Inductive Reasoning

We engage in inductive reasoning every day, often without even noticing it. Put simply, inductive reasoning is the act of forming a generalization based on a set of specific observations.¹ It begins with a premise, such as “all the Anatomy majors I know want to study medicine,” which leads to a conclusion, such as “all Anatomy majors want to attend medical school.” This, of course, is not necessarily the case; perhaps an Anatomy major wants to pursue a career in academia, or change their field of study altogether. The conclusion could be made stronger by removing the absolute and amending the line of reasoning to be: everyone I know majoring in Anatomy wants to study medicine, therefore, most Anatomy majors want to study medicine.

Inductive reasoning is a tool we use every day in order to make sense of the world around us. However, it also underlies the scientific method, which is the basis for how research is conducted. Researchers collect data – specific observations – from which they form hypotheses – generalizations – that inform further research.²

It is important to make the distinction between inductive reasoning and deductive reasoning. While inductive reasoning is referred to as “bottom-up reasoning,” because it starts with specific observations that lead to a generalization, deductive reasoning is known as “top-down reasoning,” because it begins with general principles that lead to specific conclusions.³  An example of deductive reasoning is: all students within the Faculty of Science must take an introductory Biology course, and the Department of Anatomy and Cell Biology is within the Faculty of Science. Therefore, all Anatomy majors must take an introductory Biology course.

Sample and population

A sample is a small group of people from a given population, while a population encompasses an entire group of people. For instance, everyone living in Canada represents the Canadian population, while a group of 1000 Canadians is a sample of the Canadian population. In inductive reasoning, patterns observed within samples are used to make inferences about the population.

Inductive generalizations

This form of inductive reasoning occurs when a pattern observed within a sample is generalized to the entire population,⁴ as was done in the previously mentioned example about Anatomy majors.

Statistical induction

An example of statistical induction would be to say that “95% of basketball players I have seen are over six feet tall, therefore 95% of all basketball players are over six feet tall.” It is similar to an inductive generalization, except it uses a specific statistic from a sample to make a generalization about a population.⁵

Statistical induction can be taken one step further with Bayesian statistical induction. Bayesian induction increases the strength of your conclusion by taking additional information into account.⁶ The example about basketball players could be refined by making a specification about age, location, or specifying that you are only examining professional basketball players.

Analogical induction

Analogical induction is when an inference is made based on the commonalities between two similar, but distinct groups.⁷ An example of this kind of inductive reasoning would be “geese are similar to ducks, and ducks fly, therefore, geese fly, too.”

Predictive induction

Another type of inductive reasoning is predictive induction, which is used to make a prediction about the future using information gathered from past observations of a sample.⁸ For instance:  In past school years, many employees have bought their lunch at the office cafeteria. Therefore, many employees will buy their lunches at the office cafeteria this year.

Causal inference

Causal inference is when a causality is inferred between the premise and the conclusion.⁹ An example of this could be: Traffic in the city increases at the start of the new school year, therefore, the beginning of a new school year causes an increase in traffic.

In the 17th century, Sir Francis Bacon, an English philosopher, developed the Baconian method, a framework for conducting scientific research. The steps he proposed are a description of facts, a classification of facts and, finally, the identification of what seems to be connected to the phenomena in question and a rejection of that which is irrelevant. Much like the modern scientific method that replaced it, the Baconian method is an example of an application of inductive reasoning.¹⁰

Another early modern philosopher with a notable role in the history of inductive reasoning was David Hume. Due to its lack of logical certainty, he could find no logical justification in favor of induction, yet he argued that it is a necessity of human life.⁸ Hume famously distinguished between inductive and deductive reasoning, referring to the former as a “matter of fact” and the latter as a “relation of ideas.”¹¹ Matters of fact, he claimed, are accepted as they are – thus if every swan you see is white, you may conclude that all swans are white. Relations of ideas, on the other hand, result from logical examination; so, if all birds have feathers, and all swans are birds, one can conclude that all swans have feathers.¹²  Hume reasoned that matters of fact result from associations drawn from past experiences, which is the basis of inductive reasoning.¹³

In 1912, philosopher Bertrand Russell released a book called The Problems of Philosophy.¹⁴ Here, he tackled the topic of induction. He argued that, in order to understand anything outside of our private experiences, we must make inferences. Although there is no guarantee about the accuracy of our inferences, Russell contends that they are useful for expanding our knowledge outside of the realm of our immediate experiences.

Russell gives the example of the sun rising each day. He claims that it is normal to expect the sun to continue to rise each day, yet he asks whether this expectation is a reasonable one. We expect it to rise firstly because “it has risen each day before,” reasoning which illogically assumes that the past can predict the future. We also expect it to rise because we place stock in the laws of motion which cause the Earth to orbit and bring about sunrise. However, what is it that leads us to believe that the laws of motion will be maintained from one day to the next?

