Kant famously claims that we have synthetic apriori knowledge. Indeed, this claim is absolutely central to all of his philosophy. But what is synthetic aprioriknowledge? 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.
Speaker: Dr. Scott Edgar, Associate Professor, Saint Mary's University.
Speaker: Dr. Scott Edgar, Associate Professor, Saint Mary's University.
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- Two (probably irrelevant) questions that might illuminate Kant's reasoning.
Was Kant ever exposed to a number system that was not base 10?
Could not the definition of a triangle include the angles adding to 180 degrees?(10 votes)
- I don't think your questions are irrelevant at all. I don't know if he was exposed to other number systems, which may have been after his time. As to the definition of a triangle, if you define it as having angles adding to 180 degrees, you are restricting your geometry to Euclidean Geometry. Other geometries define or can derive triangles with angles adding to greater or lesser than 180 degees. See:
- I think the example at7:40is throwing me off. Disregarding the measurement system of degrees and looking only at what it is measuring, isn't it possible for me to see that the combined angles of a triangle always add up to a straight line, or a half circle, or however one wants to say it? It could easily be demonstrated with a pair of scissors, cutting out the angles and arranging them next to each other.(3 votes)
- Aren't math and geometry bad examples for Kant's reasoning on a priori knowledge? At2:30, Dr. Edgar defines "[a priori knowledge is] knowledge that isn't justified by appeal to the senses", and at3:00, Dr. Edgar says that "you don't have to do any experiments to confirm, for example, that 7+5=12". Also, at7:45, the example "piece of mathematical knowledge" is the sum of triangle angles is 180 degrees. Yet these mathematical and geometric pieces of knowledge ARE justified by or rely on the senses, in that you MUST communicate by senses to another that you are using the Base 10 number system to justify that 7+5=12, and not 7+5=13 (which is true in Base 9), or that 7 has fundamental assumptions and 5 has fundamental assumptions and addition has fundamental assumptions which do NOT apply to clouds, since 7 clouds and 5 clouds may combine into 1 cloud, not 12 clouds. As to the 180 degree angle sum, you MUST communicate by senses to another that you are using or relying on Euclidean Geometry, and you are NOT using non-Euclidean Geometry in which angle sums of triangles may be greater or less than 180 degrees. To me, since communication with others is necessary to lay out your assumptions, math and geometry do indeed appeal to the senses, and so cannot be a priori knowledge. In fact, experiments have been done to test whether our universe is Euclidean or non-Euclidean, since you cannot assume, like Kant, that it is Euclidean = flat (reality: our universe does seem to be flat = Euclidean, within experimental error, see: http://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe). Regarding non-Euclidean Geometry, see: http://en.wikipedia.org/wiki/Non-Euclidean_geometry(2 votes)
- We do not need to communicate to others in order to have mathematical knowledge. I know that "7+5=12" even if there is nobody I could communicate with.(4 votes)
- Could this video help save philosophy by showing to anti philosophy types that hey we need philosophers to deal with this a priori stuff.(2 votes)
- When a knowledge cannot be justified by senses how can one consider such knowledge to be analytic or apriori. so one must analyse it before giving to the senses?
But the synthetic knowledge falls directly to the sense and does not need any analysis?(1 vote)
- Why can't the definition of a triangle include the concept of "any shape whose interior angles equal one hundred eighty degrees"?(1 vote)
- Would the ampliative knowledge of yesterday not be the a priori knowledge of tomorrow? I would understand ampliative knowledge as additional understanding of the properties of a triangle, adding more information to the necessary conditions of being a sufficient triangle.(1 vote)
- Ampliative knowledge is any knowledge that is not contained within the definition. It is knowledge that increases our understanding beyond the definition. The definition does not change with the day, though. The definition remains constant. So, any knowledge that was not contained within the definition yesterday will still be synthetic tomorrow.(1 vote)
- Wouldn't all knowledge at some point be grounded in empirical knowledge? 7+5 is a statement that can lead us to the answer 12 because of our notions of what '7' and '5' mean but somewhere along the line humans had to discover through synthetic judgement that when you take a certain amount of objects and another amount that you get a greater sum. So it would seem to me that all knowledge would have to be somewhat grounded in experience or empirical knowledge even though today we may be able to describe them with a priori type statements. Please correct me if I'm wrong!(1 vote)
- I think the important distinction here is whether some sorts of knowledge are justified by relevant experiences and others not. For instance, it is possible in principle for someone to have the time, the interest, and the teacher, to learn everything she needs to know about the properties of circles in a single lesson, using only one circle. Obviously, whatever she knows about circles has come through experience (she had to learn it, and did so presumably by hearing what her teacher had to say, drawing the single diagram of that particular circles, and so on). But, it is possible that, from this single lesson, she knows everything there is to know about circles, i.e., she could anticipate every property of every circle anyone could imagine. In this case, her knowledge about those other circles, i.e., every other imaginable circle except the one she learned with, is a priori, because she doesn't need to have any experience of them in order to be justified in making the claims she would about them, and because we can rest assured that her claims would be true, then we can say that she knows everything that can be known about them.
By contrast, if this same person were to learn that a baby panda, Bao Bao, was born at the National Zoo in Washington, and learned everything she could about the birth, even down to the genomic level, she wouldn't be equipped to know everything there is to know about every situation of every panda anyone could possibly imagine. The reason, of course, is that the sort of knowledge regarding future and possible pandas is contingent upon any number of things that can only be learned by experience. In this way, knowledge of this sort of a posteriori, because it is justified only once someone has had the relevant experience, i.e., experiences of this or that panda in this or than circumstance, location, situation, and so on.
I am not sure that this helps, but I hope it does!(1 vote)
- I really think that this subject is very interesting it grabs my attention inmediately but I have a question guys Which between a priori and synthetical knowledge do you think is essential for learning?(1 vote)
I don't fully understand one point made in the lesson so I hope someone here can help me understand this. How can the fact "a triangle's interior angles total to 180 degrees." be synthetic, because from my understanding of this the mathematical reasoning used to reach this conclusion is analytic. This is because I would argue that the definition of a triangle indirectly implies that it's interior angles necessarily sum to 180 degrees.(1 vote)
(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