592 



NATURE 



[February 25, 1892 



some part of the meaning of a term is determined arbitrarily ; 

 either by public opinion for general use, or by the individual 

 reasoner, if he wishes to use the term for some special purpose 

 of his own. For this does not imply that there ever was a 

 formal contract as to the meanings of terms. The fact that 

 terms do not mean the same to people of different nations is 

 enough to show that the determination of the meaning by each 

 nation is, in part at least, essentially arbitrary. It is also, I 

 think, clear that there is a part of the meaning of some terms at 

 least which is not arbiti-ary, when once the arbitrary part has 

 been settled. There is a slight ambiguity about my use of the 

 word "definition," which, however, when once noted, need 

 cause no confusion, as the context will always show in which 

 sense I am using it. Commonly a "definition" denotes an 

 assertion which determines the arbitrary part of the meaning of 

 a term ; but when I speak of " the definition " as opposed to 

 "the import" of a term, I mean not this assertion itself, but 

 that part of the meaning of the term which it determines. This 

 explains how it is that I do not regard " the definition " of a 

 term (as opposed to its import) as a thing. Even if it is clearly 

 conceived in the mind it is only an abstract idea ; but the point 

 is that it is not necessary that it should be conceived at all. 

 Thus it is not necessary that a definition by connotation should be 

 "of something," if that means that the term should have denota- 

 tion. Even if the term has any denotation, i.e. if the mind grasps 

 it as denoting a thing or idea, this denotation must, in a symbolic 

 argument, be regarded as merely "accidental clothing." 



Just as some part of the meaning of a term is arbitrary and 

 some part not, so in any system of logic some part of the system 

 is arbitrary and some part not. Now, either the denotation or 

 the connotation of a term may be laid down arbitrarily, but 

 the connection betwee^i the two is not arbitraiy. One cannot 

 arbitrarily lay it down that "such a thing possesses such attri- 

 butes." If, therefore, a definition is to be an arbitrary assertion, 

 it must only lay down either the denotation or the connotation 

 of a term, and not parts of each. It would, of course, be 

 logically permissible to use the word " definition " in a different 

 sense, but then definitions would not be arbitrary assertions. 

 This is exactly what is done if the assertion " Two straight lines 

 cannot inclose a space " is called a definition by denotation ; 

 and therefore, in my system of logic, I cannot admit it to be a 

 definition. This is one of the arbitrary features of my system. 

 But it is not arbitrary when I say that in such assertions as 

 " Nothing can both be and not be," and " Twice two is four," 

 there is nothing absolute at all. The truth of these assertions is 

 determined entirely by the arbitrary parts of the meanings of 

 their terms. Miss Jones says: "If definitions were purely 

 arbitrary, as Mr. Dixon holds, what would prevent my saying 

 that Four (i + i + i) means twice t-MO [i + i) + {i + i)}" Pre- 

 cisely ; this is exactly the point. There -vonld be nothing at all 

 to prevent it. Boole actually did this very thing, as his law of 

 indices in his mathematical analysis of logic. According to 

 hislawa'+' + ' = a(i + i)+(i + iX 



There remain one or two minor points to be answered. As 

 to induction, I think Miss Jones's view is substantially the same 

 as mine. Of course it is possible to set out an inductive 

 generalization in a syllogistic form as Miss Jones does ; only the 

 whole of the induction is then contained in the assumption of 

 the major premiss — the syllogism itself is in no sense inductive. 

 _^If Miss Jones thinks the truth of the formula {a + b)'^ = 

 a" + 2ab + b'^ is deduced by generalization from a single concrete 

 instance, howdoes she explain the fact that sometimes (a + b)'^ — o, 

 as in Grassmann's " Aeussere Multiplication," and sometimes 

 (a + b)- = a + b, as in Boole's logic ? 



I see nothing to differ from in the paragraph about S and P ; 

 except perhaps that if I define such a term as "metal" by 

 denotation 1 do not say "This and all other things like it in 

 certain respects " are metal. That would be mixing up denota- 

 tion and connotation in one definition. I say only "This, and 

 this, and this, ... are metal." 



