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Inductive Reasoning | Types, Examples, Explanation

Published on January 12, 2022 by Pritha Bhandari . Revised on June 22, 2023.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning , where you go from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

Note Inductive reasoning is often confused with deductive reasoning. However, in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Table of contents

What is inductive reasoning, inductive reasoning in research, types of inductive reasoning, inductive generalization, statistical generalization, causal reasoning, sign reasoning, analogical reasoning, inductive vs. deductive reasoning, other interesting articles, frequently asked questions about inductive reasoning.

Inductive reasoning is a logical approach to making inferences, or conclusions. People often use inductive reasoning informally in everyday situations.

You may have come across inductive logic examples that come in a set of three statements. These start with one specific observation, add a general pattern, and end with a conclusion.

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See an example

In inductive research, you start by making observations or gathering data. Then , you take a broad view of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

You distribute a survey to pet owners. You ask about the type of animal they have and any behavioral changes they’ve noticed in their pets since they started working from home. These data make up your observations.

To analyze your data, you create a procedure to categorize the survey responses so you can pick up on repeated themes. You notice a pattern : most pets became more needy and clingy or agitated and aggressive.

Inductive reasoning is commonly linked to qualitative research , but both quantitative and qualitative research use a mix of different types of reasoning.

There are many different types of inductive reasoning that people use formally or informally, so we’ll cover just a few in this article:

Inductive reasoning generalizations can vary from weak to strong, depending on the number and quality of observations and arguments used.

Inductive generalizations use observations about a sample to come to a conclusion about the population it came from.

Inductive generalizations are also called induction by enumeration.

• The flamingos here are all pink.
• All flamingos I’ve ever seen are pink.
• All flamingos must be pink.

Inductive generalizations are evaluated using several criteria:

• Large sample: Your sample should be large for a solid set of observations.
• Random sampling: Probability sampling methods let you generalize your findings.
• Variety: Your observations should be externally valid .
• Counterevidence: Any observations that refute yours falsify your generalization.

Statistical generalizations use specific numbers to make statements about populations, while non-statistical generalizations aren’t as specific.

These generalizations are a subtype of inductive generalizations, and they’re also called statistical syllogisms.

Here’s an example of a statistical generalization contrasted with a non-statistical generalization.

Causal reasoning means making cause-and-effect links between different things.

A causal reasoning statement often follows a standard setup:

• You start with a premise about a correlation (two events that co-occur).
• You put forward the specific direction of causality or refute any other direction.
• You conclude with a causal statement about the relationship between two things.
• All of my white clothes turn pink when I put a red cloth in the washing machine with them.
• My white clothes don’t turn pink when I wash them on their own.
• Putting colorful clothes with light colors causes the colors to run and stain the light-colored clothes.

Good causal inferences meet a couple of criteria:

• Direction: The direction of causality should be clear and unambiguous based on your observations.
• Strength: There’s ideally a strong relationship between the cause and the effect.

Sign reasoning involves making correlational connections between different things.

Using inductive reasoning, you infer a purely correlational relationship where nothing causes the other thing to occur. Instead, one event may act as a “sign” that another event will occur or is currently occurring.

• Every time Punxsutawney Phil casts a shadow on Groundhog Day, winter lasts six more weeks.
• Punxsutawney Phil doesn’t cause winter to be extended six more weeks.
• His shadow is a sign that we’ll have six more weeks of wintery weather.

It’s best to be careful when making correlational links between variables . Build your argument on strong evidence, and eliminate any confounding variables , or you may be on shaky ground.

Analogical reasoning means drawing conclusions about something based on its similarities to another thing. You first link two things together and then conclude that some attribute of one thing must also hold true for the other thing.

Analogical reasoning can be literal (closely similar) or figurative (abstract), but you’ll have a much stronger case when you use a literal comparison.

Analogical reasoning is also called comparison reasoning.

• Humans and laboratory rats are extremely similar biologically, sharing over 90% of their DNA.
• Lab rats show promising results when treated with a new drug for managing Parkinson’s disease.
• Therefore, humans will also show promising results when treated with the drug.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

In deductive reasoning, you make inferences by going from general premises to specific conclusions. You start with a theory, and you might develop a hypothesis that you test empirically. You collect data from many observations and use a statistical test to come to a conclusion about your hypothesis.

Inductive research is usually exploratory in nature, because your generalizations help you develop theories. In contrast, deductive research is generally confirmatory.

Sometimes, both inductive and deductive approaches are combined within a single research study.

Inductive reasoning approach

You begin by using qualitative methods to explore the research topic, taking an inductive reasoning approach. You collect observations by interviewing workers on the subject and analyze the data to spot any patterns. Then, you develop a theory to test in a follow-up study.

Deductive reasoning approach

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square goodness of fit test
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Inclusion and exclusion criteria

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

There are many different types of inductive reasoning that people use formally or informally.

Here are a few common types:

• Inductive generalization : You use observations about a sample to come to a conclusion about the population it came from.
• Statistical generalization: You use specific numbers about samples to make statements about populations.
• Causal reasoning: You make cause-and-effect links between different things.
• Sign reasoning: You make a conclusion about a correlational relationship between different things.
• Analogical reasoning: You make a conclusion about something based on its similarities to something else.

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3.4: Inductive and Deductive Reasoning

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Learning Objectives

Students will be able to

• Identify and utilize deductive and inductive reasoning

Ask somebody who has a job as to why they have a job and there is a good chance they have a reason or multiple reasons. Most likely they will respond by saying that they need the money for their basic necessities. They may even respond that they just want to keep busy or that their parents told them they had to. The point is that there are reasons.

Definition: Reasoning

Reasoning is the act of drawing a conclusion from assumed fact(s) called premise(s) .

Examples \(\PageIndex{1}\)

Identify the premise(s) and conclusion in each case of reasoning:

a) "Martha wants to buy a new smartphone, so she decides to get a job."

b) The traffic app notifies Pedro that the traffic on Interstate 215 North will cause him to arrive at his destination at 3 p.m., an hour later than he expected. The app also shows that Interstate 15 North will allow him to arrive at his destination at 2:30 p.m. Pedro decides to take the Interstate 15 North.

a) The premise is that Martha wants to buy a new smartphone and the conclusion is that she decides to get a job.

b) There are two premises in this example. One, that the traffic on Interstate 215 North will cause Pedro to arrive at his destination at 3 p.m, and the other that Interstate 15 North will allow him to arrive at his destination at 2:30 p.m. The conclusion is that Pedro takes the Interstate 15 North.

There are many different forms of reasoning defined by scholars, two of which are defined below.

Definitions: Inductive and Deductive Reasoning

Inductive reasoning: uses a collection of specific instances as premises and uses them to propose a general conclusion .

Deductive reasoning: uses a collection of general statements as premises and uses them to propose a specific conclusion .

Notice carefully how both forms of reasoning have both premises and a conclusion. The important difference between these two types is the nature of the premises and conclusion. Applying these definitions to some examples should illuminate the differences and similarities.

Examples \(\PageIndex{2}\)

Identify the premises and conclusion of the reasoning below. Identify the type of reasoning used and explain your choice.

a) “When I went to the store last week I forgot my purse, and when I went today I forgot my purse. I always forget my purse when I go to the store”

b) “Every day for the past year, a plane flies over my house at 2 p.m. A plane will fly over my house every day at 2 p.m.”

c) "All electronic devices are useful. My cell phone is an electronic device. Therefore, my cell phone is useful."

d) Spicy food makes me teary. Habanero sauce is spicy food. Habanero sauce makes me teary.

a) The premises are:

• When I went to the store last week I forgot my purse.
• When I went today I forgot my purse.

