SOAII-: PROBLEMS OI- I'liVSlCAL CONTINUITV. 



Bv Rev. Sii)M-v Ri:ai) Welch, B.A.. D.D.. Ph.D. 



In modern science and pliilosophy the word " continuity " 

 nas asstniied an importance hardly dreamed of b>' writers of 

 nfty years ago. Its general meaning has been that of a certain 

 [)ersistence, whether of movement or of being, through succes- 

 sive stages or successive transformations. When theories of 

 evokition were most popular in scientific circles, the persuasion 

 of the existence of some kind of continuity crystallised into a 

 conviction, often held \t'r\- dogmatically, that there was a greater 

 uniformity in nature than it was ever possible to prove. 



But to-dav continuit)- is looked at more from the standpoint 

 of the separate sciences which occupy the intellectual powers of 

 men. In biology we discuss the continuity of life (biogenesis), 

 of cells, of germ i:)lasms. and of variation through -^mall and con- 

 tinued increments in one direction. Psychology sees shadows 

 of the continuum in the operations of the human mind; not only 

 in the continuity of con.sciousness, which some have regarded 

 as the objective background out of which the more specialised 

 processes (^f the mind are elaborated, but also in the motor- 

 continuum, which is the ])hysica] counterijart of the constant 

 readiness to act, and the memory-continuum, which is sometimes 

 supposed to be integrated by means of the movements of atten- 

 tion. And even the mathematicians claim to have discovered a 

 vubtle attribute of the continuum, whicJT had escaped notice until 

 the seventies of the last century, and was revealed b\- the acute 

 labours of two German scholars, G. Cantor and Dedekind. who 

 were Avorking independently. Lastly, Pragmatism has given con- 

 tinuity an extraordinary extension and a new life, making it the 

 basis of all i)hilosophv. 



But at the root of all these new connotations of the word 

 lies the ancient and elementary meaning that it has always had 

 for mankind — the unbroken line, or surface, or volume, that can 

 be seen or felt. \"ery early Aristotle gave this subdivision of a 

 categorv a ])hilosophical definition, which was a commonplace 

 of Luropean philoso])hy for many centuries, in the Latin form 

 in vogue with the Scholastics : 



Continua quantitas est ciijus partes ad iinum communein tennimim 

 c<>i>"l''intiir. 



It goes without saying that stich a vague definition lent itself 

 to various senses. But its most lucid exposition is to be found 

 in one of the minor philosophical works of the great Aquinas,* 

 which we may thus translate : 



We must iniagint' a iiidvinji point ( whicli is tlie indivisible in a line) 

 which hy its motion produces the line, the mcA-ing I'ne produces a super- 



* " Logice Summa.' C. ill. As far as 1 know, no EngKsli translation 

 of this work exists. 



