: <U< . 



We bar* put forward enough to enable im intelligent studn 

 to nia stria* ol difficulties ; (or the lolution of raot of which we 

 nut refer him to Mr. Boole', writing.. 



We DOW proceed to the disruation of Sir William Hamilton's system. 

 At the outMt the learned author put* into word* a postulato * which 

 no one would suppose had been left to him to demand. It i " that 

 we be allowed to state in language what u contained in thought." Wi 

 may truet Hamiltun'* blaming for the fact that thin postulate wai 

 never MB' : but surely we ahall feel inclined to auk, who has 



erer been timid enough nut to UM it, a* wanted f Aristotle, we may 

 answer, and nearly alibi* followers. There are cases in which Arutotle 

 himself appears to doubt the right, or at least to waive the right, of 

 puahing thought beyond the bound* of usual expression ; and to this 

 day logic has been circumscribed by this want of clear apprehension 

 that language was made to express and extend thought, not to cireum 

 scribe it. The rmrtulstfi ought to be pushed further; the logician 

 ought to be allowed to state all that tan be contained in thought, 

 iinTeai indeed we are to construe it as a junction of the present and 

 future tenses, 



Among the oases in which language did not find expression for 

 possible thought, was the quantity of the predicate of a common pro- 

 position. The logicians, Hamilton at leant, and most others we believe, 

 affirm that thought dot* quantify the predicate ; for ourselves, after 

 much observation, we believe it does not. We believe that minds ol 

 ordinary cultivation, with whom logic has not been a study, when they 

 have occasion to think that no quadruped is a fish, do nut hold it in 

 thought that they are p*' 1 ' i "g about all fishes, actual and possible. 

 They may, by a process they never analysed, be able to toe this implied 

 truth ; but we do not believe they ever held it in that way in which 

 they bold the thought which is apt to find expression. Be this as it 

 may, Hamilton believed, not only that a quantity is held in thought for 

 the predicate of the ordinary proposition, but even that quantities art 

 in thought which have never been expressed in language even by 

 logicians He accordingly applied as had been done before him, 

 though the results had not been worked into a logical system bulk the 

 quantities, universal and particular, to both subject and predicate. He 

 thu* put forward, as what tee hare in thought, eight forms of predica- 

 tion, to the statement of which we add some explanation, and some 

 objection. 



1. All z is i all Y. This means that x and Y are coextensive terms ; 

 accordingly it is a complext proposition, made by compounding 

 " every x is r," and " every Y is x." It is simply contradicted by the 

 alternative of one or another of two other propositions of the system : 

 Either " some xs are not v" or " some vs are not xs." 



2. All x is some Y. This is the same as " every x is Y." 

 8. Some x is all Y. This is " every Y is x." 



4. Some x U some Y. This is " some xs are vs." 

 6. Any x is not any Y. In negatives, the word any takes the place 

 of all/for the sake of grammar. We have here, " no x is Y." 



6. Any x is not some Y. This is " some Ys are not xs." 



7. Some x is not any Y. This is " some xs are not YM." 



8. Some x is not some Y. This proposition is not in ordinary use. 

 It means that some of the xs are not some of the YS, even if they be 

 others. To contradict it we must affirm that there is but one x and 

 one Y, and that X identical with the Y. Consequently, here is a pro- 

 position which does not find its denial in the system. 



Ur. Thomson (' Outlines,' Ac.) admits the first [seven of these pro- 

 positions, but rejects the eighth : and constructs a system of syllogism 

 accordingly. 



That Hamilton really believed the above system to be in comma* 

 not the deduction of a postulated extension, is manifest. 



I thii principle, Hamilton announced mother, which had been quite 

 mgtrtted a the former : and bjr merely lending the weight which his 



I learning (arc him to theae two fundamental requirements of logic, 

 be will bars dons much to promote it, even though bU practice be not quite 

 ibiiiiil of ate preaching. Whatever Is operative in thought, mugt be taken 

 Into Mwont, and eauequrntlv be overtly cipreuible In logic ; for logic mutt 

 be, as to be it prohma, an um-iclu-ivr reflex of thought, and not mcr ly an 

 arbitrary selection a .me. of elrgant extract* out of the fornu of thinking. 

 WavtlttT Ike toon that it exhibits aa legitimate be stronger or weaker, be more 

 or leas frequently applied ; that, as a material and contingent consideration, li 

 beyond lu punkw." 



Toll Is denied. Bat if, of propositions A, s, c, A always make s and c 



ar, and s and c slway. make * follow, surely A I* Identical with the ji. 

 of s aad c. What doe. a contain mure than la In and c compounded I And 

 wksl least A proposition l eontradieted by alternative junction of two different 

 proMatnoaa, of wklsh attaer contains the other : 1* It simple or complex t 



1 lie iMMMted I* U* wo) Id the requirements for a prise rsany to be written 

 Vy hit pupils among which wa* the following : " Toe reasons why common 

 Uaguag* aae* an Miftu of the trprt*d quantity, frequently of tu. 

 aad store fieqorntly at Ike anstieoM, tkcngh both ka<e always their ,,i 

 la bought." In aajlng this, he wa* >o fully satuned that he bad announced 

 Iks pnrtiple of a -plying nery quantity to the pndic.te of mry proposition, 

 that be mad* a ikargr of plaguilun of this principle stains! one who applied It 

 after (a* ke supposed) wring this announcement, and rested the proof on the 

 (s* ke ikvoghij . btioui neaalog of the sentence abo.e. It is huiuly requisite 

 to a>y tkat " botk have tkrtr quaaUUe* " la not Ik* s.me aa " both have all 

 qua tun a," ksu e rally n rans that OM has one and snothrr another. If any 

 OM bad MM ikat two ptrasfi* " both bat* always their hobble*," no one would 

 have falhtred tkat Ik* psir kse pair of bobbies tor tkclr joint use. The present 



To this we object : but our greater objection U to the system itself. 

