In Kant's exposition on the nature of space, he defines space as an a
priori template of infinite magnitude, in which the other
significant non-physical attributes besides space itself that also
possess an a priori nature are geometric shapes. However,
these geometrical entities that exist outside of the human mind are
arrived at synthetically, rather than in a purely analytic manner,
like space itself. Through what is mostly an impenetrable fog of
verbal convolution and and excessively multi-layered complexity, Kant
arguably delivers an excellent point regarding why it is that
geometric shapes are synthetic, a priori judgments. The
essential point is that shapes, or structures corresponding to exact
geometrical laws, must first be apprehended with the impulsion to
understand their overarching and exact mathematical foundations, and
to perhaps actually apply the shapes for a technical, or intelligent
use of some sort. That is to say that a precise understanding of such
shapes, let alone application, could very well be deemed unnecessary
by a certain society or individual, and they may never even envision
what a perfected form of shapes would look like in their mind. Space
alone, on the other hand, is clearly conceived of by everyone
regardless of sensory handicaps like blindness or deafness, and it
possesses a supreme application of the highest order in terms of how
people experience the entirety of their lives in accordance to not
only the vacuous space that separates objects, but how displacement
or adjustment of objects effect their existence insofar as newly
occupied space takes on new properties, which are in turn configured
by the properties of the object(s) that now define space. Even then,
knowing the exact mathematical properties of geometric shapes could
theoretically never spell the difference between life and death, or
serve any significant practical purpose—perhaps.
Now supposing one possessed a desire to know geometric shapes to the
point of mathematical perfection, it would conceivably be necessary
for them to utilize means of systematic and scientifically rigorous
measurement to determine that shapes have specific angular measures
that are equal when the sides are also equal, and that deviation from
such exact measurements will result in a lack of cohesion, and
therefore a deficit in optimal application, whether that be for
engineering purposes or otherwise. Such measurements and scientific
work therefore entail synthetic activity (i.e., measuring and going
about the process of determining the a priori aspects of
geometric shapes), rather than a merely analytic judgment that does
require a means of discovery or verification that certain concepts
which appear in the mind are indeed not dependent on human
consciousness to exist. On the contrary, space does not require
measurements and precise calculation, or a scientific method of any
kind to judge that space in fact exists. It is recognized as an
obvious and inherent superstructure of existence that could only be
systematically doubted, or approached in a calculating sense if one
were to question whether or not they are in a machine or
hallucination (as extreme examples meant to elucidate) insofar as all
they perceive is an illusory product of a higher or invisible
intelligence, or fabrication brought upon by a substance(s) or
enigmatic technology unbeknownst to the person undergoing the
ridiculously overblown deception that comprises existence on Earth.
Moreover, space simply does not require synthetic action in order for
it be perceived as the a priori template in which all objects
and physical events are inextricably bound. It is rather
automatically experienced as a prerequisite for existence (even if
you're trapped; you're still in space), to the extent that all that
ever happens occurs within space, or interactively with any and all
objects that happened to be generated within the framework of space.
All objects, or physical components of space, are subject to
dissolution en route to conveying portals that enable an infinite
possibility of new objects to enter, combine, and take action in a
multiplicity of ways, but always to the degree that the same space is
eternal in its nature, as well as ability for expansion. Geometrical
shapes do not possess this feature though; for shapes are manipulated
and objects come to be in a manner tantamount to instantiating the
existence of the shapes by the warping of, or intrinsic operations
within the infinite and shapeless, formless entity (albeit
proto-non-entity, in a complementary sense) that space is.