Researches in the Theory and Calculus of Operations, 229 



propounded by the scholastic philosopher Scotus Erigena, 

 as follows : Everything is either 1° Cause and not Effect, or 

 2° Cause and Effect, or 3° Effect and not Cause, or 4° Neither 

 Cause nor Effect. Then, 1° God is cause and not effect; 2° 

 Force, and forces or noumena are both cause and effect; 

 3° Phenomena, or the final resultants of forces are effects 

 and not causes; and 4° Space and Time, in, and through 

 which these final results are measured and compared, are 

 neither cause nor effect. Space stands for the fabled well of 

 truth. Spatial relations are absolute truths : uncreated and 

 defying annihilation, no power or force, intellectual or phy- 

 sical, can alter the relation of the diagonal to the side of 

 the square. Not being an effect, space cannot be affected; 

 and not being a cause, it disturbs not the actions of forces 

 which encounter each other within its bosom. On the con- 

 trary, from the properties of the contents of space, we de- 

 rive only contingent truths, which can only be verified by 

 means of the sensations they produce in us, and by their 

 subsequent measures in space and time. The substance gold 

 impresses us ( but seldom) by means of its solidity, weight 

 and bright yellow color; properties which are measurable 

 by the assayer and the chemist. And these measures are 

 contingent truths dependent upon the particular constitu- 

 tion given to this metal at its creation, which constitution 

 could be changed by a new creative or alterative act. Thus 

 material substances are causes, that is, forces, and their 

 effects are termed by us their properties. The study of the 

 effects of force, as manifested in the various trajectories 

 and changes occurring in the natural world, is our hopeful 

 task. 



Space and Time are infinite and eternal; but we cannot 

 predicate these attributes for their contents. The argument 

 for the necessary existence of being fatally breaks down, and 

 we know such existence merely as an empirical fact, and 

 not a priori. Assuming, then, a beginning in time and an 