The conclusion is:

• I always forget my purse when I go to the store

This is an example of inductive reasoning because the premises are specific instances, while the conclusion is general.

b) The premise is:

• Every day for the past year, a plane flies over my house at 2 p.m
• A plane will fly over my house every day at 2 p.m.

c) The premises are:

• All electronic devices are useful.
• My cell phone is an electronic device.
• My cell phone is useful.

d) The premises are:

• Spicy food makes me teary.
• Habanero sauce is spicy food.
• Habanero sauce makes me teary.

This is an example of deductive reasoning because the premises are general statements, while the conclusion is specific.

Free Mathematics Tutorials

Mathematical induction - problems with solutions.

Several problems with detailed solutions on mathematical induction are presented.

The principle of mathematical induction is used to prove that a given proposition (formula, equality, inequality…) is true for all positive integer numbers greater than or equal to some integer N. Let us denote the proposition in question by P (n), where n is a positive integer. The proof involves two steps: Step 1: We first establish that the proposition P (n) is true for the lowest possible value of the positive integer n. Step 2: We assume that P (k) is true and establish that P (k+1) is also true

Solution to Problem 3:

Statement P (n) is defined by 1 3 + 2 3 + 3 3 + ... + n 3 = n 2 (n + 1) 2 / 4 STEP 1: We first show that p (1) is true. Left Side = 1 3 = 1 Right Side = 1 2 (1 + 1) 2 / 4 = 1 hence p (1) is true. STEP 2: We now assume that p (k) is true 1 3 + 2 3 + 3 3 + ... + k 3 = k 2 (k + 1) 2 / 4 add (k + 1) 3 to both sides 1 3 + 2 3 + 3 3 + ... + k 3 + (k + 1) 3 = k 2 (k + 1) 2 / 4 + (k + 1) 3 factor (k + 1) 2 on the right side = (k + 1) 2 [ k 2 / 4 + (k + 1) ] set to common denominator and group = (k + 1) 2 [ k 2 + 4 k + 4 ] / 4 = (k + 1) 2 [ (k + 2) 2 ] / 4 We have started from the statement P(k) and have shown that 1 3 + 2 3 + 3 3 + ... + k 3 + (k + 1) 3 = (k + 1) 2 [ (k + 2) 2 ] / 4 Which is the statement P(k + 1).

Statement P (n) is defined by n 3 + 2 n is divisible by 3 STEP 1: We first show that p (1) is true. Let n = 1 and calculate n 3 + 2n 1 3 + 2(1) = 3 3 is divisible by 3 hence p (1) is true. STEP 2: We now assume that p (k) is true k 3 + 2 k is divisible by 3 is equivalent to k 3 + 2 k = 3 M , where M is a positive integer. We now consider the algebraic expression (k + 1) 3 + 2 (k + 1); expand it and group like terms (k + 1) 3 + 2 (k + 1) = k 3 + 3 k 2 + 5 k + 3 = [ k 3 + 2 k] + [3 k 2 + 3 k + 3] = 3 M + 3 [ k 2 + k + 1 ] = 3 [ M + k 2 + k + 1 ] Hence (k + 1) 3 + 2 (k + 1) is also divisible by 3 and therefore statement P(k + 1) is true.

Statement P (n) is defined by 3 n > n 2 STEP 1: We first show that p (1) is true. Let n = 1 and calculate 3 1 and 1 2 and compare them 3 1 = 3 1 2 = 1 3 is greater than 1 and hence p (1) is true. Let us also show that P(2) is true. 3 2 = 9 2 2 = 4 Hence P(2) is also true. STEP 2: We now assume that p (k) is true 3 k > k 2 Multiply both sides of the above inequality by 3 3 * 3 k > 3 * k 2 The left side is equal to 3 k + 1 . For k >, 2, we can write k 2 > 2 k and k 2 > 1 We now combine the above inequalities by adding the left hand sides and the right hand sides of the two inequalities 2 k 2 > 2 k + 1 We now add k 2 to both sides of the above inequality to obtain the inequality 3 k 2 > k 2 + 2 k + 1 Factor the right side we can write 3 * k 2 > (k + 1) 2 If 3 * 3 k > 3 * k 2 and 3 * k 2 > (k + 1) 2 then 3 * 3 k > (k + 1) 2 Rewrite the left side as 3 k + 1 3 k + 1 > (k + 1) 2 Which proves tha P(k + 1) is true

Statement P (n) is defined by n! > 2 n STEP 1: We first show that p (4) is true. Let n = 4 and calculate 4 ! and 2 n and compare them 4! = 24 2 4 = 16 24 is greater than 16 and hence p (4) is true. STEP 2: We now assume that p (k) is true k! > 2 k Multiply both sides of the above inequality by k + 1 k! (k + 1)> 2 k (k + 1) The left side is equal to (k + 1)!. For k >, 4, we can write k + 1 > 2 Multiply both sides of the above inequality by 2 k to obtain 2 k (k + 1) > 2 * 2 k The above inequality may be written 2 k (k + 1) > 2 k + 1 We have proved that (k + 1)! > 2 k (k + 1) and 2 k (k + 1) > 2 k + 1 we can now write (k + 1)! > 2 k + 1 We have assumed that statement P(k) is true and proved that statment P(k+1) is also true.

STEP 1: For n = 1 [ R (cos t + i sin t) ] 1 = R 1 (cos 1*t + i sin 1*t) It can easily be seen that the two sides are equal. STEP 2: We now assume that the theorem is true for n = k, hence [ R (cos t + i sin t) ] k = R k (cos kt + i sin kt) Multiply both sides of the above equation by R (cos t + i sin t) [ R (cos t + i sin t) ] k R (cos t + i sin t) = R k (cos kt + i sin kt) R (cos t + i sin t) Rewrite the above as follows [ R (cos t + i sin t) ] k + 1 = R k + 1 [ (cos kt cos t - sin kt sin t) + i (sin kt cos t + cos kt sin t) ] Trigonometric identities can be used to write the trigonometric expressions (cos kt cos t - sin kt sin t) and (sin kt cos t + cos kt sin t) as follows (cos kt cos t - sin kt sin t) = cos(kt + t) = cos(k + 1)t (sin kt cos t + cos kt sin t) = sin(kt + t) = sin(k + 1)t Substitute the above into the last equation to obtain [ R (cos t + i sin t) ] k + 1 = R k + 1 [ cos (k + 1)t + sin(k + 1)t ] It has been established that the theorem is true for n = 1 and that if it assumed true for n = k it is true for n = k + 1.

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What is inductive reasoning (a definition), video: deduction vs. induction (deductive/inductive reasoning).

Why Is Inductive Reasoning Important?

• Identifying patterns and making predictions: By observing patterns and trends in specific instances, we can form general conclusions and predictions about the world (Hayes et al., 2010). This allows us to make informed decisions in everyday situations, like expecting rain after seeing dark clouds.
• Generalization: Inductive reasoning allows us to make generalizations based on specific observations or examples. By identifying patterns or trends in specific instances, we can infer broader principles or rules that apply to a larger set of situations (Heit, 2000).
• Scientific method: Inductive reasoning plays a crucial role in scientific discovery. Scientists use observations and data to form hypotheses and theories, which they then test through experimentation. This cycle of observation, induction, and testing is essential for advancing scientific knowledge.
• Critical thinking: Inductive reasoning requires you to analyze evidence, identify weaknesses, and consider alternative explanations. This helps you develop critical thinking skills, which are essential for making sound judgments (Shin, 2019).
• Problem-solving: In many problem-solving scenarios, especially those with incomplete information, inductive reasoning allows us to draw reasonable conclusions based on the available evidence. It helps us make informed decisions or solve complex problems (Heit, 2000; Shin, 2019).
• Everyday decisions: We constantly make decisions based on incomplete information and past experiences. Inductive reasoning allows us to use what we know to make informed predictions about the future, even when we can't be absolutely certain.
• Creativity : By identifying patterns and making connections between seemingly unrelated things, inductive reasoning can lead to new ideas and innovations.
• Adaptability and learning: The world around us is constantly changing, and inductive reasoning allows us to adapt our understanding based on new information. This is essential for learning and growth (Heit, 2000).

