 To find out things about the world, to gather knowledge and to understand how things work, that's what it means to look for insight. A big part of this is wondering which knowledge we think we have about the world is indeed true. Let's get started asking how we can know things are true. Basically, we want to talk about verification. Verification means to establish if something, for instance, a claim, is true, accurate or real. The word comes from the Latin word veritas, which means truth. In Roman mythology, there's even a goddess called veritas. She's often depicted as either a virgin in white, referring to innocent and original truth, or as a naked woman with a mirror, which refers to the naked, unconcealed truth. Interestingly, the goddess veritas, the personified truth, is said to be quite elusive, hiding at the bottom of a well. Well, we will quickly find that the truth is indeed quite an elusive thing. So, I feel like its mythical personification is spot on in this regard. It's actually quite hard to define what is true. There are many different theories in different areas of science and art that work with the concept of truth in some way or another. Here are some examples. Correspondence theory holds that truth is whatever truly describes a thing. Therein, a concept must correspond to its real-life equivalent for it to be true. In constructivist theory, truth is seen as determined by social, historical and situational circumstances. This view suggests that we see truth through the lens of our society. Finally, pragmatic theory is more agnostic about where truth comes from and accepts as true whatever works in practice. Those are only some ideas about truth, but by far not all. We won't try to get a more detailed overview of those theory and we won't try to define what truth actually is in the world at large. That's a task we better leave to philosophers. As you can already see, it's a task that may be harder than you might think. Instead, we will take a deep dive at some basic theories that are part of the foundation of real-world investigations of truth. First, we will focus on logical positivism, a philosophical school that focused on finding truth in definitions which must necessarily be true. An example of such a definition is the definition of a sphere, a figure whose every surface point is equidistant from its center. If we define a sphere to be a figure with these attributes, it will always be true that a sphere, according to our definition, has these attributes. If it didn't have these attributes, it wouldn't be a sphere, according to our definition. Logical positivism aimed to find these kinds of verifiable true statements about the world. To get such real-world statements of truth, the idea was to use empirical investigations, that is, real-life observations. Let's say you're a mythical figure from the Brother Grimm's fairy tale, The Frog Prince. In case you are unfamiliar with the premise, The Frog Prince is turned into a beautiful human prince after he returns a princess's golden ball which she dropped into his pond. And in return, makes her take him to the castle. So, let's say you're The Frog Prince, hanging out in your pond, and suddenly an object drops into the water. You ask the princess who is standing at the shore of the pond crying in shock, what's wrong? And she tells you she needs her golden ball back. If you were a logical positivist frog prince, you are faced with a pretty tricky problem. There are many things at the bottom of the pond that are golden, and could be the thing that the princess is in tears about. You want to find her a golden ball, so now you could go ahead, get out a tape measure, and find out if various golden objects at the bottom of the pond are indeed balls, or even spheres. You would need to measure the distance of every point at their surface to the center. Now, this would be a lot of work, and we can argue about whether this is even possible to do. And of course, measuring all objects at the bottom of the lake does not really help the princess who is still waiting anxiously. But logical positivists would agree that an empirical statement such as the princess's golden ball is a sphere can be verified by measuring this very golden ball with a tape measure. Logical positivism has inspired a lot of definitions we use in science today. The idea that we define a concept by explaining what needs to be done to capture it empirically saves us a lot of nerves. For instance, in psychology, let's say we want to study happiness. What is happiness? That is another tough question, but we could create an operational definition of happiness by explaining how we would be able to empirically detect it. For instance, we could define that individual happiness is captured by a person's answer to the question, how happy are you? That's very handy, isn't it? This approach is called operationalism. Let's go back to our definition of spheres, and let's use a bit more formal logic here. We said that a sphere is a figure whose every surface point is equidistant from its center. That means for all spheres, it is true that all of their surface points are equidistant from their respective centers. Let's further say that the princess's golden ball is a sphere. From that, it must follow that all surface points of the princess's golden ball are equidistant from its center. The frog prints can go and check, but given the two premises are true, the conclusion must be true. This form of reasoning is called deduction, and now it's time for you to deduce some things too. Formulate a deductive conclusion from these two statements. All frog princes are benevolent. Arthur is a frog prince. What is the conclusion you can draw based on deduction? Have you got it? All right. Okay, so the conclusion would be that Arthur is benevolent. Here's another exercise. If we know that all ponds contain frogs, and that the body of water in the princess's garden is a pond, we can deduce what? That's right. We can deduce that the body of water in the princess's garden must contain a frog. However, do you think these premises are necessarily true? Is it necessarily true that all ponds contain frogs? There might be reasons why there are no frogs in certain ponds, for instance, because the pond was polluted with a substance that makes it impossible for frogs to live there. Immediately, it becomes clear that as soon as one premises falls, the conclusion is no longer necessarily true. So here we have maneuvered ourselves into a really tricky situation. We can only deduce conclusions if we know the premises are indeed true. Now you've made your own deductive statements. You might think deduction is not very exciting, because we already knew the true premises. So learning a conclusion from these true premises is not really telling us anything new. As you saw, when the premises are not true, however, we cannot draw a true conclusion from them. So how can we learn something new? Outside of the box of the things we already knew. For that, we need a different type of inference called induction. Induction means trying to make an inference about what's generally true or what is a universal rule from observations. For instance, let's say we observe the princess's golden ball and see that it's a sphere. We then observe her brother the princess blue ball and see it is a sphere. Next, we look at the duchess's red ball. And again, it's a sphere. We then proceed to check some more Royals' balls and find out that they're all spheres. Can we then conclude that all Royals' balls are spheres? Well, no, not really. It might be that a bear in somewhere has a soccer ball, which isn't perfectly round, or an American football ball, which is shaped more like an egg. That means this specific ball is not a sphere. This ball will then render the statement that all balls are spheres, false. The only way the statement would be true is if we indeed observed every single ball belonging to a Royal and established that these balls were indeed all spheres. A single empirical observation of a non-spherical royal ball would render our conclusion false. The philosopher David Hume argued that these types of inferences are therefore never justified. No matter how many spherical Royals' balls we observe, we can never really infer that all Royals' balls are spheres. Basically, the argument is that we can never learn anything new without induction, but we can never really rely on our inductions to capture the truth. Let's put this into practice some more. Given the observation that Freddy the frog is green, Matilda the frog is green, Bertha the frog is green and Leonard the frog is green, would it be permissible to conclude that all frogs are green? Again, no, not really. As soon as we would find out that Jose the frog is not green, the conclusion would be proven false. Let's try another example. If the princess's carriage didn't break on the first day of use, neither on the 100th day, the 150th day or the 180th day, is it permissible to conclude that the princess's carriage is unbreakable? Again, no, if it breaks on day 181, this would prove us wrong. Finally, here's the last exercise. You will see this is not actually induction, but rather the reduction again. If we know for a fact that all frogs are green and that Freddy is a frog, can we conclude that Freddy is green? Yes, given that we know for sure that all frogs are green, we can indeed draw this conclusion. But you can imagine how hard it would be to go and look at all frogs that exist anywhere in the world. More about that later. For now, let's summarize this part of the course. We have gained a glimpse at what different schools of thought define as truth and how logical positivists used logical statements to formulate true conclusions via deduction. We have also seen that induction doesn't allow us to formulate true statements. In both cases, empirical observations, seeing what's really out there in the world, are really important to determine if statements about the real world indeed true. Now that we've seen that this is tricky to find out if things are true, in the next part of the course, we will try to see if at least we can find out what things are false.