Fer 9, 1883.] 



♦ KNOWLEDGE 



91 



LOGICAL I'lZZLEDOM. 



[714' — In niv last letter I partly confounded assertion with 

 assnmption, but that hardly tenches the question at issue. As I 

 understand the rednctin atl abintnium argument (which is little 

 mentioned in logical text-books, though so much used by Euclid), 

 tee maktf a ^uppositioti eonitiiitent icith one of the prewiixe*-, and 

 proceetl tn test it by the remaining premise or premises, and when 

 it is " eventually " contradicted by the latter we get the reductio 

 nd altsurdiim. We make no questionable wider assumption than is 

 necessary for our purpose, nor any assumption which, before it is 

 contradicted by other premises, involves an absurdity in itself. 



In the solution of the logical puzzle (p. 7, No. 62) the assnmption 

 ■' for all X's to bo Z's, Ac," is a wider assumption than is necessary 

 for the solution, the assumption " for all the X's in queKtitm to be 

 Z's, ic," being sufficient ; and the assumption uncorrected also 

 involves an absurdity in itself, before it is contradicted by other 

 premises ; being inconsistent with the first premise with which it 

 must necessarily l>e consistent ; all the X's may be more in number 

 than the Z's, and to assume that all the X's are Z'a is to assume 

 that a greater number may be equal to a smaller, which is absurd. 



It is very difficult to avoid logical pit-falls. Probably every one 

 who attempts reasoning stumbles among them more or less. I 

 shall not beg the question as to logic being the science which 

 teaches how to find truth. I take your statement as correct that 

 *' men find truth by observation, experience, and reasoning," and I 

 refer to all the important works on Inductive and Deductive Logic, 

 especially the works of Mill, Jevons, Bain, Fowler, Ac., who all 

 teach how observations and experiments are made, correctly and 

 incorrectly ; how experience is gained, and how people reason, cor- 

 rectly and incorrectly. [So far right ; but in what follows the 

 (|Uestion is begged again. — R. P.] What more can be done to teach 

 people how to find truth than to show them the right and the wrong 

 way ? [This is just what formal logic does not do, any more than 

 the criticism which points out errors or beauties in a drawing 

 teaches how to draw.. — R.P.] When the evidence as to the correct 

 method of finding truth is convincing, the mind involuntarily 

 assents to it, as to all other convincing evidence, and to a certain 

 t'xtent, at least, depending on the person's intellectual habits, acts 

 according to the correct method. 



Inductive logic is certainly the more important, though the use 

 of deduction for the purpose of verification must not be under- 



* rated. Hamilton's extension of the logical forms is somewhat puerile, 



• »"equiring as it does for its completion what De Morgan terms the 

 ^jutrious proposition — " some X's are not some Z's " — a proposition 

 ■which is necessarily true, unless there is only one X, which is also 

 the one Z. 



Deduction, or formal logic, has been greatly extended and gene- 

 ralised since the time of Whately, especially by De Morgan, Boole, 

 and the lamented Professor Jevons, whose logical " abecedarium " 

 and logical machine, enable one at once to solve complex logical 

 problems which cannot be solved by unaided mental processes. 



Thomas Common. 



[Mr. Common's account of the reductio ad absurdum is not 

 strictly correct. We alwaj-s in applying this method have the con- 

 clusion in view, — we make such a supposition as must be sound 

 if the conclusion we wish to establish is unsound, — and that is the 

 only condition we have to consider ; consistently with this we 

 may assume anything. (It is not sufficient to assume something 

 which is merely inconsistent with the conclusion.) This kind of 

 argument belongs as much to logic as to mathematics, — in fact, 

 underlies a large proportion of formal logic. In the present case 

 we have to show that " some X's are not Z's," and the only admis- 

 sible assumption for the reductio ad absurdum is that " all X's are 

 Z's." Mr. Common's remarks on this point are simply incorrect. 



Logic shows how people reason correctly and incorrectly ; but it 

 may be doubted if it ever taught more. The great observers, ex- 

 perimenters, discoverers, and inventors, reasoned correct!}- indepen- 

 dently of formal logic, and afforded the logician some of his best 

 examples. But the best logicians have not always reasoned cor- 

 rectly, witness Jevons' arguments about the exhaustion of coal, 

 and about sun-spots, and commercial crises. Logic may be com- 

 pared to criticism. Learning wliat constitutes correct drawing or 

 painting is not learning to draw or paint correctly. — E. P.] 



RIGEL. 



[715] — Will yon kindly inform me whether Rigel is a coloured 

 etar. An old friend of mine tells me that fifty years ago Rigel was 

 considered by astronomers to be red. Is that so ? 



Although I live at Streatham. I hope you won't visit on me the 

 sina of the district, for I am not one of those who made that absurd 

 request mentioned by you in your " Lecture Notes." SoL.\KirM. 



[Like ilr. Webb, I always see a bine tinge in this star. Others 

 consider it yellow. — Ed.] 