History of Inductive Reasoning

Examples of inductive reasoning.

• Every time I eat strawberries, I get hives. So I must be allergic to strawberries. (This is an observation of a pattern leading to a possible explanation.)
• I stopped drinking coffee and now I have headaches. I’m having caffeine withdrawal. (This is another observation of a pattern.)
• I see many people wearing jackets today. It must be cold outside. (This relies on the assumption that most people dress according to the weather.)
• The traffic is always heavy on Friday afternoons. Today is Friday afternoon, so the traffic will probably be heavy. (Past experience informs a prediction about the future.)
• Researchers observe that plants grow taller when exposed to sunlight. They hypothesize that sunlight has a positive effect on plant growth. (This is the first step in the scientific process, where observations lead to hypotheses.)
• A medical study finds that a new drug is effective in treating a disease in a group of patients. Researchers inductively conclude that the drug may be effective for a larger population. (Specific results lead to a broader generalization.)
• Astronomers observe patterns in the movement of stars and galaxies, leading them to theorize about the existence of dark matter. (This is based on indirect evidence, as dark matter cannot be directly observed.)

Video: What Is Inductive Reasoning​

Types of Inductive Reasoning

• Generalization: This is the most common method, where you observe a pattern in a sample and extend it to the entire population. The “all swans are white” example mentioned earlier fits into this category.
• Statistical generalization: Similar to generalization, this uses statistical data to support the conclusion. For instance, finding 95% of people surveyed prefer chocolate ice cream might lead you to say, "Most people prefer chocolate ice cream." This is more reliable than simple generalization but still has limitations due to sample bias and margin of error.
• Causal reasoning: This method seeks to identify cause-and-effect relationships. Observing that plants grow faster with fertilizer might lead you to the conclusion, "Fertilizer causes plants to grow faster." However, correlation doesn't always equal causation, and other factors could be influencing the growth.
• Sign reasoning: This method relies on identifying signs or indicators. Seeing dark clouds might lead you to think, "It will rain soon." While helpful, it's not foolproof. Other factors could influence the weather, and the sign might not always be accurate.
• Analogical reasoning: This method draws comparisons between similar situations. Comparing the human brain to a computer might lead you to conclude that the brain processes information like a computer. This can be insightful, but it requires careful consideration of the differences between the two entities.

Psychology of Inductive Reasoning

Inductive Reasoning in Math

Inductive reasoning in qualitative research, inductive reasoning in science.

• Formulate hypotheses: Based on repeated observations of a phenomenon, scientists propose a tentative explanation.
• Develop theories: As many experiments and observations support a hypothesis, it gains strength and can evolve into a theory, a well-tested and widely accepted explanation for a phenomenon.
• Make predictions: Theories allow scientists to predict how things will behave under different conditions. These predictions are then tested through further experiments.
• Developing the theory of evolution: Observing diverse life forms and their adaptations led Darwin to propose natural selection as a mechanism for change.
• Predicting the properties of new elements: Based on the periodic table, chemists can predict the behavior of undiscovered elements based on their position.
• Testing the effectiveness of a new drug: By analyzing results from clinical trials, researchers can infer the drug's potential benefits and risks.

​Methods of Inductive Reasoning

Inductive reasoning examples in literature.

• ​ Sherlock Holmes stories by Arthur Conan Doyle: In many Sherlock Holmes stories, the famous detective uses inductive reasoning to solve cases. He gathers specific details and observations from crime scenes and then draws general conclusions to deduce the identity of the culprit. ​
• Scout Finch in "To Kill a Mockingbird" by Harper Lee: Scout, the young protagonist of "To Kill a Mockingbird," uses her observations of the adult world to form her own understanding of justice and prejudice. She notices the unfair treatment of Tom Robinson, a black man falsely accused of a crime, and gradually develops her own sense of right and wrong.
• Harry Potter in the "Harry Potter" series by J.K. Rowling: Harry Potter frequently uses inductive reasoning to solve mysteries and navigate the dangers of the wizarding world. He observes suspicious behavior, connects seemingly unrelated clues, and draws conclusions about the motives and actions of others. In "Harry Potter and the Chamber of Secrets," he infers that Professor Snape is attempting to steal a hidden object based on past encounters and Snape's unusual behavior.

Inductive Reasoning Fallacy

• Hasty generalization: This fallacy occurs when a general conclusion is drawn from a small or unrepresentative sample of data. For example, someone might say, "I met two rude people from New York City, so all New Yorkers must be rude." This is a hasty generalization because it ignores the fact that there are millions of people in New York City, and it is impossible to make an accurate judgment about all of them based on the experience of meeting just two.
• False analogy: This fallacy occurs when a comparison is made between two things that are not truly similar, and a conclusion is drawn based on that false similarity. For example, someone might say, "The brain is like a computer, so thinking must be like a computer program." This is a false analogy because brains and computers are fundamentally different systems, and the way they process information is not directly comparable.
• False cause: This fallacy occurs when a conclusion is drawn based on the assumption that because one event happened after another, the first event caused the second event. For example, someone might say, "I took a vitamin C supplement and I didn't get a cold, so vitamin C prevents colds." This fallacy ignores the possibility that other factors may have been at play.
• Slippery slope: This fallacy occurs when a series of small steps are presented as leading to a disastrous outcome, often without sufficient evidence to support the claim. For example, someone might say, "If we allow same-sex marriage, then next they'll want to legalize polygamy, and then bestiality!"

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Final Thoughts on Inductive Reasoning

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• Babcock, L., & Vallesi, A. (2015). The interaction of process and domain in prefrontal cortex during inductive reasoning. Neuropsychologia , 67 , 91–99.
• Hayes, B. K., Heit, E., & Swendsen, H. (2010). Inductive reasoning. Wiley Interdisciplinary Reviews: Cognitive Science , 1 (2), 278–292.
• Heit, E. (2000). Properties of inductive reasoning. Psychonomic Bulletin & Review , 7 , 569–592.
• Mattson, M. P. (2014). Superior pattern processing is the essence of the evolved human brain. Frontiers in Neuroscience , 8 (8), 265.
• Miller, C. (2020, August 1). Inductive reasoning. Exploring communication in the real world . Pressbooks. https://cod.pressbooks.pub/communication/chapter/20-2-inductive-reasoning/ 
• Noaparast, K. B., Niknam, Z., & Noaparast, M. Z. B. (2011). The sophisticated inductive approach and science education. Procedia-Social and Behavioral Sciences , 30 , 1365–1369.
• Shin, H. S. (2019). Reasoning processes in clinical reasoning: from the perspective of cognitive psychology. Korean Journal of Medical Education , 31 (4), 299.
• Tenny, S. (2022, September 18). Qualitative study . StatPearls [Internet]. https://www.ncbi.nlm.nih.gov/books/NBK470395/ 
• The Decision Lab. (n.d.). Inductive reasoning . https://thedecisionlab.com/reference-guide/philosophy/inductive-reasoning 
• University of Minnesota. (2016, September 29). Persuasive reasoning and fallacies. Communication in the Real World . https://open.lib.umn.edu/communication/chapter/11-3-persuasive-reasoning-and-fallacies/ ​
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DEDUCTION & INDUCTION

“The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.”

― Albert Einstein

What is deductive and inductive logic?

