 If you constructed a bulletproof argument why someone should put ice cream on their apple pie, would you use a la modal logic? A while back, I made a case why philosophy should be mandatory in public schools. Of course, there are good reasons why getting fifth graders to read Kant might not be on the top of everyone's priority list. That I can understand. However, I'm absolutely mystified that some of the topics intrinsic to the study of philosophy, intrinsic to reason itself, namely logic, rigor, and critical thinking, don't have classes dedicated explicitly to them everywhere. It's true that they're tangentially referenced in many classes or even essential to them, but it's rare that they're treated as subjects of study unto themselves. We're expected to pick them up from writing persuasive essays or geometric proofs. That's kind of like expecting kids to teach themselves physics by playing kickball and PE. There's decent evidence that most adults have never actually learned or internalized these skills or simply don't know how to apply them. The Waste and Selection Task is a puzzle that requires a decent grasp of logic to complete correctly. If you're up for it, go ahead and click here. Only around 20% of people who try it get it right. At least four out of five adults just lack the skills that they need to figure it out. That's just bananas. If we want to fix that deficit, I think that we need instruction dedicated solely to teaching reasoning and expressing ideas rationally. That's hard enough on its own without requiring kids to learn long division or grammar at the same time. These next thought episodes are meant to be invitations to learn some of those skills necessary for careful, rational thought. If you're anything like I was up until my last year of college and you've never been exposed to this stuff in a formal fashion, trust me, it is just as important and life-changing as I'm trying to convey here. Man, that hair. Sometimes we believe things because we've seen or heard them ourselves. You probably believe that you're watching a thunk video right now because that's what your senses are telling you. That's easy. We also believe some things that we haven't heard or seen for ourselves. You probably believe that Mount Everest is bigger than the Squeezie toy. That isn't because you've held one up to the other and checked to see which one is bigger. It's because you've reasoned. You've used some complex rules of thought for figuring out what is or isn't true. Rules which you've been developing and changing your entire life and combining with bits of information to create these massive, intricate, interconnected webs of belief. That isn't so easy. Those rules that we've gradually cobbled together chug away behind every single debate and conversation that we have while it's easy to point out when their results are wrong. It's hard to talk about the underlying mechanisms of reasoning themselves even though they can be just as wrong. We can believe the right things for the wrong reasons. We can believe the wrong things for the wrong reasons. We can have feelings or intuitions about certain ideas that we think ought to work together but actually don't. All of these problems are mostly invisible and hard to discuss. If someone says my shoelaces look like spaghetti, therefore they must be tasty. There's no book anywhere that we can open and point to a fact that says shoelaces aren't tasty. The problem isn't just that they're wrong. The problem is that the method that they use to get from a fact to a conclusion is also wrong. The shape of their thinking isn't right and that's hard to talk about. Thankfully, there are some mental tools that we've developed to check the methods of thinking to make sure that we're getting the right answers in a way that makes sense. One of these tools is logic. Now people often use the word logical just to mean reasonable sounding. When Spock says that it's illogical for Kirk to beam down onto a dangerous planet by himself he's really just saying that that's a bad idea. However, logic is also the name of a formal, rigid system of rules for getting from one idea to another. A lot like mathematics to make sure that everything is hooked together correctly. Logic is built on two basic principles which are really just two different ways of saying the same thing. Necessity is what absolutely must be true if something else is true and contradiction is what absolutely cannot be true if something else is true. From just this, you get this. I'm not kidding when I say it's a lot like math. In formal logic, symbols like these stand for words and phrases in everyday language that have some logical significance. Just like adding or subtracting numbers, you can manipulate these symbols or the ideas they represent according to certain set rules. Rules like this one called modus tollens. If A, then always B. Not B, therefore not A. A and B are placeholders for propositions. For any propositions. That's part of what makes logic so powerful. So long as you obey the rules while you're choosing A and B, it doesn't matter what they are. This structure of thought is always valid. So long as all of its components are true, the result is true. For example, let's say A is its raining and B is its cloudy. If it's raining, then it's cloudy. It's not cloudy, therefore it's not raining. It works no matter how weird or complicated our facts get. If a vector transformation is a bijection, then that transformation is one to one. Transformation T is not one to one. Therefore, transformation T is not a bijection. Now, it's important to remember that just because the shape of a particular thought is right or wrong, doesn't necessarily mean that its conclusion is right or wrong. That depends on its content. I could make A, this pizza is delicious, and B, it has anchovies, and get a result of this pizza is not delicious. Which is clearly wrong. All logic is meant to do is to tell you when it is absolutely necessary to believe an argument's conclusion if you believe all of its parts, and, just as importantly, when it is not absolutely necessary. For example, the arrow in this logical statement only points one way for a reason. You can't say anything about the existence or non-existence of A just because you have some B. Just because it's cloudy doesn't always mean that it's raining. That distinction is subtle and easy to miss. People who don't practice thinking logically, who depend on an intuitive sense of whether or not an argument is well constructed or not, will regularly mistake something that sounds like it might be right for the real deal. That's how logical fallacies work, and why they're so dangerous. Take this example. If vaccines caused autism, then autism would develop after vaccination. Autism develops after vaccination, therefore, vaccines cause autism. Do you think any anti-vaxxers caught this? Now, logic is difficult to internalize because it works on those mechanisms of thought that are usually invisible. We're used to using them to think. We're not used to thinking about them. But learning the rules of logical necessity and how to apply them, and also how not to apply them, can allow you to evaluate really complicated ideas based solely on how they fit together, and also to make your own ideas fit together better. Passing up something that useful and that powerful would just be, you know. If you're interested in learning more about logic, there are some links in the description to get you started. And as always, please leave a comment below and let me know what you think. Thank you very much for watching. Don't forget to blah, blah, subscribe, blah, share, and don't stop thunking.