(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. Subtitles by the Amara.org community
Summary: Kant famously claims that we have synthetic apriori knowledge. Indeed, this claim is absolutely central to all of his philosophy. But what is synthetic apriori knowledge? In this Wireless Philosophy video, Scott Edgar helpfully breaks-down this category of knowledge by first walking through Kant's distinction between empirical and apriori knowledge and then his distinction between analytic and synthetic judgments. The interaction between these distinctions is then illustrated with numerous examples, making it clear why Kant, unlike Hume, thought that there is knowledge that is both apriori and synthetic and that this is the type of knowledge philosophers seek.
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Wish my professors had taught such entertaining & easily understood lectures!
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Interesting video, thanks!
this is a question i think i've heard posed before but i don't remember the answer: are all a priori truths tautologies? (i haven't finished the video yet).
edit: okay reached the end of the video but math is the perfect example of analytic truth since it all derives (in theory) from ZFC.
Slightly off-topic, but does anyone know why Americans pronounce Kant "Kahnt" when everyone else in the world (including, one would think importantly, Germans) pronounces Kant like "can't"?
The problem I see with the nature that Kant ascribes to math is, is that 7+5 is not a universal truth. It's a conclusion following from the Peano axioms. There's no inherent meaning in the symbols "7", "+" and "5" before we have established basic axioms of math that give us elementary operations. We do so by choice. We simply have created one version of math that suits our needs to do calculation.
Another example of this is the 180 degree triangle. A triangle only happens to sum up to 180 degrees in Euclidean space, in non-Euclidean space these rules don't apply. (The sum of the angles of a triangle on the surface of a sphere for example does not equate 180 degrees) image
Kant already presupposes some kind of platonic character to numbers without giving real motivation why this is intuitive. (at least from this video, I haven't read Kant admittedly.)
Would have been interesting to hear some criticism of this in the video, otherwise a very concise explanation.
To say that the sum of the interior angles of a triangle equal 180 degrees, appears to me to remain a tautological truth because the interior angles merely stand as an axiomatic relationship of a three sided object. In other words, the 180 degree interior angle summation is implicitly contained within our evolved concept of a triangle. The tautological statement “all bachelors are unmarried men” implicitly contains concepts of ceremonial coupling, domestic partnership and binding commitment, which are states of human relationships that stand opposite to a bachelor. In other words did we actually learn about the concepts of coupling and partnership from the concept of bachelor or are they contained within the concept of a bachelor?