Deductive logic is referred to as top-down logic, drawing conclusions through the elimination or examination of the disaggregated elements of a situation. Think about the simple example of the profit of a company, which equals revenue minus costs. Let’s say a company’s profit is declining, yet its revenues are increasing. By deduction, their costs must be increasing faster than their revenues, hence shrinking their profits, even though revenues are increasing.

The process of deductive logic is the typical problem solving process for management consulting projects . Once a team creates a hypothesis tree, then the team typically focuses on discovering and analyzing facts to prove or disprove the hypotheses of the tree. And, through proving or disproving hypotheses, the team creates conclusions and recommendations. Deductive logic is used when there is a discrete set of hypotheses or options , such as when trying to find the root cause of a process issue or trying to optimize a discrete system.

On the other hand, inductive logic is the inverse of deductive logic, taking observations or facts and creating hypotheses or theories from them. Inductive logic is known as bottom-up logic, which starts with selective observations and facts that lead to generalizing and inducing potential hypotheses or theories.

A Barrel of Bad Apples

Imagine there is a barrel of 100 apples and 5 apples are picked from the barrel, and they were all rotten. Using inductive logic, the fact that the first 5 apples are rotten can be generalized into a hypothesis that all the apples are rotten. The key with inductive logic is it doesn’t determine factual conclusions, only hypotheses. If all 100 apples were examined then this would be deductive logic. And, if all 100 were rotten, then it could be concluded as fact that all the apples in the barrel are indeed rotten. Though, just picking 5 that are rotten can only create a hypothesis that all 100 are rotten. Inductive logic should be used when there is an open-ended set of options or potential hypotheses, such as trying to figure out the best marketing campaign to drive sales, or potential innovations for a product, where there might be selective facts and observations that point to potential good solutions, but only after being tested can be truly confirmed as fact.

People using inductive logic to derive conclusions is a large and somewhat invisible issue in strategic thinking and problem solving. I often run across situations where someone observes something and then makes a conclusion about the root cause of a discrete problem.

An Example Using Deduction & Induction in Root Cause Analysis

Let’s go through a simple example to understand this issue better. Let’s say a company has a quality issue where customers are receiving a broken product. And, a product manager states, “The issue must be the shipping department. I’ve seen people in the warehouse drop products and then package them up and ship them.” The product manager uses inductive logic to try and conclude that the quality issue is because of the shipping department mishandling the product. Yet, this inductive logic only creates a hypothesis that the shipping department is to blame.

Deductive logic, not inductive logic, must be used to factually determine the root cause of the quality issue. With deductive logic, we first need to create MECE ( Mutually Exclusive , Collectively Exhaustive) hypotheses of what is driving the quality issue. By creating a hypothesis tree , our quality issue can be from four main hypotheses, which are poor design, the wrong materials, bad manufacturing, or mishandling of the product by the shipping department.

Then the path of deductive logic would lead one to prove or disprove the main hypotheses. To prove or disprove whether it was mishandled by the shipping department an audit could be conducted, which could include inspecting the product before shipping and inspecting the shipping & handling processes . Let’s say the shipping & handling audit showed no issues but did find that 40% of the product had a faulty part, let’s call this part B. Then, we could conduct an audit of the manufacturing and assembly processes. Let’s say during assembly process A, part B broke 40% of the time, even though the manufacturer was consistently following the assembly process instructions. Then, a supplier audit on part B could be conducted to ensure part B is authentic, high quality, and designed to specifications. Let’s say the supplier audit came back with no issues. And, then the product design could be evaluated, and let’s say it was found part B wasn’t properly designed for the assembly process and broke 40% of the time in assembly. By deductive logic, we can conclude that the quality issue was due to the poor design of Part B. Above is a visual representation of the example.

Why is inductive vs. deductive logic important?

Both inductive and deductive logic are fundamental in problem solving. Though, inductive logic is often used when deductive logic is appropriate. This is a subtle issue that most people don’t ever think about, but the consequences are often significant since false conclusions often come from inductive logic. One of the main reasons companies use top strategy consulting firms is because of their strong deductive problem solving methodologies. Deductive problem solving is comprehensive and derives factual conclusions. Most people or teams tasked with solving a problem don’t start with a problem statement , then build a hypothesis tree, and then spend weeks or months proving and disproving the different branches of the hypothesis tree, but top strategy consulting firms do. If somebody wants to figure out the true root causes of a problem, they will use deductive problem solving.

Inductive logic is also critical to strategy when it comes to connecting the dots in creating great options and solutions to a problem. Inductive logic is necessary when the context of a situation is understood, and creative and innovative options and solutions are needed. Elegant inductive logic was the driver for the simplicity of the iPhone, many of the innovations in the Tesla, and the most creative solutions to challenging situations.

EXERCISES TO IMPROVE YOUR DEDUCTION & INDUCTION

One of the core strengths of strategic leaders is the high-quality logic they apply to problems and situations. Regarding inductive and deductive logic, most of the time people use inductive logic. They take a few thoughts or facts and create hypotheses. Typically, what most people need to build up is their deductive logic. That is why we focus on it so much in this problem solving module.

Exercise 1 – Build Your Logic Awareness

Can you tell when people or even yourself are using deductive vs. inductive logic? Can you determine which logic is needed in which situation? If not, in meetings, when people are recommending a course of action, or are breaking down an argument, see if you can determine if they are using inductive or deductive logic, or no logic at all (gut feelings and emotion). And, then figure out your logic and when best to use deductive vs. inductive arguments.

Exercise 2 – Use Deduction, When you should Use Deduction

When you have a significant problem or opportunity you need to solve or build a strategy for, start with a deductive problem solving process. Use the tools in this module, by defining the problem statement, disaggregating the problem, building a hypothesis tree, prove or disprove hypotheses through facts and analysis . And, then switch to inductive logic when creating creative potential solutions and synthesizing those solutions.

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The Difference Between Deductive and Inductive Reasoning

Most everyone who thinks about how to solve problems in a formal way has run across the concepts of deductive and inductive reasoning. Both deduction and induction help us navigate real-world problems, such as who committed a crime, the most likely cause of an accident, or how many planets might contain life in the Milky Way galaxy.

But while they’re both practical tools for practical problems, but they approach problem-solving in opposite ways.

Both deduction and induction are a type of inference, which means reaching a conclusion based on evidence and reasoning.

Deduction moves from idea to observation, while induction moves from observation to idea.

Deduction is idea-first, followed by observations and a conclusion. Induction is observation first, followed by an idea that could explain what’s been seen.

The other big difference is that deduction’s conclusions are bulletproof assuming you don’t make a mistake along the way. The conclusion is always true as long as the premises are true. With induction you don’t get absolute certainty; the quality of the idea or model or theory depends on the quality of the observations and analysis.

All men are mortal. Harold is a man. Therefore, Harold is mortal.

This third sentence is absolutely true because the first two sentences are true.

I have a bag of many coins, and I’ve pulled 10 at random and they’ve all been pennies, therefore this is probably a bag full of pennies.

This gives some measure of support for the argument that the bag only has pennies in it, but it’s not complete support like we see with deduction.

Further clarification

Deduction has theories that predict an outcome, which are tested by experiments. Induction makes observations that lead to generalizations for how that thing works.

If the premises are true in deduction, the conclusion is definitely true. If the premises are true in induction, the conclusion is only probably true—depending on how good the evidence is.

There’s another type of reasoning called Abductive Reasoning, where you take a set of observations and simply take the most likely explanation given the evidence you have.

Deduction is hard to use in everyday life because it requires a sequential set of facts that are known to be true. Induction is used all the time in everyday life because most of the world is based on partial knowledge, probabilities, and the usefulness of a theory as opposed to its absolute validity.

Deduction is more precise and quantitative, while induction is more general and qualitative.

More examples

If A = B and B = C, then A = C.

