NECESSARY TRUTHS-EFFECTS OF EXPERIENCE. 663 



Sternal, and are to be found out only by the contemplation of those 

 essences. . . . Knowledge is the consequence of the ideas (be they what 

 they will) that are in our minds, producing there certain general proposi- 

 tions. . . . Such propositions are therefore called 'eternal truths,' . . . 

 because, being once made about abstract ideas so as to be true, they 

 will, whenever they can be supposed to be made again, at anytime past 

 or to come, by a mind having ihose ideas, always actually be true. For 

 names being supposed to stand perpetually for the same ideas, and the 

 same ideas having immutably the same habitudes one to another, prop- 

 ositions concerning any abstract ideas that are once true must needs 

 be eternal verities. " 



But what are these eternal verities, these ' agreements,' 

 which the mind discovers by barely considering its own 

 fixed meanings, except what I have said ? — relations of like- 

 ness and difference, immediate or mediate, between the 

 terms of certain series. Classification is serial comparison, 

 logic mediate subsumption, arithmetic mediate equality of 

 difierent bundles ol' attention-strokes, geometry- mediate 

 equality of different ways of carving space. None of these 

 eternal verities has anything to say about facts, about what 

 is or is not in the world. Logic does not say whether Soc- 

 rates, men, mortals or immortals exist; arithmetic does 

 not tell us where her 7's, 5's, and 12's are to be found ; ge- 

 ometry affirms not that circles and rectangles are real. All 

 that these sciences make us sure of is, that if these things 

 are anywhere to be found, the eternal verities Avill obtain 

 of them. Locke accordingly never tires of telling us that the 



" universal propositions of whose truth or falsehood we can have cer- 

 tain knowledge, concern not existence. . . . These universal and self- 

 evident principles, being only our constant, clear, and distinct knowl- 

 edge of our own ideas more general or comprehensive, can assure us of 

 nothing that passes without the mind; their certainty is founded only 

 upon the knowledge of each idea by itself, and of its distinction from 

 others ; about which we cannot be mistaken whilst they are in our 

 minds. . . . The mathematician considers the truth and properties 

 belonging to a rectangle or circle only as they are in idea in his own 

 mind. For it is possible he never found either of them existing mathe- 

 matically, i.e., precisely true, in his life. But yet the knowledge he 

 has of any truths or properties belonging to a circle, or any other math- 

 ematical iigure, are nevertheless true and certain even of real things 

 existing; because real things are no farther concerned nor intended to 

 be meant by any such propositions, than as things really agree to those 

 archetypes in his mind. Is it true of the idea of a triangle, that its 



