第24章 Intermediate principles

As a help to this I think it may be proposed that,for the saving the long progression of the thoughts to remote and first principles in every case,the mind should provide itself several stages,that is to say,intermediate principles,which it might have recourse to in the examining those positions that come in its way.

These,though they are not self-evident principles,yet,if they have been made out from them by a wary and unquestionable deduction,may be depended on as certain and infallible truths and serve as unquestionable truths to prove other points depending on them by a nearer and shorter views than remote and general maxims.

These may serve as landmarks to show what lies in the direct way of truth or is quite besides it.And thus mathematicians do,who do not in every new problem run it back to the first axioms through all the whole train of intermediate propositions.Certain theorems that they have settled to themselves upon sure demonstration serve to resolve to them multitudes of propositions which depend on them and are as firmly made out from thence as if the mind went afresh over every link of the Whole chain that ties them to first self-evident principles.Only in other sciences great care is to be taken that they establish those intermediate principles with as much caution,exactness and indifferency as mathematicians use in the settling any of their great theorems.When this is not done,but men take up the principles in this or that science upon credit,inclination,interest,etc.,in haste without due examination and most unquestionable proof,they lay a trap for themselves and as much as in them lies captivate their understandings to mistake,falsehood and error.