The explanation of the point about the mathematical truths is 

 simply that I do not consider the assertion " Two straight 

 lines cannot inclose a space " as a mathematical truth at all, if 

 "straight line" is defined by denotation. I certainly believe it 

 to be true, but its truth is not of the same nature as that of the 

 assertion " Twice two is four," or even " Cogito, ergo sum "; it is 

 neither a truism nor a necessary truth, in my senses of those 

 terms, but can only be established by induction. 



Edward T. Dixon. 



Trinity College, Cambridge, February 19. 



NO. I 165, VOL. 45] 



The Value of Useless Studies. 



It is rather surprising that Prof. Ayrton should indulge in 

 covert sneers at Universities for devoting themselves to useless 

 studies. It certainly ill becomes one whose life is bound up 

 with electrical science, which is of such recent growth that 

 nobody can pretend to forget how it owes its origin to those who 

 studied it while useless. If Universities do not study useless 

 subjects, who will ? Once a subject becomes useful, it may very 

 well be left to schools and technical colleges, to patent-mongers, 

 and the trade. Mr. Bury is, on the other hand, mistaken in 

 two respects. That a subject is useless is hardly worth con- 

 sidering as a recommendation for its being made compulsory on 

 students. There are too many useless subjects for that. The 

 great objection to compulsory Greek is that it is the principal 

 stumbling-stone in the way of any literature being studied by 

 ordinary University students. The Bible produced very little 

 effect until it was read in translations ; and the danger of a pagan 

 revival, if ancient literature were studied without the obstruction 

 of difficult languages, is the best reason for insisting on these 

 languages in a Christian University. The second mistake of 

 Mr. Bury is that it is any part of the business of a Universtiy to 

 teach. Universities should certainly give facilities for students 

 to learn. It is the business of the students to learn. If they 

 are so ill prepared that they have not acquired the art of learn- 

 ing, they should go to a college or school or private teachers, 

 and get taught ; for teaching is the business of these institutions 

 and persons. The business of Universities is to advance culture 

 and knowledge, and to afford students an opportunity of learn- 

 ing how to do this. Prof. Ayrton, by omission rather than by 

 commission, seems utterly unable to appreciate the value of 

 literature for its own sake. How can all this fierce toil he 

 extols so justly advance a lot of savages ? 



Geo. Fras. Fitzgerald. 



Trinity College, Dublin, February 13. 



The Nickel Heat Engine. 



In trying Mr. Smith's experiment on the rotation of nickel 

 (Nature, January 28, p. 294), I find my disk has a more 

 complex action. 



It will be remembered that the nickel is mounted on a vertical 

 axis, and has the poles of an electro-magnet put near two points, 

 A and B, 90° apart. Let C be any point in the larger arc, and 

 suppose heat is applied to A. 



I find that at first the disk moves in the direction ACB with 

 a hesitating, uneven motion ; it revolves several times, and 

 almost develops into a steady rotation, when it beats back, 

 oscillates for a while, and goes off with a brisk even spin in the 

 direction BCA. After about two minutes this fails, and a 

 new start is attempted the opposite way, but there is little more 

 movement, until time has been given for cooling. 



It makes no difference at which pole the heat is applied. 

 The disk is 50 mm. diameter, rather less than i mm. thick, and 

 is covered with lamp-black. W. B. Croft. 



Winchester College, February 12. 



THE UNIVERSITY OF LONDON. 

 pROBABLY before this letter is in type the Charter 

 -L of the Albert, or, as it is now to be called, the 

 Gresham, University, will have been presented to Par- 

 liament. What will be its ultimate fate remains to be 

 seen. But I have sat through a long night's debate in 

 the House of Commons to see a Government turned out 

 in the small hours of the morning on a University 

 question. I do not suppose that the proposed Charter 

 will raise an issue of that importance. But I think that 

 the Government may not be unmindful of past history, 

 and, in what is probably the last session of a moribund 

 Parliament, may not be willing to push very vigorously 

 what is perhaps the crudest scheme of University organiza- 

 tion which has ever been proposed in this country. 



Before Parliament takes so serious a step .as founding 

 a new educational institution, the question may fairly be 

 asked, On what ground is it necessary } Everyone 

 knows that we have a University in London which is a 

 State institution ; and one may not unreasonably inquire, 



