26 Mr Wiener, Studies in Synthetic Logic. 
This condition is manifestly implied by 
a, Perp.a+ 8. D,,2:a(int*P)B.v.B Gnt*P) a. , 
Since a (int‘P) @ merely demands that a and @ should be 
members of Xp, and that some member of a should bear the 
relation P,.|P to some member of 8, and since if # and y are 
both members of a, and aerp, «P,y, int‘P will be connected if 
eV P rane Jedi aa Oer.| 1° 2. 
Now, 
> = 
© CU ie 88 eee ro ep nace pes Teen 
Dy GI) Beng ay EA neds) GAP a 3: 
Day te (HZ) 2 Pp. ZPY V+ 2Pooh YPZ Vi. ZP oo -ZPL NV »ZP cel «LPH 
Dry = Oleee | Ye V a Yl | Pig «MY e|| Face Vile id ee 
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. 
we have just shown to be sufficient for the connectedness of int*P. 
§ 8. We have seen, then, that if 
P..| Petrans and): P| P36 Pz | Pe inigelecer: | 
Now the questions arise, what do these conditions mean when P | 
is, for example, the relation ‘noticeably brighter than’? and, are 
they true of such relations? The meaning of P,,|Petrans in 
such a case is clear, as is also its truth; P,,|P is the relation 
between two objects, # and y, when z is not merely apparently, but 
actually brighter than y, for #P,,|Py says that x is only sub- 
liminally different, if at all different, in brightness from something ~ 
that is supraliminally brighter than y. Now, the transitivity of | 
the relation, ‘brighter than,’ is obvious: at least as obvious, at 
any rate, as the existence of a series of brightnesses. | 
The meaning of P|P,,€P,.|P, however, is not quite so » 
obvious. This condition demands that if « be noticeably brighter ~ 
than something indistinguishable from y, it shall be indistinguish- 
able from something noticeably brighter than y. We may interpret — 
this demand as saying: if w is noticeably brighter than everything © 
noticeably less bright than y, then y is noticeably less bright than 
everything noticeably brighter than « A little reflection will — 
convince us that this proposition is probably true: moreover, — 
it is easy to see that its truth, and the truth of analogous © 
propositions concerning all sorts of sensory intensity, form — 
necessary conditions for the truth of the Weber-Fechner law. 
For suppose that this proposition were false: we might then 
have, to put it crudely, w and y both just noticeably brighter than a, 
and w just noticeably brighter than x, but subliminally different 
from y. Let a be the objective strength of the stimulus pro- 
duced by z; then, by Weber’s law, the strength of the stimulus 
produced by «# or y will be a(1+c), where ¢ is a constant 
If P| P,. © P,.| P, this reduces at once to the condition that | 
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