480 DE. A. N. WHITEHEAD ON 



of matter is secured by the axiom that two different extraneous relations cannot both 

 relate the same instant of time to the same point. The general laws of dynamics, 

 and all the special physical laws, are axioms concerning the properties of this class of 

 extraneous relations. 



Thus the classical concept is not only dualistic, but has to admit a class of as many 

 extraneous relations as there are members of the class of particles. 



Instead of the specific relations of occupation for the various particles, one general 

 triadic relation of occupation can be considered. Thus, O'(pAt) may be considered as 

 the statement the particle p occupies the point A at the instant t. Then for any 

 given A and t there is either one only or no particle p for which O'(pAt) is true. 

 Then the laws of physics are the properties of this single extraneous relation O. 

 But the use of this single relation apparently introduces no real simplification, 

 differing in this respect from the use of the essential relation which so simplifies the 

 statement of the axioms of geometry. The general relation remains a mere alter- 

 native statement of the facts respecting the various specific relations of occupation. 



Concept II. This concept is a monistic variant of the classical concept suggested 

 by RUSSELL.* In the classical concept the particles only occur as terms in the 

 triadic extraneous relations. If we abolish the particles (in the " classical " sense), 

 and transform the extraneous relations into dyadic relations between points of space 

 arid instants of time, everything will proceed exactly as in the classical concept. 

 The reason for the original introduction of " matter" was, without doubt, to give the 

 senses something to perceive. If a relation can be perceived, this Concept II. has 

 every advantage over the classical concept. Otherwise the material world, as thus 

 conceived, would appear to labour under the defect that it can never be perceived. 

 But this is a philosophic question with which we have no concern. 



Concept III. This is a Leibnizian concept, and also a monistic variant of the 

 classical concept, obtained by abandoning the prejudice against points moving. 



This concept can be otherwise considered, as obtained from the modern (and 

 Cartesian) point of view of the ether, as filling all space. The particles of ether (or 

 moving points) compose the whole class of objective reals. The essential relation (R) 

 is a tetradic relation, and, in each specific instance of the relation holding, three of 

 the terms are objective reals and the remaining term is an instant of time. R ; (a&c) 

 may be read as stating the objective, reals a, b, c are in the R-order abc at the 

 instant t. Instead of ~R'(abct), it will be convenient to write R ( ; (6c). Then the 

 geometrical definitions are exactly those of Concept I., replacing R everywhere by R. 

 Also the geometrical axioms are those of Concept I. ; except (i) that R is replaced by 

 R ( , (ii) that IHpR, and VII HpR, and IXHpR, are further modified by the 

 introduction of the hypothesis t e T thus I Hp R of Concept I. becomes 



;;:) Df 



Cf. ' Principles of Mathematics,' vol. I., 441. 



