Inductive Generalization: How to Use it and How to Abuse it

When arriving at a sporting event, we drive into a ten story parking garage. We drive around the entire first level, second level, then third level. After not finding any spots, we conclude that there are probably no spaces left until the upper floors and we end up just parking on the tenth floor and skipping floors 4–9. A little later, we crave a soft pretzel. The first vendor we visit is out of pretzels; so is the second, and the third. Even though there are still about a dozen more vendors we can try we conclude that all the vendors are probably sold out of pretzels, and we settle for something that resembles a hotdog instead. We’ve been going to this event monthly for many years now. After the first few months of running into the same parking and soft pretzel issues, we go directly to the tenth floor when we want to park and don’t even bother asking for soft pretzels anymore.

These are three examples of a specific type of inductive reasoning usually referred to as inductive generalization , which is using what we know from a limited number of specific observations of a certain type (sample) and making a probabilistic claim about all or most things of that type (the population). Like all inductive arguments, any inductive generalization is somewhere on the continuum of bad or weak to good or strong. With our examples, the stakes are low and at worse, we are risking some wasted time or a bad case of diarrhea. But what if we used inductive generalizations to inform our core beliefs that can affect how we live our lives? Then it is of the utmost importance to know how to evaluate inductive generalizations and know when we are being manipulated by bad arguments.

Algorithms and Heuristics

A quick refresher on two important terms in cognitive science: algorithms and heuristics . An algorithm is a process or set of rules to be followed in problem-solving operations that, if followed correctly, guarantees the correct solution. An example of an algorithm is a recipe for baking a cake or if/then computer code that responds the same way to the same inputs. A heuristic is a mental shortcut used to help us find the most probable answer. Heuristics are fast and take little cognitive resources but come at a cost: that cost is accuracy. Inductive reasoning is a heuristic. We can never be sure of the solution arrived at from inductive reasoning—it’s probabilistic.

Another Probability Primer

Since you are reading my work, I will assume that you are smart enough to realize that casinos have a statistical advantage over the players. For example, with roulette, the house will maintain a constant statistical advantage over the player. Since (American) roulette wheels have 36 numbers colored red or black, and zero and double zero spots colored green, the player making an even money bet has a 47.37% chance of winning. Despite this disadvantage, players win all the time—casinos just win more. Inductive generalizations and cognitive heuristics are like the casino where winning is like being correct or having the right solution. For any given problem where inductive reasoning was used, the solution could be completely wrong. The statistical advantage is a result of long-term use. Just because inductive generalizations, in general, are likely to lead to the right solution, it doesn’t mean that every inductive generalization is likely to lead to the right solution.

Evaluating Inductive Generalizations

As mentioned, the quality of an inductive generalization exists on a continuum. “Quality” in this context refers to the strength of the conclusion—extremely weak to extremely strong, and everything in between. In addition to this measurement, it is also possible for an inductive generalization to be invalid, which is basically saying that it makes no sense and the conclusion drawn from it is equivalent to an uneducated guess. Here is a list of questions that we can ask about any inductive generalization that will allow us to determine the validity and the quality.

1. ​​ Are the premises true? A “no” answer to this question would invalidate the entire inductive generalization. Recall our search for parking. What if while looking for parking spaces you were also texting a friend about getting tickets to the new Madonna concert: 70 and still sexy . While looking at some disturbing preview pics, you happened to miss several of the available spots on the first three floors. The premise that there are no spots on the first three floors is not true; therefore, the conclusion that there are probably only spots on the tenth floor is no longer supported by the specific observations and, thus, only as good as an uneducated guess.

2. ​​ How big is the sample? The math behind sampling is complex 35 and far beyond the scope of this book. However, the good news is that for the purposes of inductive generalizations a layperson’s understanding will do just fine. As a general rule, the fewer specific observations (i.e., the smaller the sample), the weaker our generalization. Recall our search for a soft pretzel. We tried three different vendors before we concluded that all of the vendors were probably sold out. We can debate if this was reasonable or not but what is not debatable is that trying just two vendors would mean that our conclusion is less probable and trying four would mean that our conclusion would be more probable. Common sense plays a role here as well. Concluding that all the gas stations across the country are probably out of gas because the one station we tried was out of gas, is pretty darn unreasonable.

