KiDD. — Induction and Necessary Truth. xlv 



proposition, or deduced from data consisting exclusively of propositions that are 

 self-evident. Those ultimate data are definitions and self-evident axioms. 



We now proceed to designate very briefly the relations of Necessary 

 Truth to Experience. 



1 . First, it is from experience that we acquire the conceptions of things ; 

 so that without experience we could not . form any propositions, whether 

 inductive or necessary. But haA'ing obtained from experience the conception 

 of a certain thing, or class of things, and the conception of a certain attribute, 

 we are not dependent upon inference from experience in order to decide 

 whether the definition of the subject implies the predicate ; or, in other words, 

 whether the perception of the subject-thing comprises the perception of the 

 predicated attribute. If it does, the proposition is self-evident ; and all con- 

 clusions from self-evident propositions alone are necessary truths, or general 

 propositions whose truth is known absolutely. 



2. And, secondly, it is fitting and requisite that recourse should be had to 

 experience, in order to verify our judgments. As we are liable to error in the 

 exercise of all our faculties, so we cannot assume to be exempt from fallacy as 

 to distinguishing, in all instances, what may be received as self-evident, or as 

 deduced necessary truth. It was formerly regarded as self-evident that 

 matter cannot act where it is not; but it would perhaps be impossible to 

 reconcile this assumption with now received theories of gravitation. 



3. Our conceptions of things, as we have seen, are from experience, and 

 experience verifies our judgments. But, further, it is to be remarked, both as 

 to the distinction of general propositions into Inductive and Necessary, and as 

 to the distinction of Necessary Truths into Deduced and Self-evident, that 

 these distinctions are relative. They are distinctions, not of objective things 

 themselves, but according to our faculties and our knowledge. It is recorded 

 of Sir Isaac Newton, that when he first read the treatise of Euclid the 

 greater part of the demonstrations was to him superfluous. If we thoroughly 

 understood the nature of what we call matter, we should doubtless perceive 

 that the supposition of matter devoid of gravitation, or of other experienced 

 qualities, would be self -contradictory. The progress of discovery has been con- 

 tinually removing propositions from the category of being merely or immediately 

 inductive, into that of being deducible from ulterior and wider principles. 



The consideration of the subject of which we have been treating is incom- 

 plete without some notice of what the chief thinkers upon these topics have 

 pronounced with reference to Necessary Truth ; but this paper has perhaps 

 already extended to too great a length. I have also, of course, omitted 

 altogether the application of the results, at which we have arrived, to that very 

 interesting subject, the Ground, as it is termed, of Induction, or the ultimate 

 basis of Inference from Experience, 



c3 