 We have not seen any defence of the following points which has a 

 single respectable* element, except the character of iU producers. The 

 introduction I, of a complex proposition; 2. of a proposition which is 

 not simply contradicted by any one other proposition ; 8, of a pro- 

 position which cannot be contradicted at all in the system ; 4, of a 

 proposition compounded of two others already in tin yr 



The notation of the system is as follows. Woodcuts t resembling 

 and -i- are used for assertion and denial ; a. comma signifies par- 

 ticular quantity ; a colon signifies universal quantity. Thus *,-*: v 

 signifies " tome x is not any Y." And the following diagram represents 

 the syUogum, " all x is all Y, some Y is all 7, therefore some X is 

 allz.' 



Jt: : Y, :z 



There is valid inference when the middle term U once at least taken 

 universally, and one of the propositions at least is affirmative. \\ ' 

 shall presently point out the canon of inference, when we have described 

 a notation which we prefer. We refer the student to Sir W. Hamilton's 

 own writings for the notation, &c. connected with his distinction of 

 breadth and depth. We hold it quite useless to cuter on the com- 

 parison of " all man is some animal," and " some animal is all man," as 

 cases of a fundamental subdivision t of logic into two parts ; those 

 who can may believe that, as asserted, one of these propositions is 

 mitiijJiytical and one loyii-al. 



Sir W. Hamilton invited the severest criticism : he challenged it 

 to show that his system is not more corrects in theory than that of 

 Aristotle, and not preferable in practice. He affirmed that his system 

 was intended to " place the key -stone on the Aristotelic arch," and that 

 it succeeded in so doing. We hold him to be almost a miracle of 

 learning, and, in every sort of psychological or metaphysical notion, 

 except only when it is mathematical, we feel him to have a true 

 genius for conception, a mighty power of execution, and a rare talent 

 of expression. But when quantity is in question, hia power is gone. 

 Almost in a breath he tells us, first, that hia two quantities, breadth 

 and depth, are iu reality one and the same quantity ; and ueit, that 

 the greater the one tie less is the other (' Discussions,' &c. 1st ed., p. 

 644*, 2nd ed., p. 699). He confounds equation of quantity with 

 identification of quantified matter: he asserts that a proposition is 

 " merely " equation of quantities. He uses the phrases "equation ol 

 quantities " and " coalescence of notions " as convertible ; and the 

 prize essay of an able student, published with his sanction, announces 

 that "predication is nothing more or less than the expre* 

 the relation of quantity in which a notion stands to an individual, or 

 two notions to each other." 



We now proceed to state Mr. De Morgan's views, and for brevity aa 

 well as for other reasons, we shall confine ourselves to mere statement, 

 without proof or enforcement ; referring to the works previously 

 mentioned. 



The proposition in its common form is objective, or, in old phrase, 



point, however, U the statement that this taken place in common language, and 

 tuat the elliptis, sa he calls It, U oa\f frejurnt, implying that the full exprcsi-lou 

 is not infrequent. 



To the objection that ' All x is all T ' has no single contradiction, an 

 eminent defender rep'ied that it o a contradiction ; and he produced it ; 'All 

 x Is not all v ' ; and Sir w i.v. Il.imilton assented : and both are right under a 

 little admission of unusual construction. But the assailant had only objected 

 that there was no contradiction iu tlie tytltm: and both Hamilton and his 

 defender forgot to explain how this contradiction did not find its way tula the 

 syttcm. The true explanation la that the sytcm itnelf was founded, not on Uic 

 laws of thought, but on an arbitrary extension of the application of language : 

 and the end of it is that the Hamiltonian logic is not allowed to fiml language 

 for all that is contained in thought. Tor botb Hamilton and Im defender have 

 to go out of tht tyttem to find language for what must be in thought to those who 

 think of the system, namely, the denial, when wanted, of the first of the pro. 

 position* in Ihe nrrteii.. 



t It will amuse the mathematician to sec that Hamilton, to whom all mathe- 

 matics waa repugnant, stumbles upon + for bis sign of negation, and for his 

 sign of affirmation. 



Mr W. Hamilton seems, in logie, to have nothing answering to the attribali 

 which mark* a clou: he substitutes the concrete quality, treated as a clan of 

 ndividuals. He says that Leibnitz and Newton have itt-o human natures, one 

 that one attribute of Plato Is tome Athenian.' This is quite true, and 

 the treatment of the quality, under the notion of one quality for one individual, 

 another for another, is good In Its proper and very subordinate place. But it is 

 not connected with the great distinction of comprehension and extension, herein- 

 before noticed. 



{ BU completely quantified predicate U maintained by him to be nec.snary to 

 he perfect represrniation of common thought. A living lesson on this point was 

 oon given. Sboitly nflcr Sir w. Hmnilton'a death, an ardent admirer pub. 

 ished a manual of hi* >tcm for the use of schools. But though he had seen 

 he objection to the form 'All x Is all r' having no contradict!^ 

 lunulKin's admi*-lon and defence, he actually took '.sonic x is not omc Y ' to 

 be the contradiction required. Anil when it.c error was pointid out In a 

 evlcw, he continued to maintain it, and appealed to common sense t 

 ruth, nnd to Hamilton's pupil* (one of whom ret him rijilit/ to vouch for its 

 orrect n-pret cntutinn of the system. The author ol the manual show. 

 want of acutcness in other thini**, and hi* book i* a valuable anil . . U 

 iroof that Hamilton'* *ystcm demand* more than u in common thought, though 

 not more than may fo In the thought of those who will gala it. 



