CHAP. II.] FIEST TRUTHS. 43 



noticed, and such propositions as that &quot; things which are 

 equal to the same thing are equal to one another;&quot; &quot; a thing 

 cannot both be and not be at the same time in the same 

 sense.&quot; 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 he denies that he perceives these judgments as neces 

 sarily 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, &quot; they have not clearly represented 

 to themselves the propositions they assert &quot; or his mental 

 condition is pathological. 



The judgment that the three angles of a triangle should 

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

 mental fact of quite a different kind from my inability to 

 imagine unextended colour or a boundary to space. Such a 

 judgment I see, if I 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 I see the affirmative to be absolutely and neces 

 sarily true. 



Moreover, of all my subjective certainties none are to me 

 so certain as that which affirms those judgments which 

 (rightly or wrongly) I deem absolutely and universally neces 

 sary. 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 

 existence then, as a fact, of these supreme and active per 

 ceptions as to necessity and impossibility (the existence of 

 which as distinguished from negative inconceivabilities is 

 ignored by Mr. Spencer) may be taken as one of the most 

 certain and indubitable facts of consciousness. 



If there was but the one kind of inconceivable propo 

 sitions namely, those negatively inconceivable, we should 



