148 Herbert Spencer 



propositions as that ' things that are equal to the same thing 

 are equal to each other ' ; ' a thing cannot both be and not 

 be at the same time in the same sense.' The subjective 

 difference is surely plain enough. Every sane man must 

 admit that he clearly sees — sees borne in on him^ as 

 necessary truths — that two straight lines can never enclose 

 a space; that twice five must always be ten; and that 

 ingratitude can under no circumstances be a virtue. If a 

 man denies that he perceives these judgments as necessarily 

 true in any conceivable case as it arises, then he either does 

 not understand the real meaning of such judgments — in Mr. 

 Spencer's^ words, 'they have not clearly represented to 

 themselves the propositions they assert' — or his mental 

 condition is pathological. 



The judgment that the three angles of a triangle should 

 be together equal to two right angles, we perceive to be a 

 mental fact of quite a different kind from our inability to 

 imagine unextended colour or a boundary to space. Such a 

 judgment we see, if we can see anything, to be one the false- 

 hood of which is not negatively unthinkable, but absolutely 

 and positively impossible even to Omnipotence itself, and 

 this because we see the affirmative to be absolutely and 

 necessarily true. Moreover, of all our subjective certainties 

 none are to each one so certain as that which affirms those 

 judgments which (rightly or wrongly) we deem absolutely 

 and universally necessary. If then subjective certainty is 

 our ultimate test, such judgments override all others ; and 

 to deny them invalidates every possible judgment, and 

 logically plunges the doubter, if he is consistent, into 

 absolute, unqualified scepticism. The actual presence of 

 these supreme and active perceptions as to necessity and 

 impossibihty (the existence of which as distinguished from 

 negative inconceivabilities is ignored by Mr. Spencer) may 



1 Essays, p. 322. 2 q^^ c^«., p. 372. 



