There are two distinct types of reasoning: deductive and inductive.

Deductive Reasoning

Deductive reasoning works from general rules and applies such rules to specific instances. Like this:

• PREMISE: All dogs are mammals
  
• PREMISE: Dylan is a dog
• CONCLUSION: Therefore, Dylan is a mammal
  

With deductive reasoning, as long as the premises are true (dogs are mammals and Dylan is a dog) and the conclusion is a logical result of the premises, then the conclusion is without a doubt true. Deductive reasoning is neat, tidy and unassailable.

The Problem of Induction

“The Problem of Induction” was first raised by philosopher David Hume in the 18th Century. Induction is opposite of deductive reasoning in that it reaches general conclusions from specific instances. The “problem” with induction there are unobserved instances and it is possible that such unobserved instances are contrary to the conclusion. Thus, certainty can never be reached with inductive reasoning and Hume argued it is irrational to rely on inductive conclusions. Examples:

• PREMISE: My dog has floppy ears
• PREMISE: My neighbor’s dog has floppy ears
• PREMISE: My brother’s dog has floppy ears
• PREMISE: My friend’s dog has floppy ears
• CONCLUSION: All Dogs Have Floppy Ears

Obviously, after a mere four observations, we can’t really conclude all dogs have floppy ears. But what if there were 400 observations of dogs with floppy ears? Or 4,000 or 4 million? Is that enough observations to conclude all dogs have floppy ears? Of course not. That is the problem with inductive reasoning – generalizations are always made from the observed about the unobserved.

A classic example from The Black Swan: The Impact of the Highly Improbable, by Nassim Nicholas Taleb:

Consider a turkey that is fed every day. Every single feeding will firm up the bird’s belief that it is the general rule of life to be fed every day by friendly members of the human race “looking out for its best interests,” as a politician would say. On the afternoon of the Wednesday before Thanksgiving, something unexpected will happen to the turkey. It will incur a revision of belief.

Side note: my crazy coincidence regarding this turkey story and a blown airplane engine: Induction and my crazy Southwest Airlines Story

Here’s a helpful chart, also from The Black Swan, of the turkey example:

Another example, of course, is that of swans. In Europe for centuries and after millions and millions of observations of swans only being white, it seemed a proven fact that all swans were white. Then Australia was discovered and the first black swan was observed on that continent. After millions of observations of white swans, how many black swans did it take to overturn the conclusion that all swans were white? Just one.

Thus, inductive arguments are different than deductive arguments. With deductive reasoning, the conclusions are logically entailed from the premises. With inductive reasoning, the premises merely support the conclusion, but can be overturned with yet unobserved observations. And, all it takes is one observation/instance to overturn a conclusion based on inductive inferences.

The Takeaway

The true “problem of induction” is the philosophical argument that relying on inductive reasoning is irrational and attempts to logically justify conclusions based on inductive reasoning are circular or otherwise flawed.* 

While that may be true, there is a practical aspect to living our lives that require us to act based on inductive conclusions: I assume that the elevator at work will take me to my floor and not crash into the basement, that stoplights are appropriately synchronized and I can rely on them, that I will not have a severe allergic reaction to the nuts I will consume today, etc. All this is based on prior knowledge and observations which are not deductively true.

Yet, while it is necessary to live our lives based on inductive reasoning, it is helpful to recognize that inductive conclusions cannot be airtight and there is an inherent irrational basis to inferring general rules based on specific instances and observations. Stop and think about things you believe. Are they based on inductive reasoning? If so, how can we be certain of such beliefs?

Speaking of black swans:

*A more complete statement of Hume’s problem of induction from Stephen Law from his book The Philosophy Gym:

All inductive reasoning, it seems, relies on the assumption that nature is uniform.How, then, might this assumption be justified? Only by experience, surely. But we cannot directly observe that nature is uniform. So we must infer that it is uniform from what we have directly observed, i.e. from a local uniformity. But such an inference would itself be inductive.Therefore we cannot justify the assumption. So our trust in induction is unjustified.