214 CLARKE AND SPINOZA. [CHAP. XIII. 



And his reasoning proceeds upon the expressed or assumed 

 principle, that these divisions are not only parallel, but equiva- 

 lent. Thus in Def. in., Substance is made equivalent with that 

 which is conceived by itself; whence 



Again, Ax. iv., as it is actually applied by Spinoza, estab- 

 lishes the identity of cause with that by which a thing is con- 

 ceived; whence 



y = e. 



Again, in Def. vii., things free are identified with things 

 self-existent ; whence 



/-* 



Lastly, in Def. v., mode is made identical with that which is 

 in another thing ; whence z = a/, and therefore, 



z = x. 



All these results may be collected together into the following 

 series of equations, viz. : 



x = y = 2 =f= e= \- X '=l-y'= !-/'= l-z'= l-e. 



And any two members of this series connected together by the 

 sign of equality express a conclusion, whether drawn by Spinoza 

 or not, which is a legitimate consequence of his system. Thus 

 the equation 



z = 1 - e, 



expresses the sixth proposition of his system, viz., One substance 

 cannot be produced by another. Similarly the equation 



expresses his seventh proposition, viz., " It pertains to the nature 

 of substance to exist." This train of deduction it is unnecessary 

 to pursue. Spinoza applies it chiefly to the deduction according 

 to his views of the properties of the Divine Nature, having first 

 endeavoured to prove that the only substance is God. In the 

 steps of this process, there appear to me to exist some fallacies, 

 dependent chiefly upon the ambiguous use of words, to which it 

 will be necessary here to direct attention. 



