January 14, 191 5] 



NATURE 



DO 



in ordinary languag^e, "any arbitrary element 

 of the class " as a definite object. He quite 

 rightly observes that this is not an element of the 

 class ; but he goes on to say, " In spite of this 

 * or, ' ' a or & or . . . ' is a clear experience of our 

 thinking." Of course it is for certain small finite 

 sets, but if we try to extend it, as the author does, 

 to infinite sets, there seems to be a risk of begging 

 the question at issue in the theory of selections. 

 What we want is to justify, and generalise, so 

 far as we can, such expressions as "fafee an 

 arbitrary point on the given circle," "take an 

 arbitrary prime number," and so on. 



These two examples are of the same type, but 

 they will serve to show part of the difficulty of 

 the question. When a circle is drawn, few would 

 object to the postulate " It is possible to choose 

 an arbitrary point on the circle," it seems so obvi- 

 ous intuitively. But now consider the set of 

 primes, and suppose them arranged in order of 

 magnitude ; the millionth of them is a definite 

 existent prime, but what do I mean by " taking " 

 it? I cannot take it in the same sense as I can 

 take two or three or 10 1, because it has not, so 

 far as I know, been calculated; so I must consider 

 " taking " it as specifying it by a description, 

 belonging to it and to nothing else. But what is 

 there in the general definition of a class to enable 

 us to take an element of it, in the sense required 

 for the theory of selections? How can I "take," 

 for instance, an arbitrary sound or colour? What 

 sort of set (mathematically) is that of pure musical 

 tones? Can we arrange all periodic sounds 

 ordinally? and so on. 



It is rash for an outsider to intrude upon such 

 a thorny topic, but we cannot help surmising that 

 Zermelo's axiom (or an equivalent to it) may be 

 like the axiom of parallels in geometry ; not neces- 

 sarily true, but leading, if assumed, to a large 

 body of valuable conclusions. In geometry we 

 have practically only two alternatives to the 

 parallel axiom ; it took a long time to discover 

 them, and the only way to disprove the truth of 

 Zermelo's axiom is to find a case that contradicts 

 it. Meanwhile, a safe course is to imitate White- 

 head and Russell, and introduce the axiom as a 

 working hypothesis. 



It may be noticed that the author pays a warm 

 tribute to Russell's important contributions to the 

 theory of logic. There can be no doubt that they 

 have done much to advance clear thinking, and 

 avoidance of fallacies. 



The work is, unfortunately, not quite complete, 

 as the author died before finishing the last 

 chapter. His portrait is given as a frontispiece. 



G. B. M. 

 NO. 2359, VOL. 94] 



EGYPTIAN FOLKLORE. 

 Amulets, Illustratad by the Egyptian Collection 

 in University College, London. By Prof. W. M. 

 Flinders Petrie. Pp. x + 58 + plates. (London : 

 Constable and Co., Ltd., 1914.) Price 21s. 

 net. 



PROF. PETRIE is certainly right in sug- 

 gesting that the subject of Egyptian 

 amulets is one that appeals to the reader of folk- 

 lore as well as to the Egyptologist. In amulets 

 we are dealing with magic in a concrete form, 

 and it is a problem of no small fascination to 

 recover the meaning which underlay the origin 

 and use of each. It will be obvious that a wide 

 knowledge of Egyptian religious belief is essen- 

 tial, if we are rightly to understand those amulets 

 of peculiarly Egyptian origin. But where the 

 texts fail us we are necessarily thrown back upon 

 comparison with amulets of other races, particu- 

 larly those of Central African tribes. It is here 

 that folk-lore finds its opportunity, for it not 

 infrequently supplies a clue to the meaning of an 

 otherwise obscure or doubtful symbol. 



In the work before us Prof. Petrie has com- 

 bined both these converging lines of research 

 in a remarkable degree. His material is mainly 

 drawn from amulets in the University College 

 collection, which, as the result of excavation and 

 purchase carried out for many years, he has made 

 as varied as possible; but he has also supple- 

 mented these with reference to examples in other 

 collections. He has consequently been able to 

 describe some two hundred and seventy different 

 kinds of amulets, and his classified list, largely 

 the result of pioneer work, places the study opon 

 a scientific basis. Under each heading the Egyp- 

 tian name is given when known, its meaning and 

 use are suggested, varieties, periods, and material 

 are noted, and references given to the collections 

 where specimens occur. 



In his discussion of general principles, the 

 author is certainly right in dismissing with scant 

 sympathy the "confidence theory" and the "faith 

 theory," for though these undoubtedly explain 

 the actual efficacy of amulets, they are entirely 

 out of place as explanations of origins. By far 

 the greater number of Egyptian amulets are most 

 satisfactorily interpreted on the principles of sym- 

 pathetic magic, or in Prof. Petrie 's own phrase, 

 by the "doctrine of Similars." The whole body 

 of funereal magic, as practised by the ancient 

 Egyptians, partakes of this general character, 

 and it is but natural that amulets, whether worn 

 by the living or the dead, should fall under the 

 same category. It is only when we come to 

 detailed explanation that lines of underlying 



