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.

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9 Responses to Deduction and Induction

  1. Rich Stauter says:

    Even though the two types of logical reasoning are distinctly different, both your examples demonstrate a similarity: Premise A of your inductive reasoning example is very similar in nature to Premise A of your deductive example. That is, all men are mortal is also based on observation (extensive observations to be sure); and if you observed enough white swans, the certainty of your conclusion would approach deductive reasoning.

    That also illustrates a weakness of deductive reasoning as a method for discovering truth: how does one really know the premises are true? Or does one necessarily have to start with an unprovable assumption(s) or axiom(s) (as is done in mathematics) and build from there?

    If inductive logic leads to uncertain conclusions and deductive logic requires axioms or assumptions, how does one get to truth logically?

    • Steve says:

      You could make the argument that “all men are mortal” is a premise which we hold to be true based on inductive reasoning. I think that’s accurate. However, that example was just to show the method by which we arrive at true conclusions, if we have true premises. We arrive at certain truth logically by using axioms, and we deduce from there. There are indeed axioms we can know to be true without inductive experience. Many of these are economic, and the whole theory of Austrian economics is based off of this way of thinking.

      For example, “You can not consume everything you produce and become wealthier.” Or, “By increasing the amount of money in a system, without an increase in the amount of goods, there is no increase in society’s standard of living, only an increase in prices.”

      Both of those we can know to be true a priori (before experience). How to know? We think about it; we introspect, in the same way we know mathematics to be true without having to empirically test it. All of the deductions that you draw from these premise will be true. Just with those two examples, our understanding of economics drastically changes from the mainstream perspective, which believes you can consume and inflate your way to wealth.

      A guy named Ludwig von Mises deduced a whole logical framework of economics off of the axiom “humans act”. It is impossible, upon introspection, to deny or even doubt that humans act without acting (denial and doubt are both actions). He would say this is necessarily true, and it applies to the real world.

  2. Pingback: The negation of truth | one free mind

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  5. Lizabeth says:

    You’ve really imseesprd me with that answer!

  6. Black Swan… ARRRG. I've tried to get in and failed… a movie theater worker saw me sneak in and "escorted" me out. I want to see it sooooooo baddddddd….

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