Memorabilia Mathematica; or, the Philomath's Quotation-Book
Science
Memorabilia Mathematica; or, the Philomath's Quotation-Book
Mathematics; Mathematics -- Quotations, maxims, etc.
V. Space is represented as an infinite given quantity. Now it is
quite true that every concept is to be thought as a representation,
which is contained in an infinite number of different possible
representations (as their common characteristic), and therefore
comprehends them: but no concept, as such, can be thought as if
it contained in itself an infinite number of representations.
Nevertheless, space is so thought (for all parts of infinite space
exist simultaneously). Consequently, the original representation
of space is an _intuition a priori_, and not a concept.--KANT, I.
_Critique of Pure Reason [Max Müller]
(New York, 1900), pp. 18-20 and
Supplement 8._
=2003.=
_Schopenhauer’s Predicabilia a priori._[11]
OF TIME OF SPACE
1. There is but _one time_, all 1. There is but _one space_,
different times are parts of all different spaces are
it. parts of it.
2. Different times are not 2. Different spaces are not
simultaneous but successive. successive but
simultaneous.
3. Everything in time may be 3. Everything in space may be
thought of as non-existent, thought of as non-existent,
but not time. but not space.
4. Time has three divisions: 4. Space has three dimensions:
past, present and future, height, breadth, and
which form two directions length.
with a point of indifference.
5. Time is infinitely 5. Space is infinitely
divisible. divisible.
6. Time is homogeneous and a 6. Space is homogeneous and a
continuum: i.e. no part is continuum: i.e. no part
different from another, nor is different from another,
separated by something nor separated by something
which is not time. which is not space.
7. Time has no beginning nor 7. Space has no limits
end, but all beginning and [Gränzen], but all limits
end is in time. are in space.
8. Time makes counting 8. Space makes measurement
possible. possible.
9. Rhythm exists only in time. 9. Symmetry exists only in
space.
10. The laws of time are _a 10. The laws of space are _a
priori_ conceptions. priori_ conceptions.
11. Time is perceptible _a 11. Space is immediately
priori_, but only by a perceptible _a priori_.
means of a line-image.
12. Time has no permanence but 12. Space never passes but is
passes the moment it is permanent throughout
present. all time.
Public-domain text, read in full here on John Shaqi.
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