Bauhaus-Universität Weimar

Dictionary of philosophy and psychology including many of the principal conceptions of ethics, logics, aesthetics ... and giving a terminology in English, French, German and Italian, vol. 2 [lead-zwing]
Baldwin, James Mark
while Bradley makes space 'mere appearance’ 
on the ground that it is dialectical and con¬ 
tradictory through and through (.Appearance 
and Reality, Bk. I. chap. iv). 
The general result of the discussionof Kant’s 
doctrine has been to produce a widespread con¬ 
viction that space is nothing absolutely real, 
either as a thing or as a determination of 
things; but also, on the other hand, that it either 
is or represents more than a mere form with 
which we invest the objects of our perception, 
but which, apart from our perception, has no 
sort of reality in the nature of things. For 
even if the general representation of objects 
as external in space be regarded as due to the 
subjective conditions of our sensibility, the 
compulsion we are under to represent their 
space relations in a definite order affords the 
strongest motive for regarding those relations 
at least as objectively determined. Accord¬ 
ingly, in the great systems of idealistic philo¬ 
sophy which succeeded the Kantian criticism, 
we find, even with Fichte in his later period, 
that the externality of phenomena in space is 
represented as due not specially to the subject 
as opposed to the object, but to the activity 
of a principle identical in the subject and the 
object (Fichte, Werke, i. 190; cf. 343, viii. 
415; Schelling, Werke, i. 3, 22 ff. ; Hegel, 
Werke, vii. 44 ff. ; Logik, i. 279, iii. 353; 
Encyc., § 244). The realistic Herbart, with the 
principle, £ wie viel Schein, so viel Hindeutung 
auf Sein,’ opposes to phenomenal an ‘ intelli¬ 
gible ’ space (Met., ii. 200 ff.), as denoting the 
fact of a real order of coexistence in the mul¬ 
tiplicity of elements posited as absolutely real, 
although, as Trendelenburg justly observes 
{Log. Untersuch., i. 190), the latter is modelled 
entirely on the former. Trendelenburg him¬ 
self holds that space is not the presupposition, 
but the product, of motion (ibid., 215 ff.). 
Other systems tend to a revival of the view 
of space implied in theLeibnitzian spiritualism 
(Lotze : ‘ every particular feature of our spatial 
intuition corresponds to a ground in the world 
of things,’ Met., § 113. Wundt: objective 
space, after elimination of subjective elements, 
is ‘ the regular order of a manifold consisting 
of particular independently given real objects,’ 
Logik, i. 463). Among original thinkers of 
the first rank, Schopenhauer alone accepts 
the Kantian doctrine without reserve. Amid 
this conflict of opinion, the Kantian criticism 
and the whole subjective trend of modern 
philosophy seems to have made one thing clear, 
and that is that space is a category which has 
neither meaning nor validity beyond the 
bounds of possible experience. If, therefore, 
we refuse to accept the naïve conception that 
the object is one thing and its idea in the 
mind a mere counterpart and copy, we must 
admit that there are not two spaces, one real 
for things and one ideal for minds, but that 
ideal space is only the abstraction of real 
space, and real space only the realization 
of the ideal. Whatever reality, therefore, 
and whatever ideality belong to objects 
in space belong to space also. Hence 
everything depends on the interpretation 
of experience. Cf. Space-pekception, and 
Extension. (h.n.g.) 
Literature : besides the citations made 
above, see Bibliog. B, 2, j, and G, 2, v ; see 
also Extension, and the numerous quota¬ 
tions in Eisleb, Wörterb. d. philos. Begriffe, 
‘ Baum.’ (j.m.b.) 
Space (in mathematics). The totality of 
all the positions into which a body could 
possibly be moved, were no impediment to 
motion in existence. 
This totality forms a continuum (see Con¬ 
tinuity, in mathematics), the conception of 
which is so elementary and fundamental that 
no definition can materially aid in its forma¬ 
tion. For us the parts of space are all those 
places, infinite in number, to which or in 
which a body can be conceived to move or 
exist, and, vice versa, we can conceive any¬ 
body to move into a part of the infinite 
continuum which is formed by the totality of 
those places. Space is continuous not only in 
the sense that every part joins to the parts 
around it, but that every part is susceptible 
of indefinite subdivision. 
Our fundamental conception of space assigns 
to it these properties :— 
(1) It is the same for all bodies. Wherever 
one body could move, thither could any other 
body move. 
(2) It is triply infinite. A point may move 
independently in three independent directions, 
all perpendicular to one another, called 
dimensions, to an infinite distance. 
(3) It has no qualities or differentia de¬ 
pendent either on position or direction. 
Wherever a body may be situated, its capacity 
of movement is the same for all positions and 
for all directions. 
(4) It is homoloidal. Two parallel straight 
lines may be produced indefinitely without 
either converging towards or diverging from 
each other. 
On these properties is based the science of 
geometry. Mathematicians have, however, 


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