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 missing out on a delicious salty treat. 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.
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. They 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.
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% 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.
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.
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.
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 necessarily 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.
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.
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.
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