AU VEE YY: 
ILLUSTRATED JOURNAL OF SCIENCE 
““To the solid ground 
Of Nature trusts the mind which builds for aye.’’—Worpswortn. 
THURSDAY, NOVEMBER 1, 1906. 
SOME RECENT WORKS ON LOGIC. 
(1) Symbolic Logic and its Applications. By Hugh 
MacColl. Pp. xit141. (London: Longmans, 
Green and Co., 1906.) Price 4s. 6d. net. 
(2) The Development of Symbolic Logic. By A. T. 
Shearman. Pp. xi+242. (London: Williams and 
Norgate, 1906.) Price 5s. net. 
(3) An Introduction to Logic. By H. W. B. Joseph. 
Pp. vii+564. (Oxford: Clarendon Press, 1906.) 
Price os. 6d. net. j 
(4) Thought and Things, or Genetic Logic. By James 
Mark Baldwin. Vol. i. Functional Logic, 
Genetic Theory of Knowledge. Pp. xiv+273. 
(London: Swan Sonnenschein and Co., Ltd., 1906.) 
Price tos. 6d. net. 
(1) HETHER Mr. MacColl is the Athanasius 
of symbolic logic or only its Ishmael, the 
fact remains that he seems unable to come to an 
agreement with other exponents of the subject. But 
he contends that his system ‘“* 
ability of its notation bears very much the same re- 
lation to other systems (including the ordinary formal 
logic of our text-books) as algebra bears to arith- 
metic.”’ The present work contains the results of a 
series of researches dating from the year 1872. Por- 
tions have appeared at intervals in various magazines, 
English and French. Points on which he lays con- | 
siderable stress, and in which he does not command 
the uniform assent of the other symbolic logicians, 
are these :—(a) that he takes statements and not 
terms to be in all cases and necessarily the ultimate 
constituents of symbolic reasoning; (b) that he goes 
quite beyond the ordinary notation of the symbolists 
in classifying propositions according to such attributes 
as true, false, certain, impossible, variable; (c) that 
in regard to the existential import of propositions, 
while other symbolists define the null class 0 as con- 
taining no members, and understand it as contained 
in every class, real or unreal, he, on the other hand, 
defines it as consisting of the null or unreal members 
NO: TO3iIs WOL.75 || 
or | 
in the elastic adapt- 
0,, 0, 0,, &c., and considers it to be excluded from 
every real class. A chapter is devoted to the solution 
of Prof. Jevons’s so-called inverse problem. 
(2) The sub-title of Mr. Shearman’s work is ‘*A 
Critical-Historical Study of the Logical Calculus,” 
and its author’s chief object is to show that during 
the last fifty years a definite advance has been made 
by symbolic logic. 
“T have traced the growth of the subject,’ he 
| writes, “‘from the time when Boole originated his 
generalisations to the time when Mr. Russell, pur- 
suing for the most part the lines laid down by Peano, 
| showed how to deal with a vastly wider range of 
problems than Boole ever considered.”’ 
He is careful to point out that the view which he 
expresses in his work as to the relation of mathe- 
matics to logic ‘‘is to be regarded as preferable only 
to the doctrines that were in vogue prior to the time 
of Peano’s analysis of mathematical notions.’ 
Mr. Shearman’s opinions on some disputed points 
may be noted :—(a) He can see no valid reason why 
symbols may not designate now classes, and now 
propositions. ‘‘ The only thing to be remembered is 
that the rules of procedure are not quite the same in 
the two cases.’’ (b) He rejects all attempts to deal 
with any but assertoric propositions, and holds that 
if Mr. MacColl wishes to work with such data as 
probable and variable he should introduce new terms. 
(c) He regards it as practically impossible to elaborate 
a calculus based on intension. 
In a footnote he directs attention to a remark of 
the late Prof. Adamson which seems to imply that 
all the intermediate processes in a solution ought to 
be intelligible. Our author believes, on the other 
hand, that ‘‘a calculus is a means of reaching correct 
conclusions by means of the mechanical application of 
a few logical rules, and it is quite possible that in 
the application of such rules unintelligible elements 
may temporarily appear.’’ The doctrines of Prof. 
Jevons and Mr. MacColl are subjected to some severe 
criticisms, and Mr. Shearman holds that Prof. 
Jevons’s actual contributions to the development of 
symbolic logic were few and relatively unimportant. 
B 