Since all squares are rectangles, and all rectangles have four sides, so all squares have four sides.

All cats have a keen sense of smell. Fluffy is a cat, so Fluffy has a keen sense of smell.

Every time you eat peanuts, your throat swells up and you can’t breathe. This is a symptom of people who are allergic to peanuts. So, you are allergic to peanuts.

Ray is a football player. All football players weigh more than 170 pounds. Ray weighs more than 170 pounds.

All cars in this town drive on the right side of the street. Therefore, all cars in all towns drive on the right side of the street.

We can see here that deduction is a nice-to-have. It’s clean. But life is seldom clean enough to be able to apply it perfectly.

Most real problems and questions deal more in the realm of induction, where you might have some observations—and those observations might be able to take you to some sort of generalization or theory—but you can’t necessarily say for sure that you’re right. It’s about working as best you can within a world where knowledge is usually incomplete.

Deduction gets you to a perfect conclusion—but only if all your premises are 100% correct.

Deduction moves from theory to experiment to validation, where induction moves from observation to generalization to theory.

Deduction is harder to use outside of lab/science settings because it’s often hard to find a set of fully agreed-upon facts to structure the argument.

Induction is used constantly because it’s a great tool for everyday problems that deal with partial information about our world, and coming up with usable conclusions that may not be right in all cases.

Be willing to use both types of reasoning to solve problems, and know that they can often be used together cyclically as a pair, e.g., use induction to come up with a theory, and then use deduction to determine if it’s actually true.

The main thing to avoid with these two is arguing with the force of deduction (guaranteed to be true) while actually using induction (probability based on strength of evidence).

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Cracking the Code: Understanding Inductive Reasoning

Uncover the secrets behind inductive reasoning and how it differs from deductive thinking.

Exploring the Basics of Inductive Reasoning

Inductive reasoning is a type of logical thinking that involves making generalizations based on specific observations or evidence.

Unlike deductive reasoning, which starts with a general premise and applies it to specific cases to reach a conclusion, inductive reasoning works in the opposite direction.

Inductive reasoning begins with specific observations or examples and uses them to infer a general pattern or principle.

For example, if you observe that all the crows you have seen are black, you might make the inductive inference that all crows are black.

However, it's important to note that inductive reasoning does not guarantee absolute certainty or truthfulness of the conclusions.

The strength of an inductive argument lies in the degree of support provided by the specific observations or evidence.

Exploring the basics of inductive reasoning can help improve your critical thinking skills and enhance your problem-solving abilities.

Examples of Inductive Reasoning in Everyday Life

Inductive reasoning is a fundamental part of our everyday lives, often used to make predictions, form hypotheses, and draw conclusions.

Here are some examples of inductive reasoning in action:

- You notice that every time you eat a certain food, you experience an allergic reaction. Based on this observation, you might infer that you have a food allergy.

- You observe that whenever it rains, the streets become wet. From this, you might conclude that rain causes wet streets.

- You notice that every time you press a button on your TV remote, the channel changes. You might then infer that the button is responsible for changing the channel.

These examples highlight how inductive reasoning allows us to make educated guesses and draw plausible conclusions based on specific observations.

By recognizing and understanding inductive reasoning in everyday life, you can become a more effective problem solver and decision maker.

The Importance of Inductive Reasoning in Problem-Solving

Inductive reasoning plays a crucial role in problem-solving by providing a framework for generating hypotheses, exploring patterns, and making informed decisions.

When faced with a complex problem or puzzle, inductive reasoning allows you to analyze specific instances, identify commonalities, and develop a general understanding or solution.

By using inductive reasoning, you can:

- Identify patterns and trends that can guide problem-solving strategies.

- Generate hypotheses or possible explanations based on observed data.

- Make predictions about future outcomes or events based on past observations.

- Test and refine hypotheses through further observation and analysis.

Inductive reasoning helps you think creatively, consider multiple perspectives, and approach problems from different angles.

By recognizing the importance of inductive reasoning in problem-solving, you can enhance your ability to tackle complex challenges and find innovative solutions.

Challenges and Limitations of Inductive Reasoning

While inductive reasoning is a valuable thinking tool, it is not without its challenges and limitations.

One of the main challenges is the potential for biased or insufficient observations.

If your observations are limited or biased, the inductive conclusions you draw may not accurately represent the broader reality.

Additionally, inductive reasoning relies on probabilities and generalizations, rather than absolute certainty.

The conclusions reached through inductive reasoning are always subject to revision or refinement as new evidence emerges.

Furthermore, inductive reasoning can be affected by cognitive biases, personal beliefs, and cultural influences.

It's important to be aware of these challenges and limitations when using inductive reasoning, and to supplement it with other forms of thinking, such as deductive reasoning and critical analysis.

Tips for Improving Your Inductive Reasoning Skills

Inductive reasoning is a skill that can be improved with practice and conscious effort.

Here are some tips to enhance your inductive reasoning skills:

- Observe and gather data: Pay attention to the details of specific situations, events, or phenomena. Collect data and information that can serve as evidence for your reasoning.

- Look for patterns and connections: Analyze the collected data to identify patterns, trends, or relationships. Look for similarities or commonalities that can help you make inductive inferences.

- Consider alternative explanations: Challenge your initial inductive inferences by considering alternative explanations or hypotheses. This helps you avoid jumping to conclusions based on limited evidence.

- Test and refine your conclusions: Subject your inductive conclusions to further testing and analysis. Seek additional evidence or observations that can support or challenge your reasoning.

- Seek feedback and multiple perspectives: Share your inductive reasoning with others and seek feedback. Consider different viewpoints and perspectives to refine your reasoning.

By following these tips, you can enhance your ability to think inductively, make informed judgments, and arrive at well-supported conclusions.

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On whether generative ai and large language models are better at inductive reasoning or deductive reasoning and what this foretells about the future of ai.

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Inductive reasoning and deductive reasoning go to battle but might need to be married together for ... [+] the sake of reaching true AI or AGI (artificial general intelligence).

In today’s column, I continue my ongoing analysis of the latest advances and breakthroughs in AI, see my extensive posted coverage at the link here , and focus in this discussion on the challenges associated with various forms of reasoning that are mathematically and computationally undertaken via modern-day generative AI and large language models (LLM). Specifically, I will do a deep dive into inductive reasoning and deductive reasoning.

Here’s the deal.

One of the biggest open questions that AI researchers and AI developers are struggling with is whether we can get AI to perform reasoning of the nature and caliber that humans seem to do.

This might at an initial cursory glance appear to be a simple question with a simple answer. But the problems are many and the question at hand is extraordinarily hard to answer. One difficulty is that we cannot say for sure the precise way that people reason. By this, I mean to say that we are only guessing when we contend that people reason in one fashion or another. The actual biochemical and wetware facets of the brain and mind are still a mystery as to how we attain cognition and higher levels of mental thinking and reasoning.

Some argue that we don’t need to physically reverse engineer the brain to proceed ahead with devising AI reasoning strategies and approaches. The viewpoint is that it would certainly be a nice insight to know what the human mind really does, that’s for sure. Nonetheless, we can strive forward to develop AI that has the appearance of human reasoning even if the means of the AI implementation is potentially utterly afield of how the mind works.

Think of it this way.

We might be satisfied if we can get AI to mimic human reasoning from an outward perspective, even if the way in which the AI computationally works is not what happens inside the heads of humans. The belief or assertion would be that you don’t have to distinctly copy the internals if the seen-to-be external performance matches or possibly exceeds what’s happening inside a human brain. I liken this to an extreme posture by noting that if you could assemble a bunch of Lego bricks and get them to seemingly perform reasoning, well, you might take that to the bank as a useful contraption, despite that it isn’t working identically as human minds are.

