(1) If we follow the usual definition of the mathematicians, given in
§ 99, and say that magnitude is what can be increased or diminished,
there may be nothing to urge against the correctness of the perception
on which it is founded; but the question remains, how we come to
assume such a capacity of increase or diminution. If we simply appeal
for an answer to experience, we try an unsatisfactory course; because
apart from the fact that we should merely have a material image of
magnitude, and not the thought of it, magnitude would come out as a
bare possibility (of increasing or diminishing) and we should have no
key to the necessity for its exhibiting this behaviour. In the way of
our logical evolution, on the contrary, quantity is obviously a grade
the process of self-determining thought; and it has been shown that it
lies in the very notion of quantity to shoot out beyond itself. In that
way, the increase or diminution (of which we have heard) is not merely
possible, but necessary.
(2) The quantitative infinite progression is what the reflective
understanding usually relies upon when it is engaged with the
general question of Infinity. The same thing however holds good of
this progression, as was already remarked on the occasion of the
qualitatively, infinite progression. As was then said, it is not the
expression of a true, but of a wrong infinity; it never gets further
than a bare 'ought,' and thus really remains within the limits
of finitude. The quantitative form of this infinite progression,
which Spinoza rightly calls a mere imaginary infinity (_infinitum
imaginationis,_) is an image often employed by poets, such as Haller
and Klopstock, to depict the infinity, not of Nature merely, but even
of God Himself. Thus we find Haller, in a famous description of God's
infinity, saying:
Ich häufe ungeheure Zahlen,
Gebirge Millionen auf,
Ich sesse Zeit auf Zeit
Und Welt auf Welt zu Hauf,
Und wenn ich von der grausen Höh'
Mit Schwindel wieder nach Dir seh:
Ist alle Macht der Zahl,
Vermehrt zu Tausendmal,
Noch nicht ein Theil von Dir.
[I heap up monstrous numbers, mountains of millions; I pile time upon
time, and world on the top of world; and when from the awful height I
cast a dizzy look towards Thee, all the power of number, multiplied a
thousand times, is not yet one part of Thee.]
Here then we meet, in the first place, that continual extrusion of
quantity, and especially of number, beyond itself, which Kant describes
as 'eery.' The only really 'eery' thing about it is the wearisomeness
of ever fixing, and anon unfixing a limit, without advancing a single
step. The same poet however well adds to that description of false
infinity the closing line:
Ich zieh sie ab, und Du liegst ganz vor mir.
[These I remove, and Thou liest all before me.]
Public-domain text, read in full here on John Shaqi.
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