3. ​​ How well does the sample represent the population?  The more representative the sample is of the population, the stronger the generalization. Recall our search for parking again. While there were hundreds of spaces, the spaces were grouped into floors, where the likelihood of spaces available on each floor correlated with how close the floor was to the entrance and exit. The population would be all parking spaces on all floors. Technically, each parking spot could be ranked from most desirable to least desirable. The farthest spot from the entrance and exit would be the least desirable and the closest spot to the entrance and exit would be the most desirable. Our sample is all the parking spaces on the first three floors. With each increasing floor, our sample becomes less representative of the population since the desirability of each spot becomes more unlike the desirability of the spots in our sample. Now, since we concluded that floors 4–9 were also probably full, I would say that taken together, floors 4–9 were not a good representation of our sample, and therefore, this inductive generalization is on the weak side. In practical terms, this means that we should have kept looking for spots on each floor until we found one.

4. ​​ How likely is it that there will be material changes that might affect future predictions?  If the inductive generalization refers to future events, then any possible future changes can change the likelihood of the future events. The more likely there are to be material changes (i.e., changes that affect our event) the weaker our generalization. In our opening story, after just a few months of experiencing the same unfortunate parking and soft pretzel outcomes, we conclude that every time we go there we will need to park on the top floor and soft pretzels will be sold out. If nothing has materially changed the first few times we attended the event, this could explain the consistency of the parking and soft pretzels. But there are many things that could change, including the vendors buying more soft pretzels to meet the demand or the parking garage opening up more spaces to the public. When we used inductive generalization to assume that every experience would be like the first few, we did not take into account these possible changes.

Sometimes, inductive generalizations are used as evidence for arguments. This is fine as long as the generalization is on the strong side and the evidence is presented as probabilistic and not one of certainty. If you are thinking like a scientist who is primarily concerned with the truth no matter where the truth leads rather than a lawyer who is primarily concerned with giving one side the best defense possible even at the expense of truth, then it is your duty to critically think about your inductive generalization and attempt to falsify it by providing counterexamples. We will see examples of this in the inductive generalizations for and against the gods.

Inductive Arguments For and Against the Gods

People throw around these arguments like they have found the silver-bullet in religious debate and finally put an end to the millennia-old question, “do the gods exist?” Since inductive reasoning only can provide us with a probable answer, it should be clear that this line of reasoning cannot either prove nor disprove the existence of the gods. Let’s take a look at the most common theistic and atheistic inductive generalizations beginning with the theist argument for the existence of God.

Since all complexity that we know the origin of comes from intelligent beings, then it is likely that all complexity (i.e., life) that we don’t know the origin of also comes from an intelligent being (i.e., God).

The first problem is that the theist is engaged in backward reasoning , which is deciding on the conclusion first then trying to make the evidence fit rather than starting with evidence and drawing our conclusion from there. We know this because the argument was altered from what standard generalization would conclude to make it support a monotheistic perspective. If all complexity that we know the origin of comes from intelligent beings (plural), then we would reason that the complexity we don’t know the origin of comes from intelligent beings (plural). This would support an advanced alien race or perhaps even a multitude of gods, not a single God. Additionally, out of all the characteristics of humans, why was “intelligent beings” chosen? Again, because this is one characteristic we are said to have in common with the theistic god. But couldn’t we also have chosen “flawed and imperfect beings”? Of course, we could have, but this would then appear to be evidence against the theistic god, and not for it. So the following inductive generalization would essentially cancel out the one for the monotheistic god:

Since all complexity that we know the origin of comes from flawed and imperfect beings, then it is likely that all complexity (i.e., life) that we don’t know the origin of also comes from flawed and imperfect beings.

Remember that the monotheistic argument is that intelligence is required for complexity. So if one claims that the reason they chose “intelligent being” over “flawed and imperfect being” is because intelligence is required for complexity, they are simply asserting what they have failed demonstrate through the argument. This would be like asserting that the Bible is true because it says so in the Bible.

We could stop there, but for academic purposes, let’s run this inductive generalization through our four questions.

