#37) Logic -- Doing It Wrong -- Part 1

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

Turn on the news, hit Twitter or Facebook, and you're bound to hear logical fallacies each and every day. We are living in a pandemic of "doing logic wrong" and it often leads to mistakes and bad decisions.

Next up in our Logic series, I'd like to explore these fallacies, so we can learn to see them, which can then help us to make better decisions, and become better people.

As we begin our journey, we're going to start with the basics. We'll start with "formal" fallacies, then later branch out to "informal" ones. And we may even take a look at some dubious or fake fallacies floating around the internet -- we'll see.

Before we continue, a quick warning. Today, I'm going to be using truth tables, gates, and symbols explained in earlier videos. So, if you feel like you're getting lost, you can check out these videos for a refresher.

For those of you deciding to go ahead, here's a very quick refresher. Remember that I like to use 0 for FALSE and 1 for TRUE. Also, we are going to be using the following gates as well: 

IF A THEN B.

	A->B
	A=0	A=1
B=0	1	0
B=1	1	1

NOT A.

NOT
A=0	A=1
1	0

Okay -- let's get down to business. 

We'll start with two ways of thinking backwards.

First is the Positive variety.

All humans have a face.	A -> B
Cuddles has a face.	B
Therefore, Cuddles is a human.	∴ A

Do you see something wrong with this? I'll tell you what's wrong. Cuddles is a cat, not a human. So what does this prove? It's bad to think backwards. If we know that all humans have a face, then having a face doesn't mean being human. Note how there's nothing wrong with the first two statements. It's only the conclusion that's faulty.

This is an easy fallacy to start us off, but believe it or not, I see this logical mistake every now and then in real life.

If we look at our A -> B gate, we can see what went wrong. Since Cuddles has a face, B is 1 for TRUE. Since Cuddles is not human, A is 0 for FALSE. And if we look across the second row for B=1, there are two valid possibilities for A, and we don't know which one it is. For Cuddles, the first statement is TRUE. But "A is 0" is a contradiction to the conclusion. The logic is bad.

	A->B
	A=0	A=1
B=0	1	0
B=1	1	1

We could also use a truth table to check the logic. The last column here tells us there's a contradiction in the second row. Cuddles' row. For time's sake, I won't explain the table, but you can take a look and see what it looks like -- pause the video if you'd like. I'll give you a few seconds.

a	b	(a -> b)	Conjecture: (b -> a)	Test: (a -> b) => (b -> a)
0	0	1	1	1
0	1	1	0	0
1	0	0	1	1
1	1	1	1	1

Let's switch this up and look at the Negative variety. I see this much more often, as it easily disguises itself as forward thinking.

All humans have a face.	A -> B
Cuddles isn't human.	~A
Therefore, Cuddles doesn't have a face.	∴ ~B

As I said before, Cuddles is a cat. So we know the conclusion here is wrong. 

I'll mark up the A->B table, throw up the truth table, and let you study it. Note that both checks show a contradiction. I'll give you a few seconds to pause the video and study if you wish.

	A->B
	A=0	A=1
B=0	1	0
B=1	1	1

a	b	(a -> b)	~a	~b	Conjecture: (~a -> ~b)	Test: (a -> b) => (~a -> ~b)
0	0	1	1	1	1	1
0	1	1	1	0	0	0
1	0	0	0	1	1	1
1	1	1	0	0	1	1

But wait? Weren't we thinking forwards in this example? Not really. In an earlier video I showed how negatives flip things around. Check this out:

All humans have a face.	A -> B
Stringy doesn't have a face.	~B
Therefore, Stringy isn't human.	∴ ~A

In this case, Stringy is my pet piece of string, which you may guess does not have a face. It also happens not to be human. 

Let's look at the A->B gate and the truth table.

	A->B
	A=0	A=1
B=0	1	0
B=1	1	1

a	b	(a -> b)	~a	~b	Conjecture: (~b -> ~a)	Test: (a -> b) => (~b -> ~a)
0	0	1	1	1	1	1
0	1	1	1	0	1	1
1	0	0	0	1	0	1
1	1	1	0	0	1	1

There are now no contradictions.

So, this type is not a fallacy. This happens to be correct "forward" thinking. The negative just flips things around. I'll give you a few seconds to pause the video and think about what this means until it makes sense.

In general, we can use these truth tables to test all kinds of "formal" fallacies. There are countless combinations to try. But for today, I'll just show four more popular ones. However, I'm going to skip the truth tables, because they can get complicated with these. As I fly through these, don't be afraid to pause at any moment to think things out.

Next up: Negative From Positive

All humans have a face.	B -> C
Some animals are human.	Some A -> B
Therefore, some animals do not have a face.	∴ Some A -> ~C

I believe the idea here is that if you say "some animals are human" then it's possible that some animals are not human. And since those animals are hot human, they don't have a face. But then you may recognize this is kind of a mixed up variant of Negative Thinking Backwards. ~B does not imply ~C.

In general, the rule is: if all your assumptions and observations are positive, you can't really derive a negative outcome.

If we flip this, we get: Positive From Negative

Yarn does not have a face.	B -> ~C
Some cords are not yarn.	Some A -> ~B
Therefore, some cords have a face.	∴ Some A -> C

This logic assumes that if some cords are not yarn, then some of these cords (not being yarn) must have a face. In some cases this could be true, but not this time. We know that all cords: yarn, string, rope do not have faces. So, clearly this logic is unreliable.

In general: if all your facts are negative, you can't really derive a positive outcome.

Next up: Illicit Minor

All humans have a face.	A -> B
All humans have two legs.	A -> C
Therefore, all things with a face have two legs.	∴ B -> C

This is where two or more things are true about some subject (humans). Then it would be wrong to remove the subject and make inferences from the minor clauses (faces and legs).

And finally: Illicit Major

All humans have a face.	B -> C
No watches are human.	~A -> B
Therefore, no watches have a face.	∴ ~A -> C

This one's a little tougher, but we know this one is wrong. Though, a first glance at the symbols looks right. ~A implies B. And B implies C. So, ~A should imply C. And if you filled out a truth table, it would probably tell you the same thing.

But that's only because I translated the symbols incorrectly. I did this on purpose to show how easy it is to make these kinds of mistakes. And yes -- it's the negative messing us up again. Watch what happens if we rewrite the last two sentences. Pause the video and double-check that the sentences are saying the same thing. And then we can fix the symbols.

All humans have a face.	B -> C
All watches are not human.	A -> ~B
Therefore, all watches do not have a face.	∴ A -> ~C

Then we can see the logic fails -- A does imply ~B, but ~B does not imply ~C. It turns into another Negative Backwards Thinking fallacy.

Now that we've gone over several popular "formal" fallacies, you can keep an eye out this next week and identify the ones you can find in real life -- what people say, or what's on the internet.

Later on we'll attack some of the "informal" fallacies.

If you like what you've seen, then do me a favor. Give me a Like and push that Subscribe button. Next week we'll analyze belief systems.

Thank you for watching, and I'll see you next time, here on "Always Be Better."