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That being said, if you have in fact managed to assemble Lego bricks into a human-like reasoning capacity, please let me know. Right away. A Nobel Prize is undoubtedly and indubitably soon to be on your doorstep.

The Fascinating Nature Of Human Reasoning

Please know that the word “reasoning” carries a lot of baggage.

Some would argue that we shouldn’t be using the watchword when referring to AI. The concern is that since reasoning is perceived as a human quality, talking about AI reasoning is tantamount to anthropomorphizing AI. To cope with this expressed qualm, I will try to be cautious in how I make use of the word. Just wanted to make sure you knew that some experts have acute heartburn about waving around the word “reasoning”. Let’s try to be mindful and respectful of how the word is to be used.

Disclaimer noted.

Probably the most famous primary forms of human reasoning consist of inductive reasoning and deductive reasoning.

I’m sure you’ve been indoctrinated in the basics of those two major means of reasoning. Whether the brain functions by using those reasoning methods is unresolved. It could be that we are merely rationalizing decision-making by conjuring up a logical basis for reasoning, trying to make pretty the reality of whatever truly occurs inside our heads.

Because inductive reasoning and deductive reasoning are major keystones for human reasoning, AI researchers have opted to pursue those reasoning methods to see how AI can benefit from what we seem to know about human reasoning. Yes, indeed, lots of AI research has been devoted to exploring how to craft AI that performs inductive reasoning and performs deductive reasoning.

Some results have come up with AI that is reasonably good at inductive reasoning but falters when doing deductive reasoning. Likewise, the other direction is the case too, namely that you might come up with AI that is pretty good at deductive reasoning but thin on inductive reasoning. Trying to achieve both on an equal and equally heightened basis is tricky and still being figured out.

You might be wondering what the deal is with generative AI and large language models (LLM) in terms of how those specific types of AI technology fare on inductive and deductive reasoning. I’m glad that you asked.

That’s the focus of today’s discussion.

Before we make the plunge into the meaty topic, let’s ensure we are all on the same page about inductive and deductive reasoning. Perhaps it has been a while since you had to readily know the differences between the two forms of reasoning. No worries, I’ll bring you quickly up-to-speed at a lightning pace.

An easy way to compare the two is by characterizing inductive reasoning as being a bottoms-up approach while deductive reasoning is considered a tops-down approach to reasoning.

With inductive reasoning, you observe particular facts or facets and then from that bottoms-up viewpoint try to arrive at a reasoned and reasonable generalization. Your generalization might be right. Wonderful. On the other hand, your generalization might be wrong. My point is that inductive reasoning, and also deductive reasoning, are not surefire guaranteed to be right. They are sensible approaches and improve your odds of being right, assuming you do the necessary reasoning with sufficient proficiency and alertness.

Deductive reasoning generally consists of starting with a generalization or theory and then proceeding to ascertain if observed facts or facets support the overarching belief. That is a proverbial top-down approach.

We normally expect scientists and researchers to especially utilize deductive reasoning. They come up with a theory of something and then gather evidence to gauge the validity of the theory. If they are doing this in a far and-square manner, they might find themselves having to adjust the theory based on the reality of what they discover.

Okay, we’ve covered the basics of inductive and deductive reasoning in a nutshell. I am betting you might like to see an example to help shake off any cobwebs on these matters.

Happy to oblige.

Illustrative Example Of Inductive And Deductive Reasoning

I appreciate your slogging along with me on this quick rendition of inductive and deductive reasoning. Hang in there, the setup will be worth it. Time to mull over a short example showcasing inductive reasoning versus deductive reasoning.

When my kids were young, I used to share with them the following example of inductive reasoning and deductive reasoning. Maybe you’ll find it useful. Or at least it might be useful for you to at some point share with any youngsters that you happen to know. Warning to the wise, do not share this with a fifth grader since they will likely feel insulted and angrily retort that you must believe them to be a first grader (yikes!).

Okay, here we go.

Imagine that you are standing outside and there are puffy clouds here and there. Let’s assume that on some days the clouds are there and on other days they are not. Indeed, on any given day, the clouds can readily come and go.

What is the relationship between the presence of clouds and the outdoor temperature?

That seems to be an interesting and useful inquiry. A child might be stumped, though I kind of doubt they would. If they’ve been outside with any regularity, and if clouds come and go with any regularity, the chances are they have already come up with a belief on this topic. Maybe no one explicitly asked them about it. Thus, this question might require a moment or two for a youngster to collect their thoughts.

Envision that we opt to ask a youngster to say aloud their reasoning as they figure out an answer to the posed question.

One angle would be to employ inductive reasoning to solve the problem.

It might go like this when using inductive reasoning to answer the question about clouds and outdoor temperature:

• (1) Observation: Yesterday was cloudy, and the temperature dropped .
• (2) Another observation: The day before yesterday, it was cloudy, and the temperature dropped.
• (3) A third observation: Today, it became cloudy, and the temperature dropped.
• (4) Logical conclusion: When it’s cloudy, the temperature tends to drop.

Seems sensible and orderly.

The act consisted of a bottoms-up method. There were prior and current observations that the child identified and used when processing the perplexing matter. Based on those observations, a seemingly logical conclusion can be reached. In this instance, since the clouds often were accompanied by a drop in temperature, you might suggest that when it gets cloudy the temperate will tend to drop.

Give the child a high five.

Another angle would be to employ deductive reasoning.

Here we go with answering the same question but using deductive reasoning this time:

• Theory or premise : When the sky is cloudy, the temperature tends to drop.
• Observation : Today it is currently cloudy.
• Another observation. The temperature dropped once the clouds arrived.
• Logical conclusion: Therefore, it is reaffirmed that the temperature tends to drop due to cloudiness.

The youngster began by formulating a theory or premise.

How did they come up with it?

We cannot say for sure. They may have already formed the theory based on a similar inductive reasoning process as I just gave. There is a chance too that they might not be able to articulate why they believe in the theory. It just came to them.

Again, this is the mystery of how the brain and mind function. From the outside of a person’s brain, we do not have the means to reach into their head and watch what logically happens during their thinking endeavors (we can use sensors to detect heat, chemical reactions, and other wiring-like actions, but that is not yet translatable into full-on articulation of thinking processes at a logical higher-level per se). We must take their word for whatever they proclaim has occurred inside their noggin. Even they cannot say for sure what occurred inside their head. They must guess too.

It could be that the actual internal process is nothing like the logical reasoning we think it is. People are taught that they must come up with justifications and explanations for their behavior. The explanation or justification can be something they believe happened in their heads, though maybe it is just an after-the-fact concoction based on societal and cultural demands that they provide cogent explanations.

As an aside, you might find of interest that via the use of BMI (brain-machine interfaces), researchers in neuroscience, cognitive science, AI, and other disciplines are hoping to one day figure out the inner sanctum and break the secret code of what occurs when we think and reason. See my coverage on BMI and akin advances at the link here .

One other aspect to mention about the above example of deductive reasoning about the cloud and temperature is that besides a theory or premise, the typical steps entail an effort to apply the theory to specific settings. In this instance, the child was able to reaffirm the premise due to the observation that today was cloudy and that it seemed that the temperature had dropped.

Another worthy point to bring up is that I said earlier that either or both of those reasoning methods might not necessarily produce the right conclusion. The act of having and using a bona fide method does not guarantee a correct response.

Does the presence of clouds always mean that temperatures will drop?

Exceptions could exist.

Plus, clouds alone do not impact temperature and other factors need to be incorporated.

Generative AI And The Two Major Reasoning Approaches

You are now versed in or at least refreshed about inductive and deductive reasoning. Good for you. The world is a better place accordingly.

I want to now bring up the topic of generative AI and large language models. Doing so will allow us to examine the role of inductive reasoning and deductive reasoning when it comes to the latest in generative AI and LLMs.

