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 # Logic in Education
-The term "critical thinking" gets thrown around a lot in schools, but children aren't ever sat down and explicitly told how to think. Logic needs to be introduced in primary school and reaffirmed throughout middle and high school (secondary school in the UK). Knowing how to think logically is far more important than knowing how to calculate the area of a circle, how volcanoes work, or how to use a bunsen burner. And teaching it shouldn't be politically controversial because there's an important distinction between telling kids what to think versus teaching them how to think. Logic is all about how to think. That's something we all should want others to know how to do well.
+The term "critical thinking" gets thrown around a lot in schools, but children aren't ever sat down and explicitly told how to think. Logic needs to be introduced in primary school and reaffirmed throughout middle and high school (secondary school in the UK). Knowing how to think logically is far more important than knowing how to calculate the area of a circle, how volcanoes work, or how to use a Bunsen burner. And teaching it shouldn't be politically controversial because there's an important distinction between telling kids what to think versus teaching them how to think. Logic is all about how to think. That's something we all should want others to know how to do well.
 
 The point of teaching the formal, symbolic logic starting at a young age is not so kids, teens and young adults become good at truth tables. The point is they'll internalize logic like any other concept. The pattern recognition part of their brain will automatically recognize valid arguments when they see them. It will also recognize invalid forms of argument and logical fallacies without consciously doing any heavy lifting. That's where the most value is in teaching logic.
 
-When I studied philosophy in community college, I remember there was an art student. He had a great personality and was a very likeable person. Whenever he got called on to answer a question though, he was never able to produce the right answer. It was clear to me that he never learned how to think logically. I wondered what it must be like to be a young adult never having learned that. There are also plenty of functioning older adults out there that never learned how to think logically. To be clear, studying formal logic isn't a prerequisite for logical thought. What I find to be the case with nearly everyone without training in formal logic is that they have an intuitive sense of how to reason, but there's important pieces of the puzzle they're missing. That's what I'm going to focus on in this post, the things that those without experience in formal logic get confused about. In my posts, I try not to assume prior knowledge, so I'm going to explain a bit about logic before I explain some of those missing pieces. If you're already familiar with logic, click here.
+When I studied philosophy in community college, I remember there was an art student. He had a great personality and was a very likable person. Whenever he got called on to answer a question though, he was never able to produce the right answer. It was clear to me that he never learned how to think logically. I wondered what it must be like to be a young adult never having learned that. There are also plenty of functioning older adults out there that never learned how to think logically. To be clear, studying formal logic isn't a prerequisite for logical thought. What I find to be the case with nearly everyone without training in formal logic is that they have an intuitive sense of how to reason, but there's important pieces of the puzzle they're missing. That's what I'm going to focus on in this post, the things that those without experience in formal logic get confused about. In my posts, I try not to assume prior knowledge, so I'm going to explain a bit about logic before I explain some of those missing pieces. If you're already familiar with logic, click here.
 
 # Logic
 Logic is the study of rules of inference[1]. Rules of inference allow you to draw conclusions based on premises. In other words, starting with a statement A, you can conclude statement B. For example, the earth is round is a true statement. Therefore the earth is round or up is down is also a true statement. In fact, I could replace the statement up is down with any proposition Z and the earth is round or Z would still be true. I used the rule of inference "addition" to draw my conclusion, so I'm guaranteed that it's true no matter what Z is. I can apply another rule of inference to get humans have 3 legs therefore either the earth is round or up is down. That is also a true statement. It sounds strange because the normal way of understanding "therefore" is as a causal relationship. In this context, it's a strictly logical implication, not causal. Despite how strange it sounds, humans have 3 legs therefore either the earth is round or up is down logically follows from the earth is round.
@@ -22,7 +22,7 @@ Now that I've talked about what logic is, I want to talk about some of the impor
 The first way to disprove an argument is by showing that one of the premises is false. The other way is showing that the structure of the argument is invalid[4]. People are used to thinking of arguments in terms of "arguments for" and "arguments against". That's why it's easy to get confused here. It's the attitude "There's some good arguments for a proposition and some good arguments against it and it's my job to weigh the pros and cons". But, in logic, an argument is either sound or unsound. The property of soundness[5] means that the premises are true and it has valid form. If the conclusion of an argument derives from valid rules of inference based on the premises, then the only way to disprove the argument is to show one of the premises is false. If all the premises are true and the form is valid, then the argument is sound and the conclusion is true. There's no "arguments for" and "arguments against", or "maybe it's wrong some other way". There's no two ways about it. No if, ands or buts. If an argument is sound, the conclusion necessarily follows.
 
