.' Any set of objects can be 
described in indefinitely many ways. Although we can limit ourselves to certain 
attributes and regularities if we so choose, such choices are inherently arbitrary. In 
short, 'there is still no parametric value of similariti/' (Johnson 1968: 22; see also 1989: 96). 
As a result, the notion of a general purpose classification is a metaphysical delusion 
(Ehrlich & Ehrlich 1967, Ghiselin 1969). 
For a group of scientists who were so concerned to be as hard-nosed and observation- 
based as possible, the existence of such a clearly metaphysical notion as overall similarity 
at the heart of phenetic taxonomy is disconcerting. Pheneticists expressed extreme 
doubts about our ability to reconstruct phylogeny. For most groups we have little if 
any fossil evidence, including the Proteaceae as Johnson and Briggs (1963: 22-26, 
1975: 94) readily admit. Even in those cases in which we have a reasonably rich fossil 
record, no unique ordering into phylogenetic trees is possible. Numerous alternative 
