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nature be divisible; i. e. there are no atoms, or naturally indivis 

 ible particles of matter.&quot; 



This proposition and demonstration are utterly false. The 

 demonstration that matter subsists of extension which is divisible 

 is based on Axiom 7 which asserts that the quiddity of matter 

 is extension, and on Axiom 9. The latter, however, is utterly 

 false, and consequently all the deductions from it are baseless 

 and untenable. 



Here is his 9th Axiom: 



&quot; Every extension can be divided in parts, even if it be only 

 by the mental process. No one, if he knows only the primery 

 principles of mathematics, can doubt this, for the space between 

 the tangents and any given circle can always be divided in 

 countless other and larger circles. The same is the case with 

 the asymptots and the hyperbola.&quot; 



Now this Axiom which is based upon a mathematical cal 

 culation is utterly false. For even if we say that space can be 

 divided mentally or mathematically, it must be indivisible in 

 actuality; because if space were not indivisible in actuality, there 

 would not be a mathematical point in existence. The result of 

 such a mathematical Axiom contains a contradiction in itself. 

 Let me explain my argument clearly: The mathematical point 

 is mentally indivisible, and forms the fundation of the science 

 of Geometry. Now, if extension is so ^ndlessly divisible in 

 actuality, that there is not a physical point in actual existence 

 which is indivisible by the mind, (that the mind should recogn 

 izes it as indivisible), then, there is no mathematical point in 

 the mind, and then, there is no basis for the science of Geo 

 metry. For even if the mind should recognize that there are 

 atoms, indivisible parts of matter, in actual existence in the uni 

 verse, the mind must at the same time recognize that there are 

 no mentally atoms in the mind. If the mind should conceive 

 :&amp;gt;f a physical point that it is indivisible in actuality, this point 

 :ould still be mentally divided, for every physical point, of 

 whatever nature it be, is always mentally divisible in two parts, 

 ind those rJ arts again can be divided in parts, and so forth with- 

 &amp;gt;ut end. Thus, if a point which is indivisible in actuality is still 