It seems reasonable to expect nature to sustain its constant patterns, yet there is no evidence for this assumption. This discovery led Russell to develop his principle of induction, which is as follows: “When a thing of a certain sort A has been found to be associated with a thing of a certain other sort B, and has never been found dissociated from a thing of the sort B, the greater the number of cases in which A and B have been associated, the greater is the probability that they will be associated in a fresh case in which one of them is known to be present. Under the same circumstances, a sufficient number of cases of association will make the probability of a fresh association nearly a certainty, and will make it approach certainty without limit.”¹⁵

Thanks to inductive reasoning, scientists have been able to progress human knowledge and foster innovation. The scientific method, the framework within which all scientific research is conducted, is based upon inductive reasoning. Without induction, researchers could not form hypotheses based on their observations.¹⁶ Hypotheses are essential for directing future research and developing new theories, thus scientific advancement hinges on inductive inference.

Furthermore, the inductive inferences we make in our daily lives, which we often form without much conscious effort, are incredibly useful for expanding our understanding of the world. By identifying patterns in our environment, we not only gain insight into how the world functions, but also as to how we should behave. Something as simple as knowing that you can find the necessary ingredients to make a sandwich in your refrigerator because that is where you found them the day before is an example of inductive reasoning.

Philosophers have argued that induction is inferior to deduction. When it comes to inductions, if the premise is true, the conclusion is probably true, as well. However, what makes certain philosophers favor deduction is the fact that when the premise of a deduction is true, the conclusion is certainly true.

Induction assumes that past events are predictive of future events, which is not a logical assumption to make. Scottish philosopher David Hume is famous for his “problem of induction,” which asks how one can justify the use of inductive reasoning. He points out that we often draw conclusions from a limited set of observations and that, while the conclusion may appear to be correct, it lacks logical certainty. This results in a paradox in which inductive reasoning cannot be justified by deductive reasoning but can be justified by inductive reasoning. Hume’s conclusion of this circular argument is that inductive reasoning cannot be justified. In spite of this, he argues that there are truths central to human existence that cannot be proven through deduction, such as the belief that our personality remains stable from one day to the next.¹⁷ 

While it is necessary to recognize its limitations, we should not discount the  importance of induction in our daily lives, nor its role in innovation and discovery. Despite the logical certainty of deductive reasoning, there are times when the probable conclusions elicited from inductive reasoning are more valuable.

Artificial intelligence

Artificial intelligence is defined as computers’ ability to perform tasks that typically require human intelligence.¹⁸ The term “intelligence” is a broad one. Intelligence is typically thought of as a general factor, made up of various subcomponents. When it comes to artificial intelligence, most of the research done to date has focused on a handful of specific subcomponents of intelligence: language, perception, problem-solving, learning, and reasoning.¹⁹ 

While more success has been had with deductive reasoning, artificial intelligence can now be programmed to draw inductive inferences.²⁰ This is made possible by methodologies like neural networks, which permit computers to pull together a large quantity of data.²¹ This is a promising area of innovation, but one of the biggest obstacles still to be overcome is the challenge of programming artificial intelligence not just to draw inferences, but to draw relevant inferences.²²

The goal of automating inductive reasoning in artificial intelligence is to enable these programs to develop hypotheses and use inductive reasoning to support these hypotheses. Once AI reaches this goal, scientific research can accelerate through the automation of reasoning and problem-solving skills.²³

Nassim Taleb

Nassim Taleb is a bestselling author and celebrated academic, who specializes in the area of risk and uncertainty. One of his books, Black Swan, addresses errors in induction, using the famous example of inductive reasoning in which people infer that, because they have only ever seen white swans, all swans are white. However, as rare as they are, black swans do exist, and Taleb uses this to point out the flaws of inductive reasoning. In this book, he expands upon Hume’s ideas and concludes that even our best efforts are not always sufficient for accurate prediction.

1. What is Inductive Reasoning? Learn the Definition of Inductive Reasoning With Examples, Plus 6 Types of Inductive Reasoning. MasterClass. https://www.masterclass.com/articles/what-is-inductive-reasoning#3-ways-inductive-reasoning-is-used
2. See 1
3. See 1
4. Examples of Inductive Reasoning. Your Dictionary. https://examples.yourdictionary.com/examples-of-inductive-reasoning.html
5. See 4
6. See 1
7. See 1
8. See 1
9. See 1
10. Baconian method. Encyclopaedia Britannica. https://www.britannica.com/science/Baconian-method
11. Cranston, M. (2020). David Hume. Encyclopaedia Britannica.https://www.britannica.com/biography/David-Hume
12. See 1
13. See 11
14. Russell, B. (2001). The problems of philosophy (2nd ed.). Oxford University Press.
15. On Induction. Public Consulting Media. https://www.publiconsulting.com/wordpress/theproblemofphilosophy/chapter/on-induction/
16. See 1
17. Inductive Reasoning. Philosophy Terms. https://philosophyterms.com/inductive-reasoning/
18. Artificial Intelligence. Lexico. https://www.lexico.com/definition/artificial_intelligence
19. Copeland, B.J. (2020). Artificial intelligence. Encyclopaedia Britannica. https://www.britannica.com/technology/artificial-intelligence
20. See 19
21. Littlefield II, W.J. (2019). A Type of Reasoning AI Can’t Replace. MindMatters News. https://mindmatters.ai/2019/10/a-type-of-reasoning-ai-cant-replace/
22. See 19
23. Laskey, K.B., and Levitt, T.S. (2001). Artificial Intelligence: Uncertainty. International Encyclopedia of the Social & Behavioral Sciences. 799-805. https://doi.org/10.1016/B0-08-043076-7/00395-8