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 252 W. L. DAVIDSON I up the interval that the mutually-exclusive type cannot be consistently carried out. In so far as there is mutual impli- cation among different groups, there cannot, to that extent, be mutual exclusion (the one idea cancels the other) ; and where, as in the case of living beings, of plants and animals, you have the phenomena of development and growth, of group shading into group by insensible degrees, rather than demarcated by a rigorous boundary, cross-division is unavoidable. Hence the necessity of denning a rational principle of classification in the way that we have already done, i.e., as luminous, in opposition to the arbitrary and frivolous, rather than as mutually-exclusive ; and hence the meaning of the words " having regard to the materials manipulated and the end in view " appended to the Rule in Section II. above. In dealing with living beings, any prin- ciple that may be chosen always requires you to admit of exceptions ; and the correlated properties that a fundamental character carries along with it are only true on the whole. Though the typical Vertebrate has all the points enumerated in last Section, there comes such an exception as the lance- let (Ampliioxus lanceolatus], which has the unique peculiari- ties of anomalous breathing organs, and anomalous organs of digestion and of circulation ; which, moreover, is destitute of a heart, and which has no true brain and no true skeleton, no skull, no true back-bone or vertebral column : and its position is secured to it among vertebrates only because, taking everything into consideration, it shows more affinity to these than to the invertebrates. On the other hand, several of the invertebrates show a clear approach to the vertebrate type. In the so-called cuttlefish, for example, there is a distinct brain enclosed in a kind of skull a gristly, not a bony, case. Still, because the affinities are towards the invertebrates, it is classed accordingly. Mutual exclusion, then, is not an imperative requirement in graded classifications. Are these, therefore, to be con- sidered illogical ? If their object were a purely ideal one, this conclusion would indeed be inevitable. But as their object is not a purely ideal one, but aims first and chiefly at laying hold of things as they are in fact, this conclusion is illegitimate. In classifying the emotions, we must pay regard to their subtle interdependencies as well as to their diversities and contrasts ; otherwise, it is not the emotions we classify, but something else. In schematising the sciences, we must never lose sight of the fact that these sciences have a kind of organic connexion, and that their union is of as much importance as their separation. In