This standpoint OF the reconciliation OF all contradictions has been attained in the main, we believe, 'by mankind in the Idealism founded by Kant and wrought out to perfection by his disciple Schopenhauer. For the truth of this Idealism is the more indubit ably confirmed, the more deeply we penetrate into it, by the threefold harmony which we meet in it, Â harmony with itself, harmony with nature, and harmony with the thoughts of the wisest of all times. Moreover it is the Kantian distinction between phenomena and the thing-in-itself, and this distinction alone.
For a work in the tradition of of German Idealism, this book is unusually clearly written and even rather easily readable, and the prose is also quite beautiful and inspiring at places. Unfortunately, the argumentation is not very good (at least from a modern point of view, as later developments in mathematics and natural sciences have dated it greatly); or perhaps that is fortunate, as the worldview the author arrives at is drearily pessimistic, even if he tries to present it in glowing colours. The author's metaphysical system is not very original, being mostly based on Kant and especially Schopenhauer (and the a lesser extent on Indian Advaita Vedanta philosopohy).
The proofs of the first elements of the system are very dogmatic and even naive; possible objections, which would have been raised even at that time, are not considered.
Deussen argues as follows (on page 7) for space being infinite in every direction:
"If it were not so, it would have a limit. This would be either a body or a void, therefore again in both cases space."
However, we must object that a limit need not be external to what it limits. A finite closed spatial region can have its imiting boundary contained in itself. All of space could then be such a finite closed region, even if of tremendous extent.
The author takes as a corollary of this the following: "Whatever exists, exists neces- sarily in space; otherwise it would be nowhere and consequently not at."
This does not appear to me to be at all a corollary of the infinity of space, and is in any case its proof is question-begging. Saying that being nowhere is not being at all is just a restatement in other words of the theorem to be proved, that whatever exists, exists necessarily in space.
These arguments are not very faithful to Kant either. Deussen apparently tries to prove that space is infinite by means of pure reason, while Kant held that this is impossible and leads to irresolvable antinomies.