The big question of this segment is can we ever know the truth and in what way can logic help us sort out problems and make the right decisions? [MUSIC] How do we come to know the truth about the world, how do we decide what to believe? Making the right decisions about what to accept is a matter of reasoning well. We reason whenever we draw a conclusion from a set of claims or premises or evaluation argument to decide whether to accept what were being told. Logic is a study of good reasoning. When philosophist talk about logic, often what they're referring to is what's called formal or symbolic logic. When we do a formal logic, we represent arguments and claims using symbols to make the structure of the reasoning clearer. This can look a bit mysterious at first and in fact the symbols are just there to make things easier. Think of how symbols are used in mathematics. If you wanted to work out how many days within 47 weeks for example, it might be quite difficult to do that in your head, without having any way to represent problems symbolically. Once we've represented the problem using numerals, now arithmetic symbols, we can use a simple algorithm to work out the answer. Formal logic works the same way. We represent a piece of reasoning using symbols that allows to make the structure clear. We can then use logical rules to determine whether an argument is logically good or valid or whether one claim foolish for another. Logic doesn't have to be done formally though. Whenever we examine a piece of reasoning, or evaluate the strength from an argument, we're doing a kind of informal logic. The study of logic in the formal or informal can help us to reason better by encouraging us to focus on when a phase of reasoning is strong, or weak. And what kinds of conclusion we can draw off from our distinct [INAUDIBLE] evidence? If we're thinking about how logic allows us to come to understand the truth about the world, there's a distinction that's more significant than the distinction between formal and informal logic, and that's the distinction between deduction and induction. Deductive reasoning is the kind of reasoning most commonly studied in formal logic and it has close analogies with the kind of reasoning in mathematics. What's distinctive about deductive reasoning is that it gives us certainty in a sense that if an argument is deductively valid then if it's premises are true it conclusion must be true as well. Consider the following argument, all feathered animals are warm-blooded. This animal has feathers, therefore this animal is warm-blooded. This argument is deductively valid. If its premises are true, its conclusion must be true as well. The truth of its premises would guarantee the truth of its conclusion. Now consider this argument. Every feathered animal we have ever observed has been warm blooded. Therefore all feathered animals are warm blooded. Does this argument guarantee its conclusion? This argument is a piece of inductive reasoning. It's premise is supposed to show that the conclusion is probable, and we'd be justified in accepting it. But it's not guaranteed. There might just be some kind of feathered cold-blooded animal that we haven't observed yet. Inductive arguments aren't just valid or invalid. That can be stronger or weaker depending on how much evidence they provide for their conclusion. For example, the more and more varied feather animals we've found to be warm blooded in the past, the better support we have our conclusion. But it's always possible that our conclusion will need to be revised in the light of new evidence. Even the best inductive arguments make what's sometimes called an inductive leap. Going beyond the information contained in the premises to some new claim about the world. It's because the conclusion goes beyond the information in the premises that inductive arguments can't give a certainty. So, deductive arguments give a certainty in a way that inductive arguments don't. This is when we should always use deductive reasoning to come to know the truth about the world. There are two related problems with that proposal. Firstly in practice, inductive and deductive reasoning go together. Think back to the deductive argument we considered earlier. All feathered animals are warm-blooded. This animal has feathers. Therefore, this animal is warm-blooded. Because it's deductively valid, we know that if the premises are true, the conclusion must be true as well. But how do we know if the premises are true? In particular, how do we know if the first premise is true? The way we get that kind of information about the world is through inductive reasoning. If we believe that all feathered animals are warm-blooded, it's because we've observed a lot of feathered animals that have all been warm-blooded. But we haven't experienced them all. So our evidence for the first premise is inductive evidence. The second related reason that we need to use inductive as well as deductive reasoning, is that it's the only way we can come to make new discoveries about the world. Deductive arguments make use of information we already have. And while they allow us to draw out conclusions that might not otherwise have been explicit, they don't allow us to conclude anything new. To make discoveries about the world, to make progress, we need to use inductive reasoning and be prepared to make those inductive leaps. The importance of logic, whether formal or informal, is that it encourages us to think carefully about the kind of reasoning we're employing and the kind of justification that gives us in our conclusions. It's important to remember that inductive reasoning is an essential part of our reasoning in science and in everyday context. It's how we come to derive new knowledge about the world. But inductive reasoning is not certain. And our conclusions are fallible. Our goal is to ensure that our conclusions are as well supported as possible. But we need also to be aware that our conclusions are subject to revision in the light of new evidence. And it's by drawing new conclusions and testing them that progress will be made. [MUSIC]