The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919Whitehead, Alfred North
Philosophy
The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919
Whitehead, Alfred North
Knowledge, Theory of; Nature; Science -- Philosophy
The intrinsic character of a σ-prime has a certain minimum of fullness
among those abstractive sets which are subject to the condition of
satisfying σ; whereas the intrinsic character of a σ-antiprime has a
corresponding maximum of fullness, and includes all it can in the
circumstances.
Let us first consider what help the notion of antiprimes could give us
in the definition of moments which we gave in the last lecture. Let the
condition σ be the property of being a class whose members are all
durations. An abstractive set which satisfies this condition is thus an
abstractive set composed wholly of durations. It is convenient then to
define a moment as the group of abstractive sets which are equal to some
σ-antiprime, where the condition σ has this special meaning. It will be
found on consideration (i) that each abstractive set forming a moment is
a σ-antiprime, where σ has this special meaning, and (ii) that we have
excluded from membership of moments abstractive sets of durations which
all have one common boundary, either the initial boundary or the final
boundary. We thus exclude special cases which are apt to confuse general
reasoning. The new definition of a moment, which supersedes our previous
definition, is (by the aid of the notion of antiprimes) the more
precisely drawn of the two, and the more useful.
The particular condition which 'σ' stood for in the definition of
moments included something additional to anything which can be derived
from the bare notion of extension. A duration exhibits for thought a
totality. The notion of totality is something beyond that of extension,
though the two are interwoven in the notion of a duration.
In the same way the particular condition 'σ' required for the definition
of an event-particle must be looked for beyond the mere notion of
extension. The same remark is also true of the particular conditions
requisite for the other spatial elements. This additional notion is
obtained by distinguishing between the notion of 'position' and the
notion of convergence to an ideal zero of extension as exhibited by an
abstractive set of events.
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