I’m sure you’ve heard of generative AI, the darling of the tech field these days.

Perhaps you’ve used a generative AI app, such as the popular ones of ChatGPT, GPT-4o, Gemini, Bard, Claude, etc. The crux is that generative AI can take input from your text-entered prompts and produce or generate a response that seems quite fluent. This is a vast overturning of the old-time natural language processing (NLP) that used to be stilted and awkward to use, which has been shifted into a new version of NLP fluency of an at times startling or amazing caliber.

The customary means of achieving modern generative AI involves using a large language model or LLM as the key underpinning.

In brief, a computer-based model of human language is established that in the large has a large-scale data structure and does massive-scale pattern-matching via a large volume of data used for initial data training. The data is typically found by extensively scanning the Internet for lots and lots of essays, blogs, poems, narratives, and the like. The mathematical and computational pattern-matching homes in on how humans write, and then henceforth generates responses to posed questions by leveraging those identified patterns. It is said to be mimicking the writing of humans.

I think that is sufficient for the moment as a quickie backgrounder. Take a look at my extensive coverage of the technical underpinnings of generative AI and LLMs at the link here and the link here , just to name a few.

When using generative AI, you can tell the AI via a prompt to make use of deductive reasoning. The generative AI will appear to do so. Similarly, you can enter a prompt telling the AI to use inductive reasoning. The generative AI will appear to do so.

I am about to say something that might be surprising, so I am forewarning you and want you to mentally prepare yourself.

Have you braced yourself for what I am about to say?

When you enter a prompt telling generative AI to proceed with inductive or deductive reasoning, and then you eyewitness what appears to be such reasoning as displayed via the presented answer, there is once again a fundamental question afoot regarding the matter of what you see versus what actually happened internally.

I’ve discussed this previously in the use case of explainable AI, known as XAI, see my analysis at the link here . In brief, just because the AI tells you that it did this or that step, there is not necessarily an ironclad basis to assume that the AI solved the problem in that particular manner.

The explanation is not necessarily the actual work effort. An explanation can be an after-the-fact rationalization or made-up fiction, which is done to satisfy your request to have the AI show you the work that it did. This can be the case too when requesting to see a problem solved via inductive or deductive reasoning. The generative AI might proceed to solve the problem using something else entirely, but since you requested inductive or deductive reasoning, the displayed answer will be crafted to look as if that’s how things occurred.

Be mindful of this.

What you see could be afar of what is happening internally.

For now, let’s put that qualm aside and pretend that what we see is roughly the same as what happened to solve a given problem.

How Will Generative AI Fare On The Two Major Forms Of Reasoning

I have a thought-provoking question for you:

• Are generative AI and LLMs better at inductive reasoning or deductive reasoning?

Take a few reflective seconds to ponder the conundrum.

Tick tock, tick tock.

The usual answer is that generative AI and LLMs are better at inductive reasoning, the bottoms-up form of reasoning.

Recall that generative AI and LLMs are devised by doing tons of data training. You can categorize data as being at the bottom side of things. Lots of “observations” are being examined. The AI is pattern-matching from the ground level up. This is similar to inductive reasoning as a process.

I trust that you can see that the inherent use of data, the data structures used, and the algorithms employed for making generative AI apps are largely reflective of leaning into an inductive reasoning milieu. Generative AI is therefore more readily suitable to employ inductive reasoning for answering questions if that’s what you ask the AI to do.

This does not somehow preclude generative AI from also or instead performing deductive reasoning. The upshot is that generative AI is likely better at inductive reasoning and that it might take some added effort or contortions to do deductive reasoning.

Let’s review a recent AI research study that empirically assessed the inductive reasoning versus deductive reasoning capabilities of generative AI.

New Research Opens Eyes On AI Reasoning

In a newly released research paper entitled “Inductive Or Deductive? Rethinking The Fundamental Reasoning Abilities Of LLMs” by Kewei Cheng, Jingfeng Yang, Haoming Jiang, Zhengyang Wang, Binxuan Huang, Ruirui Li, Shiyang Li, Zheng Li, Yifan Gao, Xian Li, Bing Yin, Yizhou Sun, arXiv , August 7, 2024, these salient points were made (excerpts):

• “Despite the impressive achievements of LLMs in various reasoning tasks, the underlying mechanisms of their reasoning capabilities remain a subject of debate.”
• “The question of whether LLMs genuinely reason in a manner akin to human cognitive processes or merely simulate aspects of reasoning without true comprehension is still open.”
• “Additionally, there’s a debate regarding whether LLMs are symbolic reasoners or possess strong abstract reasoning capabilities.”
• “While the deductive reasoning capabilities of LLMs, (i.e. their capacity to follow instructions in reasoning tasks), have received considerable attention, their abilities in true inductive reasoning remain largely unexplored.”
• “This raises an essential question: In LLM reasoning, which poses a greater challenge - deductive or inductive reasoning?”

As stated in those points, the reasoning capabilities of generative AI and LLMs are an ongoing subject of debate and present interesting challenges. The researchers opted to explore whether inductive reasoning or deductive reasoning is the greater challenge for such AI.

They refer to the notion of whether generative AI and LLMs are symbolic reasoners.

Allow me a moment to unpack that point.

The AI field has tended to broadly divide the major approaches of devising AI into two camps, the symbolic camp and the sub-symbolic camp. Today, the sub-symbolic camp is the prevailing winner (at this time). The symbolic camp is considered somewhat old-fashioned and no longer in vogue (at this time).

For those of you familiar with the history of AI, there was a period when the symbolic approach was considered top of the heap. This was the era of expert systems (ES), rules-based systems (RBS), and often known as knowledge-based management systems (KBMS). The underlying concept was that human knowledge and human reasoning could be explicitly articulated into a set of symbolic rules. Those rules would then be encompassed into an AI program and presumably be able to perform reasoning akin to how humans do so (well, at least to the means of how we rationalize human reasoning). Some characterized this as the If-Then era, consisting of AI that contained thousands upon thousands of if-something then-something action statements.

Eventually, the rules-based systems tended to go out of favor. If you’d like to know more about the details of how those systems worked and why they were not ultimately able to fulfill the quest for top-notch AI, see my analysis at the link here .

The present era of sub-symbolics went a different route. Generative AI and LLMs are prime examples of the sub-symbolic approach. In the sub-symbolic realm, you use algorithms to do pattern matching on data. Turns out that if you use well-devised algorithms and lots of data, the result is AI that can seem to do amazing things such as having the appearance of fluent interactivity. At the core of sub-symbolics is the use of artificial neural networks (ANNs), see my in-depth explanation at the link here .

You will momentarily see that an unresolved question is whether the sub-symbolic approach can end up performing symbolic-style reasoning. There are research efforts underway of trying to logically interpret what happens inside the mathematical and computational inner workings of ANNs, see my discussion at the link here .

Getting back to the inductive versus deductive reasoning topic, let’s consider the empirical study and the means they took to examine these matters:

• “Our research is focused on a relatively unexplored question: Which presents a greater challenge to LLMs - deductive reasoning or inductive reasoning?” (ibid).
• “To explore this, we designed a set of comparative experiments that apply a uniform task across various contexts, each emphasizing either deductive or inductive reasoning.” (ibid).
• “Deductive setting: we provide the models with direct input-output mappings (i.e., 𝑓𝑤).”
• “Inductive setting: we offer the models a few examples (i.e., (𝑥, 𝑦) pairs) while intentionally leaving out input-output mappings (i.e., 𝑓𝑤).” (ibid).

