APPENDIX A, 



ON THE WORD &quot;AXIOM. 



AXIOM, d^icD/^a, (ato a&amp;gt;, aios, $ya&amp;gt; in the sense of weighing] 

 is strictly that of which one is weighed (or counted) worthy, an 

 honour or dignity. Thence it passes on to the sense of that 

 which is thought tvorthy or Jit, a decision. And from one of 

 these senses it arrives at the Logical use of a proposition Jit 

 to be taken as a basis of demonstration. In this sense we 

 find the term used by Aristotle in his Logical treatises. It is 

 with him the title of the Major Premises of Demonstrative 

 Syllogisms. He means by it those universal statements which are 

 in necessary matter, and which no one would think of doubting. 

 In this sense the schoolmen have also used the Term, render 

 ing it into Maxima (Sententiarum) (whence our term &quot; a 

 Maxim&quot;) or, somewhat absurdly, into Dignitas. (Sanderson s 

 Logic, III. xii.) From this sense to that in which the Mathe 

 maticians use it there is but a short step ; and with them it 

 means always a self-evident Proposition. 



In modern times we find the Term used in two senses, which 

 correspond nearly with the Logical and Mathematical usages 

 just given. The one sense is almost equivalent to that of 

 &quot;Principle&quot; (nearly the Apx^ of Aristotle). &quot;Principle&quot; is 

 rightly used of &quot; all assumptions (founded either on fact or 

 Hypothesis) on which as a datum a train of reasoning pro 

 ceeds.&quot; (Sir W. Hamilton.) Thus it would, in its full extent, 

 include Axioms in their more limited sense : embracing (e. g.) 

 the Physical &quot;principle&quot; of the Continuity of the Laws of 

 Nature ; the belief in our own Identity, &c. ; and such ge- 



