IlEATIVE 8CIBNCR 



375 



form already given). The above sorites will bo reduced into 

 four HyllogiMui*. thus : 



1 2. 3. 4. 



(2) liUC. (3) CU I.. <:.) KiV, 



(i) A i it. (A [A.U i' . IAUEJ. 



[.'. A in Cj, [* * U D], L-'. A u Kj, [/. A U F]. 

 There are alno, of course, conditional Moritos, in which the 

 propositions arc conditional, iiutoad of categorical ; tmt of these 

 it ;- unnecessary to treat particularly. 



s of roanonin^ from t 



ulinjr for its validity n 

 .ionium. \Vi- eon 



ami it will !.-! -uit tho purpose we h > 

 jn tho litfht in whioh it IH viewed I 



shortly jiniiitiiij,' out the iliflWoi his opinions ami 



those.: Mill. 



According to Wliut^! 



:ues em].!. 



tion anil < .i!eetii.'_' ! 



rWW6 from the I'ael - when ascertain.',! : in.lin-tion. 

 foriniT MMisf, In-:: '.ut Hot 



like nil other rcasoni:. - 

 syllogistic form. Moreover, 



as it is tuki'n t > mean ix 



outside tho province of Log .hichis 



not to get promises, but to sec what 

 be drawn from them wl; 



tion is a process of infereWMNftr r<>iiaonin(. we nrny 

 Mill's definition : " The process by which wo conclude that 

 what is true of certain individuals of a class is true of tho 

 whole class, or that what is true at certain times will bo true in 

 similar circumstances at all times." Or wo might describe it 

 generally as tho process by which we infer a proposition to be 

 true universally from finding it to be true in a number of 

 particular instances. Thus, to take Whatcly's example : " The 

 Earth moves round tho Sun in an elliptical orbit ; so does 

 Mercury ; so does Venns ; so docs Mars, etc ; therefore, all 

 planets (tho universal term which comprehends these indivi- 

 duals) move round the Sun in such an orbit." Here we have 

 an example of inductive reasoning. But this argument, if it bo 

 reducible to the syllogistic form, ia plainly an enthymeme, being 

 incomplete as it stands. Now it is very seldom that an instance 

 is found of what is called " perfect " induction, i.e., one in 

 which there is a complete enumeration of all the individuals, 

 respecting which we assert collectively what wo had before 

 asserted separately : e.g., " John is in England ; so is Thomas ; 

 so is Peter ; so is Francis : all the sons of Edward are John, 

 Thomas, Peter, and Francis ; therefore, all the sons of Edward 

 are in England.' Besides, such au induction is practically 

 useless for the purposes of inference, as we have gained no 

 further knowledge when we have stated the truth of tho 

 universal, which is merely made up of tho particulars already 

 enumerated, and nothing more. However, in tho induction 

 commonly employed, what is meant is, not that there is a 

 complete enumeration (in many cases that would be impossible) 

 of the individuals of the class, but that those which are 

 enumerated are to be taken as a sufficient sample or nnmbor 

 of instances to warrant us in drawing the conclusion that what 

 has been found true of them is true of the rest also. Bear- 

 ing this in mind, every induction will appear to be an enthymeme 

 with the minor premise (that which contains tho statement 

 about the individuals) expressed, and can bo reduced to a 

 syllogism by supplying a major premise, which will, in all 

 cases, be found to be substantially the same. This major is, as 

 given by \Yhately, " What belongs to the individual or indi- 

 viduals wo have examined, belongs (certainly, or probably, as tho 

 case may be) to the whole class under which they come." 

 The example by which he illustrates this is from finding on 

 examination of several sheep, that they each ruminate, we con- 

 clude that the same is the case with the whole species of sheep ; 

 and from finding on examination of the sheep, ox, deer, and other 

 animals deficient in upper cutting-teeth, that they each rumi- 

 nate, we conclude (with more or less certainty) that quadrupeds 

 thus deficient are ruminants ; the hearer readily supplying in 

 sense the suppressed major premise namely, that " what 

 belongs to th individual sheep we have examined, is likely to 



felon* to the whole species," etc. Of ooone, in eeoh oa*e, th* 

 logician, M nob, ha* nothing to do with the ground* apoe 

 whioh Uw premises are given or stated to b true. The dot; 

 of Metng whether the premieas are fairly laid down in ootside bi 

 prorinoe altogether, as we have seen before. 



