hi I'm Scott Edgar I'm an assistant
professor of philosophy at st. Mary's
University and today I'm going to talk
about an argument that the German
philosopher Immanuel Kant made about the
nature of space it's an argument that
comes from his book their critique of
Pure Reason which first came out in 1781
although by that time he'd been working
on it for 10 years and philosophers call
the argument the argument from geometry
it's an argument as I said about the
nature of space but as we'll see it
hints at an incredibly striking
conclusion about the nature of all
knowledge in particular the conclusion
that we never have any knowledge of how
things really are in themselves I'll
come back to that point later right now
let's start with the question what is
the nature of space is it a real thing
that exists independently of our minds
or is it not a real thing that exists
independently of our minds
well one view you might think is really
natural is that space is real but what I
mean by real in this context is that
space is a part of the mind-independent
world that exists independently of our
knowledge of it so on this view the mind
independent things that exist in the
mind independent world are arranged
spatially and space is just one more
part of the world that's mind
independent now the point of argument
from geometry is to show that that
picture is wrong and to argue for a
completely different picture of the
nature of space on the view of space
that Kant argued for space is just
something that our own minds impose onto
our representations of the world
more specifically Khan thinks on lines
have a capacity to sense things and that
capacity to sense things is what imposes
spatial structure onto our
representations of the world this is the
view that Kant calls the transcendental
ideology of space or transcendental
idealism for short
he loves jargon so his way of putting
the view is to say that space is merely
a form of our intuition that is just a
structure our own minds impose onto our
representations and space is not a
property of things in themselves that is
it's not a property of things as they
exist independently of our
lines and of our knowledge of them so
that's the conclusion of Kant's argument
from geometry that space is merely a
form of intuition and not a property of
things in themselves what's really
interesting about the argument is its
strategy con strategy is to argue for
that conclusion on the basis of certain
facts about geometry that is you think
certain facts about the nature of
geometry and geometrical knowledge turn
out to mean that space has nothing to do
with mind independent objects and it's
really just something our own minds
impose onto our representations so the
arguments first premise is about the
nature of geometry here it is
geometrical knowledge is synthetic a
priori now if you don't know what
synthetic a priori knowledge is you
should go back and watch the video that
explains that and then come back here
because what I'm about to say will make
a lot more sense if you do that so the
question is why does Khan think our
knowledge of geometry is synthetic a
priori well first geometrical knowledge
is necessary and universal it's
plausible to think that a geometrical
truth like say the theorem that the
interior angles of a triangle sum to 180
degrees isn't just contingently true it
can't possibly turn out to be wrong but
also it's not the kind of truth that
there are exceptions too it's not like
the theorem says that the interior
angles of some triangle sum to 180
degrees it doesn't even say most
triangles it applies to all triangles
without exceptions but can't learn from
the Scottish philosopher David Hume that
we can't get knowledge of anything
necessary or universal from experience
so Khan thinks since geometric knowledge
is necessary and universal it can't be
empirical has to be a priori but our
knowledge of geometry is also a con
called amplitude of that is it's not
just a matter of empty or trivial
definitions or conceptual truths but
rather it genuinely extends our
knowledge of course geometry does have
definitions like any other science so
for example when we say that a triangle
is a three-sided figure enclosed a plane
that's true by definition and so it
seems kind of trivial but when we're
dealing with theorems like the one that
says the interior angles of a triangle
sum to exactly 180 degrees it seems like
we're dealing with a different situation
that theorem actually teaches us
something new about triangles that we
didn't already know
from the definition of a triangle in
that sense geometry genuinely extends
our knowledge of things like triangles
and conflicts that means geometrical
knowledge is synthetic so that's the
first premise of Kant's argument from
geometry that our knowledge of geometry
is synthetic a priori now let's look at
non second premise it's got to connect
the idea that geometry is synthetic a
priori to Kant's conclusion that space
is just something our own minds impose
onto our representations of the world
and not a real part of the
mind-independent world itself the
premise says that synthetic a priori
knowledge is possible only if space is
merely a form of our intuition and not a
property of things in themselves in
other words the second premise of Kant's
argument says that synthetic a priori
knowledge is possible only if his view
of the nature of space is true so why
should we think that premise is true
here's Kant's argument the first point
to make is that geometry is the
mathematics of space so when we're
talking about our knowledge of geometry
we're really just talking about our
knowledge of space and so if our
knowledge of geometry is synthetic a
priori our knowledge of space has to be
synthetic a priori - so far so good but
now Khan thinks we have to ask ourselves
what would it take for synthetic a
priori knowledge of space to be possible
well first then I'll just synthetic so
it can't just be a matter of
definitional or conceptual truths
because those are being analytic but
second the knowledge is also a priori so
it can't be based on our experience of
external objects because we can only
ever know about external objects
empirically through the senses so Khan
concludes that our knowledge of geometry
has to be based on nothing but our own
minds his thinking seems to be that
there are external objects that exist
independently of our own minds and then
there are our own minds since our
knowledge of space can it be based on
the first choice it has to be based on
the second when we have knowledge of
space like our knowledge in geometry all
we really have knowledge of is a
structure our own minds or imposing onto
our representations that's why our
knowledge of space can be completely
independent of experience which is to
say that's why it can be a priori but as
we already know the idea of its face is
nothing but a structure
our own minds impose onto our
representations is just what Kant means
when he says in his second premise that
space is merely a form of our intuition
and not a property of things in
themselves so that's the second premise
of Kant's argument when we put the two
premises together we get Kant's
conclusion space is merely a form of our
intuition and not a property of things
in themselves there's still a lot of
questions you might have about it
whether it's a good argument or a bad
argument whether the premises are true
whether they're false and we'll look at
those next time
you