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Unformatted text preview: l reflect the form of my sensibility; which is to say
that· I can know a priori that I can intuit objects of the senses only in accordance with this
form of sensibility. It follows that there can be ·and we can know· propositions that
concern merely this form of sensibility, that such propositions are valid for objects of the
senses, and that they cannot be applied to anything except objects of our senses.
Section 10
Thus it is only through the form of sensible intuition [= ‘form of sensibility’] that we can
intuit things a priori. Such a priori knowledge, however, concerns objects only as they
appear to us through our senses, and not as they may be in themselves. If a priori
knowledge of synthetic propositions is to be possible, and we are to understand how it is
possible, it must be subject to this ·limitation to how things appear as distinct from how
they are in themselves·. 20
Now, space and time are the two intuitions on which pure mathematics grounds all
its judgments that present themselves as certain and necessary. Pure mathematics must
construct its concepts on the basis of pure intuition, ·that is, the kind of intuition that is
conducted a priori , with no reliance on the senses·. Mathematics cannot proceed
analytically by dissecting concepts, but only synthetically; so without pure intuition it
cannot take a single step, since only pure intuition provides the material for synthetic a
priori judgments. Geometry is based on the pure intuition of space. Arithmetic forms its
own concepts of numbers by successively adding units in time. Our representations of
space and time are merely intuitions, however, ·rather than concepts·; and here is why.
Start with empirical intuitions of bodies and their changes, and strip them of everything
empirical  that is, everything you know about through sensation  and what you are left
with is space and time. These are therefore pure intuitions. They must be involved in all
empirical intuitions, and can never be omitted, because they underlie everything empirical.
But just because they are themselves pure a priori intuitions, they must be mere forms of
our sensibility. They precede all our empirical intuition, i.e. all our perceptions of real
objects; through them we can know objects a priori, though indeed only as they appear to
us ·and not as they are in themselves·.
Section 11
That solves the problem about how mathematics is possible. Pure mathematics is possible
only because it bears on mere objects of the senses. The empirical intuition of such objects
is grounded a priori in a pure intuition of space and time, and this pure intuition is merely
the mere form of our sensibility. It precedes the actual appearance of objects, since it
makes it possible for them to appear to us. ·Objects can appear to us only through our
sensibility; and anything we get through our sensibility bears the marks of the form of
sensibility·. Our a priori intuitions don’t involve the content of the appearance, the
element of sensation in it, for that belongs to the empirical realm; they involve the form of
the appearance, namely space and time. If you suspect that space and time are features of
things in themselves rather than mere features of how things relate to sensibility, then tell
me: How in that case could we know a priori  in advance of any experience of things what the intuitions of space and time must be like? Yet we do know this. There is no
problem about this knowledge so long as space and time are taken to be nothing more
than formal conditions of our sensibility, and the objects are taken to be merely
appearances. For then the pure intuition that embodies the form of sensibility can be
understood as coming from us  from our side of the transaction with objects  which
means that it can be had a priori rather than empirically.
Section 12
To clarify and confirm all this, we need only to look at how geometers do (and absolutely
must) go about proving that two figures are completely congruent, meaning that one can
be replaced at all points by the other. All such proofs ultimately come down to this: The
two figures coincide with each other; which is obviously a synthetic proposition resting on
immediate intuition. This intuition must be given pure and a p riori, otherwise the
proposition couldn’t hold as absolutely certain and necessary. If it rested on an empirical 21
intuition, it would only have empirical certainty, and would mean: So far as our
experience has shown us, this proposition has held up till now. That space has three
dimensions, and that no space could have more, is built on the proposition that not more
than three lines can intersect at right angles in a point. This proposition can’t be shown
from concepts, but rests immediately on intuition, and indeed (because it is necessary and
certain), on pure a priori intuition. That a line can be drawn to infinity, or a series of
changes continued to infinity, presupposes a representation of space and time...
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This note was uploaded on 03/12/2013 for the course PHIL 105 taught by Professor Mendetta during the Spring '13 term at SUNY Stony Brook.
 Spring '13
 mendetta
 Philosophy, Kant, Critique of Pure Reason

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