It has become increasingly clear, in the last few decades, that discussions of the course of evolution in groups of organisms which lack a comprehensive fossil record are futile so long as those who hold opposing views base their arguments on preeconceived ideas. Nowhere does this apply with greater force than to the evolution of flowering plants, where the fossil record, restricted as it is to postJurassic times, gives little or no direct evidence. Under these circumstances, before any further progress can be made, a radical change is essential both in mental approach and in thought processes. In ridding our minds of all personal convictions not founded on scientific evidence, not only must we examine in the minutest detail our basic assumptions, their factual justification and their logical implications whenever our own beliefs differ from those of others, but we must also do so even when there. is little or no disagreement. Only then shall we be in a position to build a theoretical structure which is likely to survive. Yet, reading through the works of students of evolution, how seldom it is that the full reasoning is clearly stated. Frequently, it is true, basic assumptions are stated, but not the evidence on which they are based. Thus, in the field of dicotyledon evolution, it is common to find listed a number of trends which are assumed to have occurred, e.g. (Bessey, 1915) from woody habit to herbaceous, from hermaphrodite to unisexual, etc., but one looks in vain for the' thought processes lying behind these assumptions. Of the two quoted, the first assumption is almost universally accepted, for there are few who do not agree that, among dicotyledons, the woody habit is primitive. But what real evidence has been. Dut forward in support of this view? All too often in such cases, as Turrill (1942) has emphasised, the evidence can be reduced to a circular argument around primitive characters and primitive organisms. Yet most of the phylogenetic schemes of classification, so far produced, are based on such insecure foundations. The criticism lies not so much with the basic assumptions themselves, for many of them are probably correct, as with the reasons for their acceptance. It was with such thoughts in mind that a few years ago, (Sporne, 1948 and 1949), I made an attempt to cut the Gordian knot by reducing to mathematical terms the discussion of evolution in large groups of organisms, thereby avoiding, as far as possible, the effects of personal bias. The starting point lay in the generally acceptable view that the process of evolution involves the acquisition of new characters in addition to, or in exchange for, old ones. On this were based a number of definitions, to which no objection has, so far, been made. In addition, there was the hypothesis that trends in evolution have occurred, i.e. that certain changes have taken place in several different lines of evolution. It was then shown that, if such hypothesis be correct, the characters concerned in these trends will exhibit mathematical correlation. Thus, within a particular group of organisms, if two ancestral characters A and B have shown a tendency to evolve into the advanced states A' and B', statistical analysis of the whole group should show a positive mathematical correlation between A and B and also one between A' and B'. (Similarly, there should be negative correlations between A and B' and between A' and B.) It is to be emphasised that such correlations are to be expected, whether the group is monoDhyletic or not. provided