Elements of metaphysicsTaylor, A. E. (Alfred Edward)
Philosophy
Elements of metaphysics
Taylor, A. E. (Alfred Edward)
Metaphysics
§ 4. _Characteristics of the Conceptual Time and Space Order._ The
following characteristics of the conceptual space and time created by
the construction we have just examined, call for special notice.
Conceptual space and time are necessarily taken, for reasons already
explained, to be _unlimited_, and _indefinitely divisible_. Though it
does not seem inevitable that they should be _continuous_, we appear to
be unable to attach any positive meaning to the notion of their
discontinuity, and, in the practical need for the application to them of
the complete number-series, we have a valid positive ground for taking
them as continuous. But space and time are thus resolved, in the process
of their conceptual construction, into _continuous infinite series_ of
which the terms are spatial and temporal positions or points. Unlike the
_parts_ of perceptual space and time, these conceptual terms are not
themselves spaces or times, as they contain no internal multiplicity of
structure. Conceptual space and time are thus not wholes or aggregates
of parts, but systems of relations between terms which possess no
quantitative character.
Between any two terms of the spatial, or again of the temporal, series
there is one unique relation, which is completely determined by the
assignment of the terms, their _distance_. In the temporal series, which
has only one dimension, you can only pass from any one given term to any
other through a series of intermediate terms which is once and for all
determined when the initial and final terms are given, hence nothing is
required beyond the terms themselves to fix their distance. The spatial
series is multi-dimensional, _i.e._ you can pass from any one term in it
to any second by an indefinite variety of routes through intermediate
terms, but it is still true that there is one and only one such route
which is completely determined when the terms in question are known,
namely, the straight line passing through both. This straight line
constitutes the unique _distance_ of the two points from each
other.[147] Thus the genuine concept of which those of space and time
are species is not that of _magnitude_ or _quantity_, but of _serial
order_.
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