26 



• KNOWLEDGE • 



[Jan. 12, 1883. 



LOGICAL PUZZLE. 



I FEAR you have made some slips in your e.xplanations 

 of the logical puzzle, at p. 7, No. 62. 



In the first explanation you say, " for all ^s to be -2r's," 

 «ta " This can o)tli/ be true, sri iiposhtg the A''s lo he rijiial 

 in uiiiaber to the Z's : but, as we know nothing as to the 

 number of the X's, except that they are at least equal to 

 all the Z'a, and may be any greater number, mc can make 

 no (taitcriion wlmlecer vntli regard to (he X's. Conse- 

 quently, in the case in which the X's are in excess of the 

 Ji's, to speak of ALL Xs being Z'x is utterly absurd, atul has 

 no iifanint/ whatever. 



Your second slip is of more importance, and depends on 

 the application of the word some. Some, in ordinary lan- 

 guage and in logic, implies one or more, and may signify 

 ALL. Your second explanation only applies to one of the 

 alternatives — the case in which some does not imply all. 

 Yet you pass this off as a full explanation of the prolilem, 

 while in fact it is only half the explanation. It can only 

 be taken as the full solution by supposing the word some, 

 in certain cases, to imply no7ie at all, which is absurd. 



You say there are "so many Zs which are not Y's, and 

 so many which are l''s." By what process of conversion 

 or transmutation do you extract the first of these proposi- 

 tions from the simple premise, " Some Y's are Z's 1" " Some 

 Z's are not Ys " can never be deduced from the premise. It 

 may possibly be true in certain cases, but does not neces- 

 sarily follow. It is quite possible that all the Z's may be 

 Y's, and then none of the Z's would he not Y's. In that 

 case, unless the word some signifies none — which it cer- 

 tainly does not signify in ordinary language and in logic, 

 whatever it may signify in mathematics — yoiir explanation 

 is altogether insufficient, and ought to be supplemented by 

 the case in ivhich all Z's are Y's. To take the concrete 

 example, the roicing men may be exceedingly numerous, and 

 include all the 1,350 football players, and many others. 



I consider logic — as the science which teaches how to 

 find truth — to be one of the most important studies. 



Thomas Common. 



[Our correspondent has afforded us, not intending it, a 

 curiously apt illustration of the way in which formal logic 

 interferes with ready reasoning by taking one off the track 

 to follow side issues. The thing to be shown being that some 

 X's are not Z's, we pointed out how the assumption that 

 all X's are Z's leads at once to a contradiction — this being, 

 in point of fact, precisely the way in which a soundly- 

 reasoning mind deals with the matter : our correspondent 

 objects to this, that we can make no assertion whatever 

 with regard to all the Xs — confounding assertion with 

 assumption. In using the argii mentum. ad absurdum' one 

 always does assume what is eventvially shown to be absurd, 

 or " utterly absurd," if Mr. Common likes strong adverbs. 



As " a more important objection," and as making our 

 explanation " only half an explanation," he notes that we 

 omit all reference to the case in which all Z's are Y's, — 

 of which, if we had thought it worth while to speak at all, 

 we should have noted simply that it requires no explana- 

 tion. C>ur correspondent seems not to have noticed that 

 if all Z's are Y's, the syllogism reduces simply to this — 

 All Z's arc V's ; 

 Some X's are not Y's ; 

 .•. Some A''s are not Z's. 

 \N'oukl it have been worth while to point out the truth 

 of this (a common syllogism in liaroko) to readers of 

 Knowledge 1 



Our correspondent gives further illustration of inexact 

 reasoning by quietly " begging the question " at the close 



of his letter. If logic is the science which teaches how 

 to find truth it is unquestionably one of the most im- 

 portant studies. But men find truth by observation, ex- 

 perience, and reasoning, — not by logic. Logic is only the 

 science which teaches men what they do when they reason ; 

 (even Whately does not claim that the study of logic 

 t(facljes men how to find truth) ; and many, after they have 

 learnt logic, pay more attention to the question whether 

 they are reasoning in Barbara or Cdarent, than to the 

 truth of their premisses or the validity of their con- 

 ilusions. RiciiD. A. Proctor.] 



' Let Knowledge grow from more to more." — Alfred Texxtsok. 



iettersi to tfte ©iiitor* 



Only a small proportion of Letters received cmi po.«sibZi/ he in- 

 serted. Correspondents 'inust tiot he of ended, therefore, should their 

 letters not appear. 



All Editorial communications should be addressed to the Editoe of 

 Knowledge; all Business commujiications to the Publishers, at the 

 Office, 74, Great Queen-street, W.C. If this is not attended to, 



DELAYS arise FOR WHICH THE EDITOR IS NOT RESPONSIBLE. 



All Remittances, Cheques, and Post Office Orders should be made 

 payable to Messrs. Wyman & Sons. 



The Editor is not responsible for the opinions of correspondents. 



No COMMUNICATIONS ARE ANSWERED BY POST, EVEN THOCGH STAMPED 

 AND DIRECTED ENVELOPE BE ENCLOSED. 



SINGULAR PHENOMENON. 



[683] — In 1881 I tried, late in the year, marking a tennis coort 

 with tape. This remained on the ground only one day. My surprise 

 was great in November to see the court marked out one frosty 

 morning, as though the hoar-frost had been brnshed from off the 

 lines where the tape had been. In spite of it never having been 

 used again, I still, with the return of winter, see my court marked 

 every morning as before. If you or any of your readers would give 

 me a satisfactory explanation of this, I should be much obliged. 



E. Skinner. 



SHIPS IN A CALM. 



[684] — In answer to the question relating to the onward motion 

 of a ship in a calm, I beg to give the following explanation : — 



If a wooden sphere or hemisphere be dropped from any height 

 into water, it will sink and rise alternately until it comes to rest 

 on the surface at the exact spot in which it first struck the water. 

 This i.s because the resistance its surface offers to the water is equal 

 in all directions. If, however, the form be altered to that of a 

 ship, it will not be found to remain in the same spot after repeated 

 oscillations, because the bottom offers more resistance at one end 

 than the other ; and, of course, the ship moves in the direction of the 

 less resistance. Now a, ship on the sea is constantly being raised 

 and allowed to fall again into the sea from a "swell " which exists 

 oven in calm seas. Thus a ship is always oscillating up and down, 

 at one time a little more out of water than it would be if the mass 

 of w.ater were perfectly still, and at another time a little deeper in 

 than it would be under the above-mentioned circumstances. This 

 up and down motion of the sea is always acting ; but when the 

 surface is rough, this action on the motion of the ship is in- 

 finitesimal, compared wnth that due to the action of the wind, and 

 so is no*-, noticed ; but when there is a calm, there is no other force 

 at work, and, therefore, that is the only one noticed. 



James Shcter. 



THE RAINBAND.— A NEW ZEALAND GUM. 



[GS5] — I thank you and Mr. Bramley-Moorc for tlic "Rainband" 



information (page 4S5). May 1 ask you to insert in future numbers 



corrcBpondcnco on the subject of the Rainband ? Perhaps some one 



w ould give a table for — say a month — of daily weather, with spec- 



