An essay on the foundations of geometry

By Bertrand Russell

Page 189

is essential to distinguish clearly
between empty space and spatial figures. Empty space, as a form
of externality, is not actual relations, but the possibility of
relations: if we ascribe existential import to it, as the ground,
in reality, of all diversity in relation, we at once have space as
something not itself relations, though giving the possibility of all
relations. In this sense, space is to be distinguished from spatial
order. Spatial order, it may be said, presupposes space, as that in
which this order is possible. Thus Stumpf says[195]: "There is no
order or relation without a positive absolute content, underlying
it, and making it possible to order anything in this manner. Why and
how should we otherwise distinguish one order from another?... To
distinguish different orders from one another, we must everywhere
recognize a particular absolute content, in relation to which the
order takes place. And so space, too, is not a mere order, but just
that by which the spatial order, side-by-sideness (_Nebeneinander_)
distinguishes itself from the rest."

May we not, then, resolve the antinomy very simply, by a reference to
this ambiguity of space? Bradley contends (Appearance and Reality,
pp. 36-7) that, on the one hand, space has parts, and is therefore
not mere relations, while on the other hand, when we try to say what
these parts are, we find them after all to be mere relations. But
cannot the space which has parts be regarded as empty space, Stumpf's
absolute underlying content, which is not mere relations, while the
parts, in so far as they turn out to be mere relations, are those
relations which constitute spatial order, not empty space? If this
can be maintained, the antinomy no longer exists.

But such an explanation, though I believe it to be a first step
towards a solution, will, I fear, itself demand almost as much
explanation as the original difficulty. For the connection of empty
space with spatial order is itself a question full of difficulty, to
be answered only after much labour.

=203.= Let us consider what this empty space is. (I speak of "empty"
space without necessarily implying the absence of matter, but only
to denote a space which is not a mere order of material things.)
Stumpf regards it as given in sense; Kant, in the last two arguments
of his metaphysical deduction, argues that it is an intuition, not
a concept, and must be known before spatial order becomes possible.
I wish to maintain, on the contrary, that it is wholly conceptual;
that space is given only as spatial order; that spatial relations,
being given, appear as more than

Last Page Next Page

Text Comparison with Proposed Roads to Freedom

Page 0
Page 4
Although, for the most part, they have more belief than their neighbors in human nature's inherent capacity for a good life, they are so conscious of the cruelty and oppression resulting from existing institutions that they make a wholly misleading impression of cynicism.
Page 5
They seem to him on the whole kindly, decent folk.
Page 9
Indeed, he usually spoke as though each business were owned by a single man.
Page 12
It compels legislative recognition of particular interests of the workers, by taking advantage of the divisions among the bourgeoisie itself.
Page 21
in America, and among Industrial Unionists and Guild Socialists in Great Britain.
Page 37
A Bourse du Travail is a local organization, not of any one trade,.
Page 39
Page 45
This is no doubt partly explicable by the special circumstances of America, where the recent immigrants are apt to be voteless.
Page 47
[35] The ideas of Guild Socialism were first set forth in ``National Guilds,'' edited by A.
Page 68
[50] On this subject there is an excellent discussion in the before-mentioned work of Monsieur Naquet.
Page 69
'' Kropotkin, ``Anarchist Communism,'' pp.
Page 76
Page 85
In such circumstances, all the passions and interests required to produce a war would exist, in spite of the establishment of Socialism in both countries.
Page 91
From populations largely deprived of the simple instinctive pleasures of leisure and love, sunshine and green fields, generosity of outlook and kindliness of dispositions are hardly to be expected.
Page 98
Apart from this difficulty, selection by older men would lead to jealousy and intrigue and back-biting, producing a poisonous atmosphere of underground competition.
Page 102
If this is done, it may be presumed that each Guild will be continually seeking for new processes or inventions, and will value those technical parts of scientific research which are useful for this purpose.
Page 110
The difficulties are stupendous, but they must be overcome if the.
Page 116
And there is no doubt that intellect would work more keenly and creatively in a world where instinct was less thwarted, where the joy of life was greater, and where consequently there would be more vitality in men than there is at present.
Page 120
craft, 73 Trusts, 75, 141 Utopias, vii, $, 200 Vagabond's wage, 177, 193, 208, 212 Villeneuves Saint Georges, 71 Violence, crimes of, 121, 122, 199 Violence, Reflections on, 29 Viviani, 60 Volkstimme, 27n.