[710] — I am an engineer and millwright by trade, and am about 

 to leave Old England either for America or Australia, to seo if the 

 climate will benefit me for a bronchial complaint, and seeing from 

 Knowledge that you have travelled in both places, can you kindly 

 give me any advice as to what parts of either country will be moat 

 suitable ? I have thought about Minnesota, in America, and New 

 South Wales, in Australia. R. H. M. 



[I cannot advise " R. U. M." bettor than by suggesting that he 

 should obtain the excellent little book on emigration published by 

 Messrs. Wyman & Sons. — R. P.] 



NATURE'S REST. 



[717] — In yonr number of January 10 you say, " When nature 

 stops working every seventh day, come and tell us that the God of 

 Nature wishes us to do likewise." There is to be remembered that 

 nature docs rest for many weeks in the winter time. la this 

 rest beneficial ? or is it useless ? A Clergvm.^.n's Wife. 



[It seems to be imagined that my Answers to Correspondents — 

 discontinued for this among other reasons— were addressed to 

 readers generally, and not to special querists. There might be 

 remembered also that animals, men included, sleep at times, and 

 this rest is decidedly beneficial. So with the winter's rest — in our 

 latitudes at least — for there is no such rest in the tropics. Quorsum 

 htrc tain pufida tendunt ^ I believe even, as society haa come to be 

 constituted, that the seventh-day rest is good for our working 

 claases, or, at least, it might be, if they were not so cruelly robbed 

 of its benefits. One of tho best and purest teachers the world has 

 known, perhaps the very best, taught that this seventh-day's rest 

 was devised for the benefit of man— which is true, whatever theory 

 of the origin of the observance is accepted. But it is used as if it 

 had been made for man's punishment and to benefit only a certain 

 small class of persons.] 



FOSSIL GUM. 



[718] — Referring to Mr. Clark's inquiry about fossil gum, I think 

 it may possibly interest some of your readers to know that it is dug 

 up in tracts of country (in the northern island of New Zealand) 

 where large forests of Kauri are supposed to have existed ages ago. 

 The gum is exported largely to England for reshipment to America, 

 for the purpose of making varnish. Good quality realises as much 

 as £20 per ton. 



Some beautifully clear specimens of this gum are used for orna- 

 mental purposes. I possess a piece in the rough which, in colour 

 and transparency, resembles very clear barley-sugar. There are 

 three kinds of Kauri — tho white, the red, and the mottled. The 

 latter is comparatively scarce. It is a conifer, I believe. The 

 Kauri tree (white) grows to a great height (tho stem attaining to 

 90 ft. before throwing out a branch). It has been known to grow 

 to 200 ft. from the ground to the head, the stem having a diameter 

 of 12 ft. This wood is very tough, and takes a good polish ; conse- 

 quently it is very useful for building purposes, both for houses as 

 well as for ships. It is, I think, the only wood that shrinks end- 



ways. 



A. C. K. 



A PUZZLE. 

 [719] — "A squirrel is sitting upon a post and a man is standing 

 facing the squirrel, the squirrel presently turns round and the man 

 moves round with it, always keeping face to face. When the man 

 has been round the post has he been round the squirrel ? " 



BlBBENHALt. 



LETTERS RECEIVED.— CONTENTS NOTED. 



R. H.— R. R.— C. C. R.—Senex— Language— H. A. A.— F. W 

 Cleworth— C. J. Brown— J. M. Hunt- H. S. S.— G. E. Clarke— 

 W. H. S. M.— Jocelyn— T. R. Street— T. K. D.— Inquirer— Luke— 

 G. T. Shan— T. Quilliam— G. Sidus— W. Waterhouae— More Light 

 — C. Craven — G. I. I.— Constant Reader — Israelite— C. Eyre — J. 

 Venn— J. G.— G. Alston— G. S. M.— G. M. G.— F. H. M.— J. 

 Graham — M. B. A.— J. Esham — T. B.— L. Thomson— Pleiades — 

 J. B.— B. G— C. H. Johns— M. Ridley— F. R. G. S.— A Clergyman's 

 Wife— Upsala— E. C. S.— W. Graudy— C. Carua Wilson— Z.—F. C. 

 Rearden— E. Keelan— J. U. W.— W. G.— F. J. C. Trenton— R. E. C. 

 — J. 'Watson— S. M. B.— W. J. W. Rees- Fide tutus aclatns— 

 E. T. C. W.— T. S. Bayley—Faciebat— Julie Magny— H. A. Kay— 

 W. J. O.— R. J. Whitley— E. C. R.— R. R. Baldrey— R. R.— T. V. R. 

 — A Country Clergyman — T. Claydon — T. Conimon — P. J. T. — 

 H. J. M.— Tycho.— Rev. E. L.— W. More.— W. Clift— Familiar 

 Experience — M. E. Hoskiss- Rev. P. T. L.— C. Murray, sen.— 

 L. L. K.— Doctor of Divinity — Evolution — K. Kuster— R. M. 

 Rollins— K. Saptander— Cornish Miner— A Pleased Subscriber- 

 Dr. D. T. M.— &c. 



