Mr Wiener, Studies in Synthetic Logic. 23 
then what we would naturally call density would be the property 
of R which can be written 
| Gc) -20,ceO'R -D:. (qb). h(a, b,c) iv sac: 
Provided that C‘P Cs‘ap, then if P is any triadic relation having 
this property, then ins‘P, and hence, as may be seen easily, 
(ns‘P), and ins{(ins‘P);], will have this property. 
| Let us now turn to the second topic to be treated in this 
paper, the problem of the synthesis of the series of sensation- 
‘intensities from the relations between sensations given in ex- 
‘perience. This problem, in itself, is not one of pure logic or of 
pure mathematics, but its solution depends upon the solution of 
a purely logical and mathematical problem. In my previous 
article*, as I said at the beginning of this paper, I showed how 
: from the relation of complete succession between the events in 
‘time, we can construct the series of the instants in time. The 
method was the following: we make the definitions: 
(12) P,,=(2P=P)P OP Df. 
(13) maleate ee Dé. 
(14) insb= QP(Q=(esP) Ere} Df. 
If P is the relation between two events, # and y, when «# is over 
before y begins, then P,, is the relation between two events which 
occur together at some moment; Tp is the class of all instants of 
time—that is, the class of all those classes, a, such that a is made 
up of events in such a manner that every two events in @ occur 
together at some moment, and if an event occurs at the same 
moment with every member of a, then it belongs to a; and inst‘P 
is the relation between two members of tp—that is, instants— 
when some event at the first instant is over before some event at 
the second instant begins: that is, it is the relation between an 
instant and a succeeding instant. If P|P,,| PGP, whether P is 
a temporal relation or not, inst‘P will be a series. Now, let P 
stand for the relation, say, between any coloured object and a 
noticeably brighter one. Then P,, will be the relation between 
two coloured objects when the first is apparently of the same 
brightness as the second, for it is the relation between two members 
of the field of P—that is, coloured objects—when neither is in the 
relation P to the other. Now, it is obvious that when «P| P..¥, 
# must be, noticeably or unnoticeably, more bright than y, for this 
proposition says that w is noticeably brighter than some object 
which, at the brightest, is indistinguishable from y. Therefore, it 
is obvious that if wP|P,,| Py, # is brighter than something 
noticeably brighter than y, and hence is noticeably brighter than 
* See Proc. Camb. Phil. Soc., vol. xvu1, Part 5, pp. 441—9. 
