Part IV, Chapter 11: The Method of the Sciences reduced to Eight principal Rules
WE may conclude from what has been said, that in order to have a method which should be still more perfect than that which is in use amongst the geometers, we ought to add two or three to the rules which were given in the second chapter, so that all these rules may be reduced to eight: —
Of which the two first relate to ideas, and may be referred to the First Part of this Logic;
The third and fourth relate to axioms, and may be referred to the Second Part;
The fifth and sixth to reasonings, and may be referred to the Third Part;
And the two last relate to order, and may be referred to the Fourth Part.
Two Rules touching Definitions.
1. Not to leave any terms at all obscure or equivocal, without defining them.
2. To employ in definitions only terms perfectly well known, or already explained.
Two Rules for Axioms.
3. To demand as axioms only things perfectly evident.
4. To receive as evident that which requires only a slight attention to the recognition of its truth.
Two Rules for Demonstrations.
5. To prove all propositions which are at all obscure by employing in their proof only the definitions which have preceded, or the axioms which have been granted, or the propositions which have been already demonstrated.
6. Always to avoid the equivocation of terms, by substituting mentally the definitions which restrict and explain their meaning.
Two Rules for Method.
7. To treat of things, as far as possible, in their natural order, by commencing with the most general and simple, and explaining everything which belongs to the nature of the genus before passing to its particular species.
8. To divide, as far as possible, every genus into all its species, every whole into all its parts, and every difficulty into all its cases.
I have added to these two rules—as far as possible,—because there are, indeed, many occasions on which we cannot rigorously observe them, either because of the limits of the human mind, or of those which we are obliged to set to every science.
This occasions us to treat often of a species when we cannot treat of everything which belongs to the genus: as we treat of a circle in common geometry without saying anything in detail of the curved line which is its genus, which we are satisfied with simply defining.
Neither can we explain, in relation to a genus, every thing which might be said of it, since this would often be too long; but it is enough that we say of it all that we intend to say before passing to its species.
But I believe that a science cannot be treated perfectly, except great attention be paid to these two last rules, as well as to the others, and that we should consent to dispense with them only on necessity, or to secure some great advantage.