Th* chief qtUMtion at uue, in reference to induction, be. 



tween Whatoly and Mill, u as to this major premise, and iU 



origin. Archbishop Whatoly'a theory i* that, although it may 



I be true that it can always be ultimately resolved into an aa- 



|M||HHMMMMtalg^y|yWH of Nature," or, M Mill 



" ^ happens onoe, will, under a ufflctent degree 



eircuin*tiuiw, happen again, and not only 



an often M the aame dronmnUnoee recur," yet rill 



u whatsoever is ultimately reducible to the 



vhilo ho agree* with Whately that every 

 i ByHogkfp with the major premise 



: .itii'-r, thii* iction may be thrown into 



-"in, by supplying a major premise; yet 



holds tii.it this : f obtained by an indnftMrn, 



. >n, and induction by no 



mou This, the ultimate major 



lido of all ' then be got by an iiiduc- 



/ cage where an inference is drawn 



frum i: ,ed to a mere guess), we most form 



a judgment that tho instance or instances taken is or are 

 t to ' 'nj conclusion drawn. If, he says, we 



express t: Is, we shall have the very major 



premise before given. To acknowledge this, therefore, u to ac- 

 knowledge that every instance, without exception, of reasoning 

 from induction ia capable of being thrown into the syllogistic 

 form, which ia all that he contends for, as he considers an> 

 inquiry into the origin of our belief in the constancy in th 

 laws of Nature foreign to the subject. This, however, seem* 

 hardly satisfactory, when the point in dispute, whether all in- 

 ductions can be exhibited in the syllogistic form, just depend* 

 upon whether Mill ia right in the account he gives of the m*nw* 

 by which this belief is gained. 



Example only differs from induction in having a singular 

 instead of a general conclusion, and in being founded on a 

 single case instead of on a number : e.g., " Cesar was regardless 

 of human life ; therefore this individual conqueror will be "- 

 the suppressed major being such as this : " What is true of one 

 conqueror .we may expect to be true of another." 



We shall next proceed to consider and illustrate the nature 

 and classification of the various kinds of Fallacies. 



RECREATIVE SCIENCE. XV. 



THE MICROSCOPE AND ITS REVELATIONS ( 



IN the previous paper mention was made of Kcade's new way 

 of illuminating microscopic objects, and in order to give the 

 reader a better idea of the mode of using the reflecting 

 prism, a drawing of the whole arrangement ia given in section 

 (Fig. 1). 



The lamps shown in Fig. 1, also those in Figs. 2 and 3, are 

 those arranged by Highley to meet the requirements of " Beado's 

 Diatom Prism," with an adjustable diaphragm, B, to regulate 

 tho amount of light, and a means to convert ordinary into 

 polarised light by the introduction of a Nicol's Prism, P, in the 

 path of the rays, all extraneous light being cut off by making 

 the chimney, M, of metal instead of glass, and also to serve 

 as a support for the accessory appliances, o is the object 

 illuminated by oblique rays from D, the Diatom Prism, whioh 

 can be turned on its axis by means of a milled-head H, and 

 rotated or placed at any inclination by the motions provided 

 in the fittings, F F, mounted on tho mirror tube, T (or secondary 

 stage), of the microscope. L is the reservoir of the lamp ; w. 

 the wick enclosed in a metal chimney, M, that forms a support 

 for the condenser, c ; B, the adjustable diaphragm to regu- 

 late the amount of light ; A, tho pivot on which the arm rotate* 

 that carries the polariser, p. The lamp (Fig. 1) is mounted 

 on a telescopic rod, so that the condenser can be raised to the 

 height of 10 inches, or brought low to the table as may be 

 desired. Whoa out of use it may be pocked in a pocket caae, 