1. ​​ Are the premises true? There is one premise which is “all complexity that we know the origin of comes from intelligent beings.” This is a highly debatable claim for two reasons. First, it could be argued that nature is the origin of complexity and nature is not a being. Second, intelligence is the result of complexity, not the source. At least in humans, without the complexity of the brain, there would be no intelligence. Therefore, human-created complexity cannot “come from” intelligence. Of course, if you are dealing with someone who believes in mind/body dualism (i.e., that the mind is separate from the brain and not dependent on the brain) then attempting to argue this would likely just take you down a rabbit’s hole. While we certainly could invalidate this entire inductive generalization from a scientific perspective, we don’t need to.

2. ​​ How big is the sample? The sample is potentially billions of demonstrations of human complexity, so the sample is certainly large enough.

3. ​​ How well does the sample represent the population? When dealing with complexity, we have two very distinct categories: complexity found within nature (e.g., DNA, the human brain, etc.) and human-created complexity (e.g., supercomputers, rockets, etc.). Our population is all complexity found in the universe, and our sample is only human-created complexity. The differences between the two groups, nature and human-created, are significant. The sample contains only one type found within the population and, therefore, not representative of the population.

4. ​​ How likely is it that there will be material changes that might affect future predictions? We are not dealing with future predictions, so this doesn’t apply.

In summary, this inductive generalization for the monotheistic god could also be modified to support the idea that life was created by a plurality of gods, an advanced alien race, or even flawed and imperfect beings, which would directly contradict the monotheistic “perfect being” God. Scientifically, this inductive generalization is invalid because of the false premise that human-created complexity comes from intelligence. If we need to go even further, at the very least, this would be a very weak generalization because the sample is not a good representation of the population.

Now, what about the argument against the gods? This inductive argument usually goes something like this:

Every explanation that we have uncovered has been a naturalistic one requiring nothing supernatural. Therefore, it is likely that everything we don’t have an explanation for also has a naturalistic explanation.

This argument basically says that every time throughout history when we credited or blamed the supernatural for a phenomenon (such as the apparent motion of the sun, thunder, lightning, disease, mental illness, etc.), and we eventually used science to explain what we could only attempt to explain through mythology and superstition, that explanation was a non-supernatural one. Or as it has been said, the more we learn through science, the less we need the gods. The inductive part of the argument then states that since there has been a consistent pattern of naturalistic explanations replacing supernatural ones (and never the other way around), it is likely that all the unexplained phenomena can eventually be explained naturally.

Let’s run this inductive generalization through our four questions.

1. ​​ Are the premises true? There is one premise which is “every explanation that we have uncovered has been a naturalistic one requiring nothing supernatural.” Yes, this is true. Never has the supernatural even been demonstrated to exist, let alone found to be an “explanation” to anything.

2. ​​ How big is the sample? The sample is potentially billions of naturalistic discoveries since recorded history. This is certainly large enough.

3. ​​ How well does the sample represent the population? Our population is all things able to be explained. Our sample includes how babies are made, why the sun “sets” each day, the diversity of life on the planet, and other concepts that seem to require an explanation, which appears to be representative of the population.

4. ​​ How likely is it that there will be material changes that might affect future predictions? We are dealing with future predictions here so we need to consider what is likely to change in the future that might make a supernatural explanation more likely. I can’t think of anything.

It could be argued that, by definition, we cannot explain the supernatural like we can explain the natural. That is, the “supernatural” itself is used as the explanation, just like “magic” would be. How does Dr. Strange create a space portal? Magic—that’s it. If it could be explained, it wouldn’t be magic. More important, how do we identify a supernatural explanation? Perhaps the supernatural appears to us as a “mystery,” which can either have an unknown natural explanation or a supernatural explanation (no explanation). The point is, in order for this inductive generalization to be of any real value, we need to be clear on what a supernatural explanation would look like.

We make inductive generalizations every day. Most of them are insignificant and fortunately, relatively accurate. Others we might rely on too heavily for some of life’s most important questions. For these especially, we need to accurately assess the likelihood of such generalizations and identify the flaws in them. We can do this through the four questions mentioned. When we put the most common inductive generalizations about the existence of the gods to the test, we see that the monotheistic one fails and the atheistic one only works if those who accept the generalization could agree on how a supernatural explanation would be identified. When it comes to inductive generalizations, stick to the more trivial applications. When it comes to the important questions in life, use other methods of reasoning that require more thinking and less guessing.