Space, when clearly possessed, gives rise to geometrical 

 Axioms, and is thus the foundation of the Science of Geo- 

 metry. The Idea of Mechanical Force, (a modification of 

 the Idea of Cause,) when clearly developed in the mind, 

 gives birth to Axioms which are the foundation of the 

 Science of Mechanics. The Idea of Substance gives rise to 

 the Axiom which is universally accepted, that we cannot, 

 by any process, (for instance, by chemical processes,) create 

 or destroy matter, but can only combine and separate ele- 

 ments ; and thus gives rise to the Science of Chemistry. 



Now it may be observed, that in giving this account of 

 the foundation of Science, I lay stress on the condition that 

 the Ideas must be clearly and distinctly possessed. The Idea 

 of Space must be quite clear in the mind, or else the Axioms 

 of Geometry will not be seen to be true : there will be no 

 intuition of their truth ; and for a mind in such a state, there 

 can be no Science of Geometry. A man may have a confused 

 and perplexed, or a vacant and inert state of mind, in which 

 it is not clearly apparent to him, that two straight lines can- 

 not inclose a space. But this is not a frequent case. The 

 Idea of Space is much more commonly clear in the minds of 

 men than the other Ideas on which science depends, as Force, 

 or Substance. It is much more common to find minds in 

 which these latter Ideas are not so clear and distinct as to 

 make the Axioms of Mechanics or of Chemistry self-evident. 

 Indeed the examples of a state of mind in which the Ideas 

 of Force or of Substance are so clear as to be made the 

 basis of science, are comparatively few. They are the 

 examples of minds scientifically cultivated, at least to some 

 extent. Hence, though the Axioms of Mechanics or of Che- 

 mistry may be, in their own nature, as evident as those of 

 Geometry, they are not evident to so many persons, nor at so 

 early a period of intellectual or scientific culture. And this 

 being the case, it is not surprising that some persons should 



