Jan. 5, 1883.] 



KNOWLEDGE 



A LOGICAL PUZZLE. 



By Rioiard A. Proctor. 



SEVERAL correspondents find the syllogism quoted in 

 a footnote to our review of Prof. De Morgan's Life 

 as " hard " as De Morgan considered it ; and not a 

 few can make, it would seem, " neither head nor tail " of 

 it 1 will give it again, with the explanation of it, — which, 

 in mj' judgment, takes longer in the reading than the syl- 

 logism ought to take in interpretation and acceptance. 

 It runs thus : — 



(1) For every Z there is an X which is not )". 



(2) Some }''s are Z'%. 



. •. Some A''s are not Zs. 



Surely the conclusion is an obvious one. We are told 

 l>y (1) that there are at least as many not-J' X"s as there 

 are Z's. So that for all X'a to be Z's, the Z's must bo nil 

 not-T's; but some Z's are Y's; therefore all A''s are 

 not Z's. 



The thing may be put in many ways. Here is another — 

 There are so many Z's which are not Y's, and so many 

 which are Y's; and as many not- l'A''s as there are Z's 

 ■of both kinds. Now as many of these not-1' A"'s as there 

 are not- )' Z's mai/ be Z's ; but the rest cannot be ; for 

 all the Z's left are Ys. Thus a certain number of A^s are 

 not Z's. 



Concrete examples are always better than abstract ones ; 

 so let us take a simple concrete example of this syllogism. 

 (Of course such an example is allbrded by the passage 

 we quoted from De Morgan's letters ; but he is there at 

 some pains to wrap up the absurdity involved by a rejec- 

 tion of the syllogism — the only chance, so far as 1 can see, 

 of misleading any one who, not being a student of formal 

 logic, is not necessarily a darkened reasoner) : — 



For every football player there is a non-rowing cricketer. 

 Some rowing men play football ; therefore some cricketers 

 <lo not play football. 



If, wliich I cannot imagine, this last case should perplex 

 anyone, make it still more definite by using numbers, 

 noting that you can use almost anj- numbers you please : — 



There are in all 1,3.")0 football players, and there are 

 1,350 cricketers who do not row ; now, L'31 rowing men 

 play football; hence only 1,119 football players do not 

 row ; and as there are 1,3.")0 cricketers who do not row, 

 231 cricketers, a( feasl, cannot be football players. In 

 such a case as this no logic is wanted. We see at once 

 that our 1,350 football players are divisible into two lots — 

 the rowers 231 in number, and the non-rowers 1,119 in 

 number: but among cricketers there are 1,350 non-rowers, 

 or 231 more non-rowers than there are among football 

 players ; so that there must be at least that number of 

 cricketers in excess of the number of football players. 



The reasoning may be generalised thus: — 



If there are A Z's of which ii are also }''s, so that 

 {A — w), and no more, are not-J"s : then if there are 

 A' A's which are not- )''s, only (A — n) of these A's can 

 possibly be Z's ; the remaining n A's must of necessity be 

 not Z's. 



To prove that there is any use whatever in the syllogism, 

 over the credit of inventing which Sir W. Hamilton and 

 Professor De Morgan disputed, it ought to be shown that 

 in any case whatever (in some ojc case at least), depending 

 on the law supposed to he worth demonstrating, any person 

 of average intelligence would fail to arrive at a Just con- 

 clusion. But this seems utterly incredible. For instance, 

 if any one were told that among football players a fourth 

 are rowing men, and that there are as many non-rowing 

 cricketers as there are non-rowing and rowing football 



players together, could he fail to see at once that there 

 are more cricketers than football players, so that some 

 cricketers cannot possibly be football players 1 



THE 



PLEASANT HOURS WITH 

 MICROSCOPE. 



Bv Henry J. Slack, F.G.S., F.R.M.S. 



DISEASE GERMS. 



''piIE subject of these papers will be varied from one 

 J_ fortnight to another to suit the tastes and amount 

 of c.Kperience of various readers. To-day, Disease Germs 

 will occupy us. For a long time it has been thought 

 that a large group of diseases, including many of the most 

 fatal, were produced by speciiic germs inhaled by the 

 sufierer with the air, drank with some fluid, or deposited 

 on some sore place. Through the researches of Pasteur 

 and others the general facts leading to this theory are 

 now placed beyond doubt, and in several cases a well- 

 trained observer can distinguish one disease germ from 

 another, and an experimenter like Pasteur can prove his 

 conclusion right by inoculating some animal with the 

 germs, and producing in it the expected disease. Experi- 

 ments of tliis kind, merely to gratify curiosity, could not 

 be defended, but they have a ditlerent character, when, as 

 in Pasteur's case, they are guided by a benevolent 

 purpose, and have enabled him — besides assisting the 

 physician to lessen human suflering — to show farmers 

 how to secure sheep, fowls, and pigs from disorders that 

 occasioned a sad devastation. The non-professional and 

 elementary student cannot expect to do more than form a 

 notion of the sort of things disease germs are and how 

 they act. When one particular organism is said to be the 

 specific germ of splenic disease in sheep, and another of an 

 enteric fever in man, it must not be assumed that either 

 the germs or the diseases are specific in the old and very 

 narrow meaning of the term. This we shall see as we go 

 on. The most common forms of disease germs are those 

 of extremely minute rods — bacteria, or minute round 

 bodies called micrococci (little berries) by no means a good 

 term, as the objects are not really like any berry. 



Half-a-dozen Preston salts bottles are convenient things 

 for experiments that will throw some light upon tliese sub- 

 jects, although they may not exhibit any actual disease 

 germs, but only some of their more innocent relations, or 

 perhaps objects specifically the same as disease germs, but 

 not in a mischievous condition. Put a little water into 

 four of the bottles, and add to one a pinch of chopped 

 hay ; to another a bit of raw meat as big as a small pea ; 

 to a third a little dust swept from the walls or floors ; put 

 a little milk in the fourth ; a little flour paste in the fifth ; 

 and a little boiled rice in the last. Place all in a warm 

 room, and watch from day to day. As soon as a thin skin 

 (pellicle) forms in any one, put a drop on a slide, cover 

 with thin glass, and view with a power of about one quarter 

 of an inch, which with a ten-inch tube microscope 

 will magnify about 200 linear with an A or No. 1 

 eye-piece. The observer is sure to see a large number 

 of very small, ."straight objects, some quiet, and 

 others moving with a wriggling motion. Some of 

 these may shov/ with that magnification that they are 

 beaded, or contain minute beads, others would show it 

 with a much higher power, and some again are so small 

 and delicate as to defy all attempts to discover structure. 

 After a few days, it is most likely that many rather larger 

 thread-like objects will appear, twisted like corkscrews, 



