Induction, Abduction, Deduction

"Err... don't you mean 'theory?'" Zac asked. "Aren't you just another crackpot who has come up with some grand scientific theory to explain how reality works?"

"No," I chuckled. "This isn't a theory. It's more like a theorem."

"Aren't they the same thing?"

"No."

"What's the difference?"

"I'm using deduction, not induction."

"Huh?" Zac looked confused.

"Okay," I sighed, "this is actually quite important, so let me explain. What do you think science is?"

"Science is how humans find the objective truth," Zac answered. "Scientists form hypotheses, and then test those hypotheses by running experiments."

I nodded in agreement. "Okay, so science is a process. You form a hypothesis, collect data, and then compare the data to your hypothesis. If the data disagrees with your hypothesis, then your hypothesis is wrong.

This scientific process generally uses inductive reasoning. Induction involves figuring out the general rule of something by studying a sample of it. You start specific, then generalize. For example, let's say I'm living in England a few hundred years ago. Everywhere I go, I observe white swans. I then form a hypothesis: 'All swans are white.' This is a sweeping generalization. I've taken a specific observation about the world and then extrapolated a general statement to describe the data I have observed. Make sense?"

Zac nodded. "One problem, though..."

"What's that?"

"All swans are not white. We have black swans in Australia."

"Exactly," I said. "That brings me to my next point. Induction is never certain. Inductive reasoning can only give you a probability of something being true. For example, you could be living in England and running experiments that involve the observation of swans. Every swan you observe is white, so your rule, 'all swans are white,' is the accepted theory to explain this observation. Your theory is supported by evidence.

However, your theory is never certain. You could observe millions of white swans, and it's always still possible that there is a non-white swan out there in the world somewhere that would render your theory wrong. That's why sound science relies on falsification — the ability to prove your theory wrong, not right. As soon as I observe one non-white swan, my theory is incorrect."

"Yeah, I get it," Zac said. "If your theory states that all swans are white, then you just need to observe one swan that isn't white to prove your theory false."

"Correct."

"So," Zac continued, "can you falsify your first principle?"

"You mean, can I falsify the statement 'I think, therefore I am?'"

Zac nodded.

"Well, yeah," I replied. "I know with 100 percent certainty that statement is true because the very act of me doubting and questioning that statement means I am thinking, and therefore I exist. To prove that statement false, I would need not to have any thought at all. Since I do think, I do exist.

I don't know anything beyond that, though. It's a leap of faith to say there is a world 'out there,' separate to myself. If I lock myself in a bunker at the center of the earth for a week, did the sun rise every morning when I wasn't observing it? Maybe, maybe not. Like I mentioned earlier, for all I know, I currently exist in a computer game, or a dream, or the Matrix. But I do 100 percent know that I exist as some kind of conscious entity. Because I know that statement is true, I am happy to accept it as an axiom."

Zac cradled his head in his hands. "Argh! There are too many terms. Induction, falsification, theorem, axiom-"

"Sorry. I'll try another approach that might make things clearer. Hold on... I need some paper to explain this."

I grabbed Zac's backpack and rummaged through its contents, eventually retrieving a bent notebook and a pen. After flipping through pages of Zac's messy diagrams and designs and inventions and ideas, I found a blank spot to use.

"Can I draw on this?" I asked.

"Sure."

I began scribbling. "Every logical argument can be broken down into three parts: the rule, the cause, and the effect. Mathematics is the purest form of logic, so I'll explain this concept using basic math. Here is an example of a simple equation broken into its logical components..."

The argument: 7 + 8 = 15
The rule: x + y
The cause(s): x = 7, y = 8
The effect: 15

"The cause and effect are specific numbers. The rule describes, in general terms, how to transform the cause into the effect. Does that make sense?"

Zac nodded.

"Good. Now I want to show you the difference between induction and deduction. Let's say someone gives you these two pieces of a logical puzzle: the cause and the effect."

The cause(s): x = 2, y = 2
The effect: 4

"You only have one specific data point at the moment. You know that somehow 2 and 2 produce 4, but you aren't sure what the general rule is. You now have to use induction to figure that out. You look at the cause, then you look at the effect, and you guess the general rule that transforms the cause into the effect. So, what do you think the rule is?"

"It's the same as before," Zac said with an air of confidence. "You just add the numbers together. 2 plus 2 equals 4."

"Are you sure about that?"

He hesitated. "I guess you could also multiply the numbers together. 2 multiplied by 2 equals 4."

"Yes," I agreed. "You could also say 2 to the power of 2 equals 4."

"Oh yeah..." Zac took the notebook from my hands and scribbled down the three hypotheses.

Hypothesis #1: x + y
Hypothesis #2: xy
Hypothesis #3: xy

"Do you see how induction doesn't give us certainty?" I asked. "There could be multiple rules that accurately describe the cause and effect."

"So how do we figure out which rule is correct?"

"Well, once we have a hypothesis — a potential rule — we can collect more data. If the data doesn't match the rule, the rule is wrong. There are no ifs or buts about it. So let's say the next dataset we observe is this..."

The cause(s): x = 5, y = 3
The effect: 116

"We can run that data through our potential rules and see which one it fits." I started scribbling on the notebook again.

Hypothesis #1: 5 + 3 = 8
Hypothesis #2: 5 x 3 = 15
Hypothesis #3: 53 = 125

I then proceeded to cross them all out.

Hypothesis #1: 5 + 3 = 8
Hypothesis #2: 5 x 3 = 15
Hypothesis #3: 53 = 125

"They're all wrong," Zac said, puzzled.