 ## How Logical Fallacies Work
-A logical fallacy is an error in reasoning. It can be formal[6] or informal[7]. Formal fallacies have to do with the structure of an argument. If an argument has bad structure, it is invalid. Informal fallacies have to do with the content of an argument. In my experience, it's more rare for people to commit formal fallacies. This is because there are so many more ways to commit informal fallacies than there are ways to commit formal fallacies. There are only a few ways to structure an argument improperly, but there are virtually endless ways to get the content wrong since the content can be anything at all. Take a look at yourlogicalfallacyis.com[8]. It's good to become familiar with informal fallacies by name and be able to call them out in realtime. To challenge yourself, try doing that during a live presidential debate. There's so many logical fallacies in those it's impossible to keep up, at least for me.
+A logical fallacy is an error in reasoning. It can be formal[6] or informal[7]. Formal fallacies have to do with the structure of an argument. If an argument has bad structure, it is invalid. Informal fallacies have to do with the content of an argument. In my experience, it's more rare for people to commit formal fallacies. This is because there are so many more ways to commit informal fallacies than there are ways to commit formal fallacies. There are only a few ways to structure an argument improperly, but there are virtually endless ways to get the content wrong since the content can be anything at all. Take a look at yourlogicalfallacyis.com[8]. It's good to become familiar with informal fallacies by name and be able to call them out in real time. To challenge yourself, try doing that during a live presidential debate. There's so many logical fallacies in those it's impossible to keep up, at least for me.
 
 The thing people get confused about when they're unfamiliar with logical fallacies is they think fallacies are a minor problem for an argument, similar to the "arguments for" and "arguments against" I talked about earlier. They see the fallacy as the "argument against" part. That's completely the wrong way to think about logical fallacies. The presence of a single logical fallacy in an argument means that argument is toast. A logical fallacy is not a "counterpoint" to an argument. It fully invalidates the argument. An entirely new argument is needed to prove the conclusion.
 
@@ -56,7 +56,7 @@ This one is the most widely-known. It simply means that many people believe some
 The genetic fallacy is whenever someone says something is good or true because it comes from a certain source. We can look at the media for example. While it is certainly true that some news sources are more reliable than others, the truth of an argument doesn't change depending on which news source makes it. This doesn't diminish the importance of having reliable sources of news. As a personal example, when Nick Bostrom[22] releases a new paper, I make an educated guess that I'll find it interesting based on his previous work being interesting. But the new paper that I read won't be interesting because all his previous work is. It will be interesting because of the contents of the paper. If you pick good sources of information, then that's actually not a bad heuristic for truth. You will only end up with a bad heuristic for truth if you pick bad sources of information, such as Facecrook. Just remember that the source of information has no bearing on the truth of the information. I'm really beating this point to death, but it bears repeating. The only determining factors for the soundness of an argument are the truth of the premises and the validity of the argument.
 
 ### Nature
-The appeal to nature fallacy happens when someone says something is good, just or ideal because it's "natural". Two problems with that. For one, everything that happens is natural because we live in the natural world. But let's entertain the fallacy for a moment and define "natural" as things that aren't products of human intelligence. By that definition, coronavirus is natural. Natural disasters are natural. It's even in the name. Lots of horrible things are natural. "Unnaturalness" is often used to argue against homosexuality. Other species of primate also show homosexual behavior, so homosexuality is natural even in non-human animals. To sum up, appealing to nature is a bad heuristic since it's hard to define what counts as natural and many natural things everyone agrees are natural are not good, while things people call "artificial", such as vaccines, are good.
+The appeal to nature fallacy happens when someone says something is good, just or ideal because it's "natural". Two problems with that. For one, everything that happens is natural because we live in the natural world. But let's entertain the fallacy for a moment and define "natural" as things that aren't products of human intelligence. By that definition, Coronavirus is natural. Natural disasters are natural. It's even in the name. Lots of horrible things are natural. "Unnaturalness" is often used to argue against homosexuality. Other species of primate also show homosexual behavior, so homosexuality is natural even in non-human animals. To sum up, appealing to nature is a bad heuristic since it's hard to define what counts as natural and many natural things everyone agrees are natural are not good, while things people call "artificial", such as vaccines, are good.
 
 ### Middle Ground
 Taking the "middle ground" position between two extremes is probably an even poorer heuristic for truth than the bandwagon. People think taking the middle ground means they're unbiased. They think having an "extreme" position means you are heavily biased. They perceive the middle ground as "balanced" and fair. But how do you go about deciding where the extremes are? Popular opinion? If that's the case, then we're back at the bandwagon fallacy. If you have some other way of determining the extremes, then what is it exactly? What if the middle ground is ambiguous?