(intro music)
Hi, my name is Scott Edgar.
I'm an assistant professor at Saint Mary's University,
and today I'm going to talk about Immanuel Kant
on metaphysics and synthetic a priori knowledge.
So let's start with a question about philosophy.
What kind of knowledge is philosophy?
And what kind of knowledge is knowledge of metaphysics?
What's its nature?
You might think there's a good reason to wonder about that.
It can seem like philosophers have a bad track record
of actually establishing much
in the way of metaphysical knowledge.
And it seems, sometimes, like nobody can agree on anything
in metaphysics, and so it doesn't seem to get anywhere.
That was a problem the German philosopher Kant
was really worried about at the end of the eighteenth century.
So, he really wanted to know what kind of knowledge
philosophical knowledge is, and especially
what kind of knowledge metaphysical knowledge is.
Answering that question was one of the things he
wanted to do in his first major book,
The Critique of Pure Reason.
Kant argues that knowledge in metaphysics
has to be what he called "synthetic a priori knowledge."
And actually, the idea of synthetic a priori knowledge
is absolutely central to Kant's entire philosophy.
He thought the idea of it was one
of his most important philosophical discoveries,
and a lot of the rest of his philosophy
depends on it in one way or another.
So I wanna give you an explanation of what
synthetic a priori knowledge is,
and then I'll give you one example of it
that was really important for Kant.
And then finally, I'm gonna explain
why Kant thought philosophical, or metaphysical, knowledge
had to be synthetic a priori knowledge.
Okay, so the idea of synthetic a priori knowledge
is based on two different distinctions.
The distinction between a priori knowledge
and empirical knowledge, and the distinction
between analytic judgments and synthetic judgments.
So let's start with the distinction between
a priori knowledge and empirical knowledge.
Empirical knowledge is any knowledge
that comes from, or is justified by, appeal to the senses.
All kinds of everyday knowledge
are examples of empirical knowledge.
So, for example, you know what the weather is like
when you look out the window and observe.
So, that's a kind of empirical knowledge,
because it depends on the senses.
But all kinds of scientific knowledge are also empirical.
So for example, if you're close to the surface of the Earth,
gravity accelerates objects in free fall
at a rate of 9.8 meters per second squared.
That's something we only know because
it's backed up by a lot of experimental evidence,
and those experiments all relied on our senses.
So that scientific knowledge is empirical.
The opposite of empirical knowledge is a priori knowledge.
It's knowledge that isn't justified by appeal to the senses.
So, for example, think of the truth that all roses are roses.
That's a pretty boring truth because
it doesn't tell us very much.
But it's true.
And you know it's true without having
to rely on your senses at all,
because it's just true by definition.
So, since that truth isn't justified
by appeal to the senses, it's a priori.
But Kant also thinks math is a priori.
So for example, you don't have to do any experiments
to confirm, for example, that seven plus five equals twelve.
Kant thinks we ultimately justify that truth
without appealing to our senses at all,
so it's an example of a priori knowledge.
Now Kant thinks a priori knowledge
has a couple of really special characteristics.
First, it's necessary.
We don't think that seven plus five just contingently
turns out to equal twelve, and it's not
an accident that seven plus five equals twelve.
We think it's not possible for seven plus
five to equal anything other than twelve.
In that sense, seven plus five necessarily equals twelve,
and Kant thinks the same goes for all a priori knowledge.
Second, a priori knowledge is universal.
That is, a priori truths like "seven plus
five equals twelve" are true without exception.
There's no time and there's no place
where seven plus five doesn't equal twelve.
It's not like there's this one region of space
on the other side of the galaxy where
seven plus five equals something other than twelve.
So in that sense, Kant thinks, math is universal,
and the same goes for all a priori knowledge.
These two characteristics of a priori knowledge
are important because they give us a kind of test
for figuring out if knowledge is a priori or empirical.
If knowledge is necessary or universal, then it's a priori.
If it's not necessary or universal, then it's empirical.
So that's the distinction between a priori
and empirical knowledge for Kant.
Now let's think about his distinction
between analytic judgments and synthetic judgments.
Kant says that an analytic judgment is one
where the concept of the judgment's predicate
is contained in the concept of the judgement's subject.
What he means by that is roughly that
analytic truths are true by definition.
So take the judgment "a bachelor is unmarried."
That's analytic, because the concept "unmarried"
is implicitly contained in the concept "bachelor."
Why?
Well, you can think of the concept "bachelor"
as just being made up of the concepts "unmarried" and "man."
That is, the definition of the concept "bachelor"
just is "unmarried man."
