Deduction and Induction

Two methods of reasoning: deduction and induction. If you want to have sharp critical thinking skills, you must understand the difference between these two. It isn’t too difficult to understand, and the benefits are enormous.

Example #1: Inductive reasoning.

A: Every swan that I have ever seen is white;
B: Therefore, all swans are white.

OK, let’s break this down. If I were to claim such a thing, “All swans are white.”, a proper skeptic should immediately ask, “How do you know (what was the thinking-process which led to that conclusion?)”

I would respond, “Well, I have gone out and tested this claim, and every single data point which I have has been a white swan. I have gained empirical data about the real-world, and all of it points to the whiteness of swans.” Simple. 

This way of thinking seems fine, as long as you never find a black swan. As soon as you gather new data which doesn’t conform with your old data, you have to throw out your conclusion. Now, some people say this is a credit to scientific thinking; it is always adjusting to new data, and it doesn’t (and shouldn’t) claim absolute certainty about anything.

I disagree. At least, perhaps our fundamental worldview shouldn’t be build off of such ways of thinking, if there are more accurate alternatives. After all, with inductive reasoning, if you start with true premises, you can still end up with false conclusions (like the example above). Keep in mind, inductive reasoning is the backbone of modern science. This should scare you if you seek truth. But is there an alternative?

Example #2: Deductive reasoning.

A: All men are mortal.
B: Socrates is a man.
C: Therefore, Socrates is mortal.

As good skeptics we challenge such a conclusion, “How do you know Socrates is mortal?” Let’s break it down.

Premise A rephrased: Every single case where there is a man, it is always a mortal man, without exception. (this is what “all” means)
Premise B rephrased: Socrates is one of the previous cases: a man.
Therefore, Socrates must be a mortal man.

This is the hallmark of deductive reasoning: If it is the case that our premises are true, the conclusion necessarily follows. How powerful is that?!

Now, as skeptical people, we should challenge the premises. “How do you know that all men are mortal?”

Good question. Some might say it is within the definition of what a man is, that he is mortal. Others (myself included) think this is a more empirical claim, and it really is impossible to have absolute certainty about it.

Well, where does that leave us? Hmm… wouldn’t it be amazing if we could have a premise, which we knew with certainty was true, and then we deduced from there? Wouldn’t it be incredible if our worldview could start with certain accurate beliefs, and use a method of reasoning which leads to certain accurate conclusions? Can we relegate inductive reasoning to practical things (how to build a car, how to put satellites up in space, etc.), and leave deductive reasoning for the most important stuff?

Indeed, I think we can. There are all sorts of necessarily true premises which lead to necessarily true conclusions. There is a whole economic theory based on this way of thinking (sometimes called “axiomatic-deductive” reasoning). If you want to know a few necessarily true premises, discover your presuppositions.

It is important to keep the different reasoning methods at the front of your mind. You will spot endless erroneous conclusions drawn from attempted, but poor, deductive reasoning. More importantly, understanding the flaws in inductive reasoning keeps you intellectually humble. Here’s what I mean:

If I am holding a ball a few feet above the ground, what will happen when I drop it? Will it fall down or up?

Are you sure?

How do you know?

One might respond with a line of reasoning like this:
A: Every time I have seen a thing be dropped in the past, it has fallen towards the earth.
B: Therefore, all things dropped fall towards the earth.

Look familiar? Indeed, it takes a painful amount of humility to say that you do not know whether or not the ball will fall down. Gravity seems necessary (of course, why is this the case? Because all of our personal, empirical data points to gravity being necessary). This does not mean that gravity is necessary. The conclusion does not logically necessarily follow from the premises, likely as we may think “the ball will fall towards the earth” is to happen.

If this is true, if something as ubiquitous as gravity should only be believed without absolute certainty, perhaps our worldview should not conclude much about empirical things. If we seek certain knowledge, not just reasonable beliefs, perhaps empirical claims really should not have much of a role at all.