"Yep," I confirmed. "All of those rules are wrong. No rule produced 116."

"Hmmm..." he mused. "So where to now? How do we figure it out?"

"We go back to the drawing board. Since none of those rules are correct, we need to use induction again to come up with a new hypothesis. What about this one..."

The new hypothesis: x3 - y2

Apply first data set: 23 - 22 = 4
Apply second data set: 53 - 32 = 116

"Ohhh..." Zac said. "You cube the first number and then subtract the squared second number."

"Exactly," I replied. "That general rule fits both datasets, so it is a valid hypothesis at the moment. However, there is still the possibility that we are wrong. To increase our confidence in our hypothesis, we should collect many more datasets and make sure our rule matches all of them. If there is one case where our rule doesn't match, our hypothesis is wrong and we'll have to go back to the drawing board.

This is how science works. Scientists are making observations about the world and collecting data, then using induction to hypothesize a general rule to describe that data. The general rule needs to be able to make accurate, repeatable predictions. The predictions part is where deduction comes into play."

"You haven't told me what deduction is yet," Zac said.

"I know. I'll do that now. I'll show you induction, then abduction, then deduction. Remember our three parts of a logical argument? The rule, cause, and effect?"

Zac nodded, and I continued. "If we know the cause and the effect, we use induction to guess the rule. I just demonstrated that process with our maths equation.

If we know the rule and the effect, we use abduction to find the cause. For example, a doctor uses abduction to diagnose you with a disease or ailment. She observes your symptoms and then checks them against a list of  rules that describe which diseases produce which symptoms. The disease is the cause, and the symptoms are the effect. Of course, multiple diseases can share the same symptoms, which is why misdiagnosis happens. Like induction, abduction also doesn't give us certainty that we are right.

Finally, we come to deduction. Deduction is the only form of logical reasoning that gives us absolute certainty in our conclusion. We use deduction when we know the cause and the rule, and want to find the effect.

A simple example is, of course, a maths equation. When I solve 1 + 1 = 2, I am using deduction. I know the rule and the cause, so I can calculate the effect, 2, with perfect certainty. As long as the rule is true, the effect must be true.

We can also represent a deductive argument with a set of premises, like this..."

Premise 1: All men are mortal.
Premise 2: Socrates is a man.
Conclusion: Socrates is mortal.

"If all men are mortal, and Socrates is a man, then Socrates is definitely mortal. As long as the premises are true, the conclusion is necessarily true as well.

This brings me to the difference between a theory and a theorem. The scientific method is an inductive process that produces theories. Scientists observe the world and find the sets of rules, or theories, that best explain the world. There is always the possibility that the theory is wrong because induction will never give us certainty.

On the other hand, mathematics — the purest form of logic — uses deduction to produce theorems. A theorem is a statement that has been proved true using a rigorous proof."

"Were the last few hours of me listening to you ramble supposed to be a rigorous proof?" Zac asked.

"Yep. A rigorous proof is a sound deductive argument that starts with statements that we know are true, and then makes small logical steps, each one building on the previous ones, until it reaches a conclusion. If we start with statements we know are true, it is impossible for the conclusion to be false. That's what I'm doing with this proof. I'm going to place your mind in a logical straight jacket so you'll have no choice but to accept the counter-intuitive conclusion at the end. There is no way around it. You can't escape."

"That sounds a bit psychopathic," Zac said. "What if I don't want my mind locked in a straightjacket?"

"Zachary," I sighed. "Like many things in life, it's a paradox. You see, right now your mind is so free that you can believe anything you want. And that's why your mind is in a prison. You think you're free, but you're not. It's an illusion. You're just absorbing the beliefs of authority figures who've told you what to believe: your teachers, mentors, parents, scientists, politicians, the media. Of course, I'm not saying that all the beliefs you've picked up are bad or wrong, per se, but I am saying it's delusional to think you're free. Carl Jung was right — until you make the unconscious, conscious, it will direct your life, and you will call it fate.

So there's the paradox. To truly free your mind — to see the world the way it really is — you have to constrain it very tightly and only let it march down a logical path from first principles. If you give your mind too much freedom, it will naturally gravitate towards what is intuitive and safe and comfortable. As Richard Feynman once said, 'The first principle is that you must not fool yourself, and you are the easiest person to fool.'

The scientific community's delusional belief in a material, mechanical universe is a great example of this. There is literally no evidence to support materialism. Zero. Nothing. Zip. Nada. And yet if you try to challenge their unquestioning faith in materialism and suggest that consciousness is more fundamental than a material reality, they'll call you 'woo woo' and laugh you out of the room.

To quote the outspoken materialist and atheist, Richard Dawkins — 'Faith is the great cop-out, the great excuse to evade the need to think and evaluate evidence. Faith is belief in spite of, even perhaps because of, the lack of evidence.' I think he hits the nail on the head. Of course, he was referring to religion when he said those words, but they are just as applicable to himself as to anyone else.

If faith is belief in spite of evidence, then Dawkins' faith in a mechanical, material universe is the ultimate irony. He has evaded the need to think by simply accepting what is right in front of him. That's another interesting observation about life — you often become the thing you fight against.

It's funny how scientists pride themselves on their skepticism but conveniently forget to apply any skepticism to their own pet belief system. They aren't playing by their own rules. They think they are enlightened free-thinkers, and for the most part, they are. However, they've also spent generations parroting the same false axioms that were passed down to them in textbooks, as if those textbooks were Bibles."