314 SIR WILLIAM Hamilton's philosophy : 



of thought which arise from the Law of the Conditioned ; and these 

 are thus shown to be merely the irresistible recoil of the mind from 

 either of two unthinkable contradictories. When from ray inability 

 to think a certain proposition I am driven back without choice upon 

 its. contradictory and find that there is no counter inability to think 

 this, then the necessity to think it is positive and arises from a power 

 of the mind. For example, I am unable to think that 2 + 2 is not 

 equal to 4, and I am consequently forced to the contradictory judgment 

 that 2 + 2=4. Now there is no repulse from this latter contradictory 

 as inconceivable, similar to the repulse from the former. But in the 

 case of the necessities now to be considered, when our inability to con- 

 ceive one of two contradictories forces us back on the other, this we 

 find ourselves equally unable to conceive with that. We must there- 

 fore regard the necessity which repels us from either contradictory as 

 negative, as originatin-g from an impotence of the mind ; and the Law 

 of the Conditioned should not be viewed as valid beyond our own 

 thought, of whose limitation it is the expression (IL, pp. 366 — 9). 



It would be manifestly out of place to attempt the classification of 

 those contingent and derivative relations, which we frequently employ 

 in the exercise of our cognitive faculties ; and therefore we limit our- 

 selves to those relations which are necessary and original. These 

 arise either (_L) from the subject and form the relation of Knowledge, 

 or (IL) from the object and form the relations of Existence, 



I. The former isithe relation between subject and object, which 

 requires that everything must be thought as belonging wholly to 

 either or partly to both of these correlatives. 



II. The latter are either (I) intrinsic or (2) extrinsic. 



1. The intrinsic, which may also be called the qualitative, relation 

 is that of substance and quality ^ For while qualities can be conceived 

 as existing not in themselves, but only in a substance, substance itself 

 can be conceived only as the inconceivable correlate of qualities ; so 

 that, in different aspects, every substance is a quality, and every quality 

 a substance (I., pp. 137 — 8, and 149 ; Discussions, p. 605). 



2. The extrinsic may also be called quantitative and are three in 

 number, as constituted by three species of quantity. 



i. Protensive quantity, Frotension or Time may b,e considered^r.s#/y 

 in itself: and as such it is (a) positively inconceivable either a as 

 absolute, i.e., as absolutely beginning or ending, or /? as infinite, i.e., 

 as unbeginning or unending, and also either a as an absolutely indi- 



