#9) Logic: Introduction

Hello, and welcome back to "Always Be Better" with Mel Windham.

After so many introductions, this week I'm actually going to teach something -- an introduction to classical logic. Hmmm ... wait ... does this make this another introduction?

Well, let's go ahead and dive in.

We'll start with a simple statement.

If Sam is human, he has a face.

That makes sense, right? Can you think of a human who doesn't have a face? In classical logic, statements can be assigned a value of True or False. We can look at this statement and determine that this particular one is True. Let's add another statement.

Sam is human.

This is a simpler statement. You can probably look at Sam and tell if this statement is True or False. For now, let's say that we've examined Sam and have determined that he is indeed human. So, now we're up to two True statements. With the information given to you, can you think of another third statement that automatically follows from these two statements? You can pause the video to think about this before the answer comes in five seconds.

It should seem natural to conclude this:

Therefore, Sam has a face.

Now, let me show you another way to write these statements. Instead of saying "Sam is human," I can write simply "A." In other words, "A" means "Sam is human." And let's say that "B" means "Sam has a face." Then I can use an arrow to show the IF THEN, like this. If A then B. And then we can use these cute little three dots for THEREFORE, and we've completed the symbolic representation.

A -> B

A

∴ B

With the simplified version on the right, it may be easier to follow the logic. When we write statements as symbols like this, we assume that we've already determined that they're true. "IF A THEN B" is given as True. And we know that "A" is True. When we combine the two statements, the third one follows naturally, so "B" is also True.

Please take a few seconds -- as long as you like to study the statements on the left and their simplifications on the right, and notice the simplicity. I'll continue in five seconds.

When reduced to its basic components, logic is actually one of the simplest things to understand. So easy that I could understand full blown classical logic at the young age of 4. And I've taught these same lessons to my children, which were well received.

Even non-thinking computers can fully "comprehend" logic. To them it's literally all 1's and 0's. A 1 (the existence of a current) represents True, and 0 (the absence of a current) represents False. So, instead of saying True and False, I find it easier, myself, to use 1's and 0's. You see this more in later videos.

So some of you may be wondering: if logic is so easy, why do we humans seem to struggle with it? The answer is two-fold. Many humans aren't taught the simple rules of logic -- which I believe any of us can learn. And even with a good handle on logic, further difficulties can arise when we attempt to apply that logic to complex human concepts. But we'll get there. For right now -- we're going to stick with the basics.

Now back to our system, let's switch things up. What if Sam does not have a face? What can you deduce about Sam? This one is a bit trickier, but I'll tell you the answer in five seconds. Pause the video for as long as you'd like.

If Sam is human, he has a face.

Sam does not have a face.

Therefore, Sam is not human.

Okay, if you figured it out, you saw that this one requires thinking backwards. You should be able to deduce that Sam is not human. By the way, if you came up with other answers, feel free to share them in the comments -- I'd like to hear what else you came up with.

Now, let's add the symbols. From before, B meant "Sam has a face." This is now False. So, to make it true, we can apply a tilde in front of it to mean "NOT." So, our second statement can be read as "NOT B." And therefore we have concluded that the NOT of A is also True.

A -> B

~B

∴ ~A

Some things to consider for later. What if Sam is a cat? What if Sam is a clock? Or what if Sam is a stapler? We'll talk more about this in later lessons, but you can go ahead and get your brain thinking about these things.

Now, let's go back to the original system, but this time let's change the words.

If dark clouds are approaching, it will probably rain.

Dark clouds are approaching.

Therefore, it will probably rain.

I've intentionally added some ambiguous words to make these statements True. You've probably seen instances of dark clouds approaching and no rain occurs, but most of the time, it does rain. So, the word "probably" makes the first statement True.

Before I finish, let me show you something. Let's say we wanted to write a program to predict the rain using our system here. We could write this simple BASIC program.

INPUT "Are dark clouds approaching? (Y/N)" A

IF A = "Y" THEN PRINT "It will probably rain."

ELSE PRINT "It might not rain."

The first line of code asks the user, "Are dark clouds approaching?" And the user can answer "yes" or "no." In the second line, the computer looks to see if the answer is "yes." If it does, it reports, "It will probably rain." And the third line is a catch-all. If the user doesn't answer "yes" then the computer reports, "It might not rain." 

And now think about this: when this program runs, what does the computer think? Does it have any idea what dark clouds are? Do you think it understands rain? Probably not. The only thing it cares about is what letter the user types on the keyboard. And this is very important.

Once you reduce logical arguments into their principle components, they become simple abstract constructs which you can then analyze completely devoid of bias and/or emotions. This can become a very important tool in many situations -- when used correctly.

If a human being (someone with a face) were to see dark clouds approaching, he may say, "I don't think it's going to rain," because perhaps they planned an outdoor function, or maybe they just hate rain. In other words, a human may be likely to let their desires and needs corrupt the logical process.

I'm not saying emotions and humanity are bad, but eventually we're going to learn how to identify this kind of bias and learn how to handle or adjust for it. But first, we're going to need to learn more basic principles.

I hope you enjoyed this quick introduction, and we'll continue on in April. Logic is just one of several tracks I'll be starting soon, all of which will need to be watched in order. I'll explain more later.

Over this next week, I'd like you to look around. Listen to what people say, and try to recognize some of these logical concepts. Can you take what you hear and break it down into simpler logical components? Perhaps you can even begin to see mistakes in logic -- there are plenty of examples surrounding us every day. We'll learn more tools later to help, but in the meantime, you can figure out some of these basic concepts on your own.

Thanks for watching, and remember. We can "Always Be Better."