In the case of the analytic judgment
"a bachelor is unmarried," all the judgment is doing
is taking one of the concepts that's already implicitly
contained in the concept of "bachelor" and making it explicit.
Synthetic judgments are the opposite of analytic judgments.
Kant says judgments are synthetic when they
take the concept of the subject
and then they connect a new concept to it that
wasn't already implicitly contained in it.
In other words, synthetic truths are not true by definition.
So take the proposition "a bachelor is happy-go-lucky."
The concept "happy-go-lucky" isn't
contained in the concept "bachelor."
It's not part of the definition of "bachelor."
So that proposition is a synthetic judgment.
Kant calls synthetic judgments "ampliative,"
because unlike analytic judgments, they actually
connect up new information to the judgment's subject
concept that wasn't already contained in it.
In that sense, they actually extend our knowledge
beyond what was already contained
in the definition of the subject.
Okay, so now we have these two distinctions,
a priori and empirical, and analytic and synthetic.
Now we need to think about how they relate to each other.
The first thing we can say is that
all analytic judgments are a priori.
Why?
Because if they're analytic, they're true by definition,
or as Kant would put it, they're true just in virtue
of how the judgment's subject concepts
and the predicate concepts relate to each other.
But if the judgments are just conceptual
or definitional truths, their truth
doesn't depend on experience or the senses.
So, they're a priori.
It also turns out that all empirical knowledge is synthetic.
Why?
Well, because if it's empirical,
the knowledge does depend on experience and the senses.
But then the knowledge depends on more than
just the definitions of the concepts it involves.
So empirical knowledge can't be analytic,
and it has to be synthetic.
So you might think Kant's two distinctions
overlap each other perfectly, so that really
you've just got one distinction with
a priori knowledge and analytic judgments on one side
and empirical knowledge and
synthetic judgments on the other.
On this view, analytic judgments make up
all the a priori knowledge there is,
and empirical knowledge makes up all
the synthetic judgments there are.
Or to put the view more precisely,
all and only analytic judgments can be a priori
and all and only synthetic judgments can be empirical.
If that seems right to you, you're in good company.
That's how most philosophers before Kant saw it.
The Scottish philosopher, David Hume, was somebody
who laid that view out especially clearly.
But Kant thinks that view is wrong.
It misses something, and recognizing what it misses is really important.
Of course, Kant thought what it missed
is the possibility of synthetic a priori knowledge.
So what's an example of synthetic a priori knowledge?
Kant's main example is math.
So for example, take the piece of mathematical knowledge
that the interior angles of a triangle sum to 180 degrees.
We've already seen some of Kant's reasons
for thinking that math is a priori.
We can't justify geometrical truths like this one
by doing experiments, or relying
on our senses in any other way.
What's more, truths like this one seem necessary and universal.
The interior angles of a triangle
sum to 180 degrees without any exceptions.
Kant didn't think it made sense to think
there could be a triangle on the other side
of the galaxy whose interior angles
didn't sum to 180 degrees.
But on the other hand, Kant thinks
mathematical truths like this one are synthetic, too.
The concept of "the interior angles of a triangle"
doesn't seem to implicitly contain
the concept of exactly 180 degrees,
at least not in the same simple sense
that the concept of "triangle" contains
the concept of "three sides."
The definition of the triangle is "a
three-sided figure enclosed on a plane."
But the fact that the triangle's interior angles
sum to 180 degrees seems to go beyond its definition.
It adds genuinely new information that wasn't
already contained in the concept of the triangle.
So the truth that the interior angles
of a triangle sum to 180 degrees is ampliative,
in Kant's sense, and so it's also synthetic.
So, Kant thinks, if we don't have the concept
of synthetic a priori knowledge, there's no way for us
to understand the kind of knowledge that math is.
But now, we can also finally come back to the question
of the nature of our knowledge of metaphysics
and why that knowledge has to be synthetic a priori.
Lots of philosophers before Kant, especially
in the main tradition of philosophers
in Germany in Kant's own time, thought metaphysics
was supposed to cover truths that
are necessary and universal.
But if metaphysical knowledge
is supposed to be necessary and
universal, it has to be a priori, too.
At the same time, metaphysics isn't supposed
to be just a bunch of empty definitional truths.
Metaphysics is supposed to genuinely extend
our knowledge beyond definitional truths.
But that means metaphysics is supposed to be ampliative,
and so it has to be synthetic.
So Kant thought this tells us something
about what kind of knowledge metaphysical
knowledge would have to be.
It tells us something about the nature
of metaphysical knowledge.
If philosophers are ever going to establish
any metaphysical knowledge, it's going
to have to be synthetic a priori.
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