(intro music)
Hi, I'm Scott Edgar.
I'm an assistant professor at Saint Mary's University.
And last time I was talking about
Kant's argument from geometry,
which was his argument about the nature of space.
And now I'm gonna tell you a little bit about
some objections that philosophers have made
to the argument,
and also how, if the argument is good,
it hints at a really sweeping conclusion
about the nature of knowledge.
Now, lots of philosophers don't think
Kant's argument is any good.
And they've found different reasons
to object to both of Kant's premises.
So let's take a look at the first premise first.
One really big objection to it
comes from twentieth-century physics and math,
and in particular the theory of relativity.
According to the theory of relativity,
the question of what geometry correctly describes
the actual, physical universe
is a question we need to do a bunch of physics to answer.
But physics is empirical, not a priori.
So that makes geometry empirical too.
since, along with the physics,
geometry is ultimately justified at least in part
by a bunch of experiments in physics.
If that's right, it looks like Kant was wrong
to think that geometry was a priori,
and the first premise of his argument is wrong.
For more than a hundred years now,
probably most philosophers have thought
this objections makes real problems for Kant.
This is a really influential objection.
But some contemporary Kantians
think there's a way to save Kant's argument here.
They say, "Grant that twentieth-century physics does show
"that geometry is empirical, because it does,
"but there might still be other mathematical structures,
"ones that are much more abstract
'than the geometry we all learn in school,
"and those other mathematical structures
"might still by synthetic a priori."
So maybe Kant got it wrong
that geometry is synthetic a priori,
but if we could find the right mathematical structures
that were synthetic a priori,
then maybe Kant's argument could still go through.
There's a lot more you could say about that objection
and the responses to it that I've sketched,
but for now, let's look at the second premise.
There's an objection to this premise that goes back
almost to when Kant was alive.
It goes like this.
Grant, just for the sake of argument,
that Kant's argument successfully shows
that space is a form of intuition,
that is, a structure our own minds impose
onto our representations of the world.
But now, the objection goes, that doesn't mean
that space isn't also a property of objects
in a mind-independent world,
because why can't it be both?
That seems like a possibility that Kant just ignores:
the possibility that space is both a form of intuition
and a property of things in themselves.
So philosophers have called this the
"neglected alternative objection".
But here's one strategy Kant suggests
for responding to that objection.
Suppose, just for the sake of argument,
that space were a property of things in themselves.
What would our knowledge of that space be like?
Since it would be knowledge of something out there
in the mind-independent world,
it would have to be empirical,
because the only way we can get knowledge
of anything about mind-independent objects,
is through our senses.
And as we've already seen, if the knowledge is empirical,
then it can't be necessary.
That would mean that the geometry that describes that space
can't be necessary.
But, Kant thinks, that's impossible,
because all geometrical knowledge is
necessary and universal.
So he thinks this argument really does show
that space isn't a property of things in themselves.
That is, isn't a property of objects
in the mind-independent world.
Now, that's definitely not the last word on that objection,
but it'll do for now.
So that's Kant's argument about the nature of space.
That in particular, space is really just something
our own minds impose onto our representations,
and not a real feature of the mind-independent world.
Now, let me leave you with a more general conclusion
that Kant's argument from geometry hints at.
Think about the fact that everything we perceive,
or have knowledge of in the external world,
we represent spatially.
Medium-size things like trees and mountains,
big things like planets and galaxies,
and really small things like molecules and atoms.
We represent all of those things as
being somewhere in space, and taking up
some amount of space.
But if space isn't a real property of things
as they exist in themselves,
then when we represent things spatially,
we're not really representing them as they are.
We're only representing them as they appear to us,
with the spatial structure our own minds impose onto them.
Even in modern science, when, for example,
we represent a molecule as having a particular shape
and being in a particular place,
we're not really representing the molecule
as it really is in itself.
All we're ever getting at is how the molecule appears to us.
So Kant thinks there's this distinction
between how things appear to us
and how they really are in themselves,
and he thinks all human knowledge is limited
to the appearances-side of that distinction.
All we can ever have knowledge of,
is how things appear to us.
We can't ever have any knowledge
of how things really are in themselves.
That's the view that Kant is going to argue for.
It's a pretty sweeping view of
the nature of human knowledge,
and you might think it's a view that puts
some pretty shocking limits
on what it's possible for us to know.
But maybe the most shocking thing
about Kant's argument is what gets it all started.
Because what gets it all started?
The nature of geometry.
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