PHILOSOPHY. 
217 
with regard to time, the world cannot be infinite, but mull 
have had a beginning, which is the neceffary condition 
of its exiftence ; which was to be proved. 
As to the fecond, if we maintain the oppofite, namely, 
that the World with refpedt to Space is infinite, then 
this infinite world, with regard to fpace, is thought as 
exilting at a given inftant; therefore at any prefent time 
it is wholly there. Confequently in this very reprefenta- 
tion it is confidered as a quantity, whofe fynthefis is finite, 
wherein however we contradidt the conception of a World 
infinite with refpedt to fpace, becaufe this is the reprefen- 
tation of a quantity whofe fynthefis can never be com¬ 
pleted. Therefore, with regard to fpace, the world can¬ 
not be infinite, but enclofed in certain limits; which was 
fecondly to be proved. 
Remark.— The proof of it reds upon this; that the 
world muft be confidered as a Quantity that is given, both 
with regard to time and [pace. It is given according to 
time, becaufe the whole time of its exiftence at every in¬ 
ftant is elapfed ; according to fpace, becaufe in a certain 
point of time the whole world is there, (that is, no parts 
are fucceflively added.) Now we may think an infinite 
quantity, inafmuch as the fynthefis by which it is pro¬ 
duced is arbitrarily afl'umed. But, when a quantity is 
given, then the fynthefis, confequently the number of the 
repetitions of the unity by which it is produced, is deter¬ 
mined ; and fuch a quantity cannot therefore be confi¬ 
dered as infinite; that is, we cannot fay that we can never 
come to an end with its fynthefis. 
Time and Space, indeed, are reprefented as infinitely- 
given quantities : this means, that the fynthefis may pro¬ 
ceed at pleafure without any-where neceffarily ceafing. 
But it is quite different with filled fpace and filled time ; 
becaufe, in this cafe, fomething is given in Time and Space; 
confequently objects, whofe fynthefis muft be immediately 
determined and can never be thought as infinite. 
This demonftration is irrefutable, and muft not be con¬ 
founded with the following one. In order to refute the 
infinity of the world with regard to Time and Space, it has 
been ufual to conclude thus : Infinite is a quantity beyond 
which there is no greater poftible. But now no quantity 
is the greateft, becaufe every aftignable quantity can be 
thought greater. Confequently no quantity can be infi¬ 
nite; and the world therefore can neither be infinite as to 
Time nor Space. But the conception of the infinite is 
here that of a maximum. On the contrary, the true con¬ 
ception of an infinite quantity is that of a quantity whofe 
lucceftive fynthefis can never be completed ; and the 
proof of the thefis muft Ihow that the fynthefis by which 
the world is thought as a given quantity muft come to 
an end. 
Second Contradiction.—Thesis. 
All the fubftances in the world confiftof fimple parts; 
and there is nothing that exifts but thefe fimple parts, 
and that which is compofed of them. 
Proof. —For, let us fuppofe that compound fubftances 
do not confift of fimple parts. Now this compofition is 
either an accidental relation of fubftance, fo that in 
thought it may be feparated from it ; or the compofition 
is effential to fubftance. In the latter cafe, no compound 
fubftance would be thought, but only a fimple one. In 
the former cafe, after having done away with all compofi¬ 
tion of a fubftance, nothing compofed would remain ; and 
as alfo no fimple parts are to remain, nothing at all would 
remain ; whence however it would follow, that no fub¬ 
ftance had been given. Since now both contradidl the 
affumption, every compofed fubftance in the world muft 
confift of fimple parts. 
Therefore nothing but the fimple exifts in the world; 
and, though we may never be able to reprefent infulated 
the elementary fubftances by any phyfical feparation, 
Reafon muft ftill think them as the firft fubjeft of all 
compofition as fimple beings. 
Vol, XX. No. 1362. Remark. 
Let us alfo fuppofe that the World, with regard to Space, 
is enclofed in boundaries. As bounds feparate one (pace 
from another, the world muft be furrounded by empty 
fpace; but now there can only be a relation between 
fpaces in as far as they are filled. For we muft fqmehow 
denote them in order to be able to have an empirical 
intuition of them. An empty fpace therefore that fur- 
rounds the world is impoftible. Therefore the world as 
to fpace is not enclofed in bounds, but it is infinite. 
Remark. —The demonftration of the Antithefis refts 
upon this ; that, if the world had a beginning, and is 
alfo bounded in extent, an empty time muft have elapfed 
before this beginning of the world, and empty fpace muft 
bound it; but both time and fpace muft be in that cafe 
particular objedls, and exift of themfelves, which is not 
poftible, becaufe the lapfe of time is only conceivable by 
means of change, and fpace is only fomething relatively 
to the objefts that fill it. Empty fpace can only be admit¬ 
ted as exifting together with the world, fince in that cafe 
it is determined by the objects, and is a (omething in as 
far as there are objedls. But an empty fpace that bounds 
the world would be a correlative of the objects; that is, 
would be a real objedl itlelf. The fchool of Leibnitz en¬ 
deavours to evade the proof of the Antithefis by changing 
the conception of the world, fo that the conception of 
boundaries is converted into that of limits. In this repre- 
fentation of the beginning and of the boundaries of the 
world, therefore, nothing more can be faid of time and 
fpace. The Thefis, however, fpeaks of Mundus phenome¬ 
non. If we imagine a mere intellectual world, we abftradl 
from the conditions of intuition, confequently from the 
mannerin which the world is given to us, and retain only 
an arbitrary conception of an objedl: in general, with re- 
fpedt to which therefore no Jyntheticalpojition is poftible. 
Antithesis. 
No fubftance in the world confifts of fimple parts, and 
there is nothing exifting that is fimple. 
Proof. —For, let us fuppofe that a compound fubftance 
cpnfifts of fimple parts. Since an objedl that is thought 
by the conception of fubftance can only be given in fpace, 
as the permanent in the external intuition, the fimple of 
which a fubftance is compofed muft alfo occupy a fpace. 
But now each fpace confifts of fpaces, and that which fills 
fpace confifts of as many parts as fpace itfelf. The fimple 
is confequently fomething compofed of parts. As this 
now contradidls itfelf, no compound fubftance in the 
world can confift of fimple parts. 
In experience, however, no objedl can occur that is ab- 
folutely fimple. For, if we even fuppofe an objedl given 
of whofe compofition we are unconfcious, it by no means 
follows that it muft be abfolutely fimple. 
3 K Remark. 
