Memorabilia Mathematica; or, the Philomath's Quotation-Book
Science
Memorabilia Mathematica; or, the Philomath's Quotation-Book
Mathematics; Mathematics -- Quotations, maxims, etc.
=1975.= Direct and inverse ratios have been applied by an
ingenious author to measure human affections, and the moral worth
of actions. An eminent Mathematician attempted to ascertain by
calculation, the ratio in which the evidence of facts must
decrease in the course of time, and fixed the period when the
evidence of the facts on which Christianity is founded shall
become evanescent, and when in consequence no faith shall be
found on the earth.--REID, THOMAS.
_Essays on the Powers of the Human Mind
(Edinburgh, 1812), Vol. 2, p. 408._
CHAPTER XX
THE FUNDAMENTAL CONCEPTS, TIME AND SPACE
=2001.= Kant’s Doctrine of Time.
I. Time is not an empirical concept deduced from any experience,
for neither co-existence nor succession would enter into our
perception, if the representation of time were not given _a
priori_. Only when this representation _a priori_ is given,
can we imagine that certain things happen at the same time
(simultaneously) or at different times (successively).
II. Time is a necessary representation on which all intuitions
depend. We cannot take away time from phenomena in general,
though we can well take away phenomena out of time. In time alone
is reality of phenomena possible. All phenomena may vanish, but
time itself (as the general condition of their possibility)
cannot be done away with.
III. On this _a priori_ necessity depends also the possibility of
apodictic principles of the relations of time, or of axioms of
time in general. Time has one dimension only; different times are
not simultaneous, but successive, while different spaces are
never successive, but simultaneous. Such principles cannot be
derived from experience, because experience could not impart to
them absolute universality nor apodictic certainty....
IV. Time is not a discursive, or what is called a general
concept, but a pure form of sensuous intuition. Different times
are parts only of one and the same time....
V. To say that time is infinite means no more than that every
definite quantity of time is possible only by limitations of one
time which forms the foundation of all times. The original
representation of time must therefore be given as unlimited. But
when the parts themselves and every quantity of an object can be
represented as determined by limitation only, the whole
representation cannot be given by concepts (for in that case the
partial representation comes first), but must be founded on
immediate intuition.--KANT, I.
_Critique of Pure Reason [Max Müller]
(New York, 1900), pp. 24-25._
=2002.= Kant’s Doctrine of Space.
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