with the formulation of but one; and perhaps it is just here that a kinship still remains between him and Thales and other philosophers of the school. He, no more than they, seems to have definitely raised the question, How are we to account for, or formulate, the principle of difference or change? What is it that causes things to come into being out of, or recalls them back from being into, the infinite void? It is to be confessed, however, that our accounts on this point are somewhat conflicting. One authority actually says that he formulated motion as eternal also. So far as he attempted to grasp the idea of difference in relation to that of unity, he seems to have regarded the principle of change or difference as inhering in 13 the infinite itself. Aristotle in this connection contrasts his doctrine with that of Anaxagoras, who formulated two principles of existence-Matter and Mind (see below, p. 54). Anaximander, he points out, found all he wanted in the one.

As a mathematician Anaximander must have been familiar in various aspects with the functions of the Infinite or Indefinable in the organisation of thought. To the student of Euclid, for example, the impossibility of adequately defining any of the fundamental elements of the science of geometrythe point, the line, the surface-is a familiar fact. In so far as a science of geometry is possible at all, the exactness, which is its essential characteristic, is only

ABSTRACTION AND REALITY

II

attainable by starting from data which are in themselves impossible, as of a point which has no magnitude, of a line which has no breadth, of a surface which has no thickness. So in the science of abstract number the fundamental assumptions, as that I = 1, x=x, etc., are contradicted by every fact of experience, for in the world as we know it, absolute equality is simply impossible to discover; and yet these fundamental conceptions are in their development most powerful instruments for the extension of man's command over his own experiences. Their completeness of abstraction from the accidents of experience, from the differences, qualifications, variations which contribute so largely to the personal interests of life, this it is which makes the abstract sciences demonstrative, exact, and universally applicable. In so far, therefore, as we are permitted to grasp the conception of a perfectly abstract existence prior to, and underlying, and enclosing, all separate existences, so far also do we get to a conception which is demonstrative, exact, and universally applicable throughout the whole world of knowable objects.

Such a conception, however, by its absolute emptiness of content, does not afford any means in itself of progression; somehow and somewhere a principle of movement, of development, of concrete reality, must be found or assumed, to link this ultimate abstraction of existence to the multifarious phenomena

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of existence as known. And it was, perhaps, because Anaximander failed to work out this aspect of the question, that in the subsequent leaders of the school movement, rather than mere existence, was the principle chiefly insisted upon.

Before passing, however, to these successors of Anaximander, some opinions of his which we have not perhaps the means of satisfactorily correlating with his general conception, but which are not without their individual interest, may here be noted.

The word husk or bark (pλoiós) seems to have been a favourite one with him, as implying and depicting a conception of interior and necessary development in things. Thus he seems to have postulated an inherent tendency or law in the infinite, which compelled it to develop contrary characters, as hot and cold, dry and moist. In consequence of this fundamental tendency an envelope of fire, he says, came into being, encircling another envelope of air, which latter in turn enveloped the sphere of earth, each being like the 'husk' of the other, or like the bark which encloses the tree. This concentric system he conceives as having in some way been parted up into various systems, represented by the sun, the moon, the stars, and the earth. The last he figured as hanging in space, and deriving its stability from the inherent and perfect balance or relation of its parts.

THEORY OF DEVELOPMENT

13

Then, again, as to the origin of man, he seems to 16 have in like manner taught a theory of development from lower forms of life. In his view the first living creatures must have come into being in moisture (thus recalling the theory of Thales). As time went on, and these forms of life reached their fuller possibilities, they came to be transferred to the dry land, casting off their old nature like a husk or bark. More particularly he insists that man must have developed out of other and lower forms of life, because of his exceptional need, under present conditions, of care and nursing in his earlier years. Had he come into being at once as a human creature he could never have survived.

The analogies of these theories with modern speculations are obvious and interesting. But without enlarging on these, one has only to say in conclusion that, suggestive and interesting as many of these poor fragments, these disjecti membra poetæ, are individually, they leave us more and more impressed with a sense of incompleteness in our knowledge of Anaximander's theory as a whole. It may

be that as a consistent and perfected system the theory never was worked out; it may be that it never was properly understood.

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CHAPTER II

THE SCHOOL OF MILETUS (concluded)

III. ANAXIMENES.-This philosopher was also a native of Miletus, and is said to have been a hearer or pupil of Anaximander. As we have said, the 19 tendency of the later members of the school was towards emphasising the motive side of the supposed underlying principle of nature, and accordingly Anaximenes chose Air as the element which best 18 represented or symbolised that principle. Its fluidity,

readiness of movement, wide extension, and absolute neutrality of character as regards colour, taste, smell, form, etc., were obvious suggestions. The breath also, whose very name to the ancients implied an identity with the life or soul, was nothing but air; and the identification of Air with Life supplied just that principle of productiveness and movement, which was felt 20 to be necessary in the primal element of being. The process of existence, then, he conceived as consisting in a certain concentration of this diffused life-giving element into more or less solidified forms, and the