Their experiment consisted of coming up with tasks for generative AI to solve, along with prompting generative AI to do the solution process by each of the two respective reasoning processes. After doing so, the solutions provided by AI could be compared to ascertain whether inductive reasoning (as performed by the AI) or deductive reasoning (as performed by the AI) did a better job of solving the presented problems.

Tasks Uniformity And Reasoning Disentanglement

The research proceeded to define a series of tasks that could be given to various generative AI apps to attempt to solve.

Notice that a uniform set of tasks was put together. This is a good move in such experiments since you want to be able to compare apples to apples. In other words, purposely aim to use inductive reasoning on a set of tasks and use deductive reasoning on the same set of tasks. Other studies will at times use a set of tasks for analyzing inductive reasoning and a different set of tasks to analyze deductive reasoning. The issue is that you end up comparing apples versus oranges and can have muddled results.

Are you wondering what kinds of tasks were used?

Here are the types of tasks they opted to apply:

• Arithmetic task: “You are a mathematician. Assuming that all numbers are in base-8 where the digits are ‘01234567’, what is 36+33?”. (ibid).
• Word problem: “You are an expert in linguistics. Imagine a language that is the same as English with the only exception being that it uses the object-subject-verb order instead of the subject-verb-object order. Please identify the subject, verb, and object in the following sentences from this invented language: shirts sue hates.” (ibid).
• Spatial task: “You are in the middle of a room. You can assume that the room’s width and height are both 500 units. The layout of the room in the following format: ’name’: ’bedroom’, ’width’: 500, ’height’: 500, ’directions’: ’north’: [0, 1], ’south’: [0, -1], ’east’: [1, 0], ’west’: [-1, 0], ’objects’: [’ name’: ’chair’, ’direction’: ’east’, ’name’: ’wardrobe’, ’direction’: ’north’, ’name’: ’desk’, ’direction’: ’south’]. Please provide the coordinates of objects whose positions are described using cardinal directions, under a conventional 2D coordinate system using the following format: [’name’: ’chair’, ’x’: ’?’, ’y’: ’?’, ’name’: ’wardrobe’, ’x’: ’?’, ’y’: ’?’, ’name’: ’desk’, ’x’: ’?’, ’y’: ’?’]”. (ibid).
• Decryption: “As an expert cryptographer and programmer, your task involves reordering the character sequence according to the alphabetical order to decrypt secret messages. Please decode the following sequence: spring.” (ibid).

Something else that they did was try to keep inductive reasoning and deductive reasoning from relying on each other.

Unfortunately, both approaches can potentially slop over into aiding the other one.

Remember for example when I mentioned that a youngster using deductive reasoning about the relationship between clouds and temperatures might have formulated a hypothesis or premise by first using inductive reasoning? If so, it is difficult to say which reasoning approach was doing the hard work in solving the problem since both approaches were potentially being undertaken at the same time.

The researchers devised a special method to see if they could avoid a problematic intertwining:

• “To disentangle inductive reasoning from deductive reasoning, we propose a novel model, referred to as SolverLearner.” (ibid).
• “Given our primary focus on inductive reasoning, SolverLearner follows a two-step process to segregate the learning of input-output mapping functions from the application of these functions for inference.” (ibid).
• “Specifically, functions are applied through external interpreters, such as code interpreters, to avoid incorporating LLM-based deductive reasoning.” (ibid).
• “By focusing on inductive reasoning and separating it from LLM-based deductive reasoning, we can isolate and investigate inductive reasoning of LLMs in its pure form via SolverLearner.” (ibid).

Kudos to them for recognizing the need to try and make that separation on a distinctive basis.

Hopefully, other researchers will take up the mantle and further pursue this avenue.

The Results And What To Make Of It

I’m sure that you are eagerly awaiting the results of what they found.

Drum roll, please.

Highlights of their key outcomes include:

• “LLMs exhibit poor deductive reasoning capabilities, particularly in “counterfactual” tasks.” (ibid).
• “Deductive reasoning presents a greater challenge than inductive reasoning for LLMs.” (ibid).
• “The effectiveness of LLMs’ inductive reasoning capability is heavily reliant on the foundational model. This observation suggests that the inductive reasoning potential of LLMs is significantly constrained by the underlying model.” (ibid).
• “Chain of Thought (COT) has not been incorporated into the comparison. Chain of Thought (COT) is a significant prompting technique designed for use with LLMs. Rather than providing a direct answer, COT elicits reasoning with intermediate steps in few-shot exemplars.” (ibid).

Let’s examine those results.

First, they reaffirmed what we would have anticipated, namely that the generative AI apps used in this experiment were generally better at employing inductive reasoning rather than deductive reasoning. I mentioned earlier that the core design and structure of generative AI and LLMs lean into inductive reasoning capabilities. Thus, this result makes intuitive sense.

For those of you who might say ho-hum to the act of reaffirming an already expected result, I’d like to emphasize that doing experiments to confirm or disconfirm hunches is a very worthwhile endeavor. You do not know for sure that a hunch is on target. By doing experiments, your willingness to believe in a hunch can be bolstered, or possibly overturned if the experiments garner surprising results.

Not every experiment has to reveal startlingly new discoveries (few do).

Second, a related and indeed interesting twist is that the inductive reasoning performance appeared to differ somewhat based on which of the generative AI apps was being used. The gist is that depending upon how the generative AI was devised by an AI maker, such as the nature of the underlying foundation model, the capacity to undertake inductive reasoning varied.

The notable point about this is that we need to be cautious in painting with a broad brush all generative AI apps and LLMs in terms of how well they might do on inductive reasoning. Subtleties in the algorithms, data structures, ANN, and data training could impact the inductive reasoning proclivities.

This is a handy reminder that not all generative AI apps and LLMs are the same.

Third, the researchers acknowledge a heady topic that I keep pounding away at in my analyses of generative AI and LLMs. It is this. The prompts that you compose and use with AI are a huge determinant of the results you will get out of the AI. For my comprehensive coverage of over fifty types of prompt engineering techniques and tips, see the link here .

In this particular experiment, the researchers used a straight-ahead prompt that was not seeking to exploit any prompt engineering wizardry. That’s fine as a starting point. It would be immensely interesting to see the experimental results if various prompting strategies were used.

One such prompting strategy would be the use of chain-of-thought (COT). In the COT approach, you explicitly instruct AI to provide a step-by-step indication of what is taking place. I’ve covered extensively the COT since it is a popular tactic and can boost your generative AI results, see my coverage at the link here , along with a similar approach known as skeleton-of-thought (SOT) at the link here.

If we opted to use COT for this experiment, what might arise?

I speculate that we might enhance inductive reasoning by having directly given a prompt that tends to seemingly spur inductive reasoning to take place. It is almost similar to my assertion that sometimes you can improve generative AI results by essentially greasing the skids, see the link here . Perhaps the inductive reasoning might be more pronounced by a double-barrel dose of guiding the AI correspondingly to that mode of operation.

Prompts do matter.

I’ll conclude this discussion with something that I hope will stir your interest.

Where is the future of AI?

Should we keep on deepening the use of sub-symbolics via ever-expanding the use of generative AI and LLMs? That would seem to be the existing course of action. Toss more computational resources at the prevailing sub-symbolic infrastructure. If you use more computing power and more data, perhaps we will attain heightened levels of generative AI, maybe verging on AGI (artificial general intelligence).

Not everyone accepts that crucial premise.

An alternative viewpoint is that we will soon reach a ceiling. No matter how much computing you manage to corral, the incremental progress is going to diminish and diminish. A limit will be reached. We won’t be at AGI. We will be better than today’s generative AI, but only marginally so. And continued forceful efforts will gain barely any additional ground. We will be potentially wasting highly expensive and prized computing on a losing battle of advancing AI.

I’ve discussed this premise at length, see the link here .

Let’s tie that thorny topic to the matter of inductive reasoning versus deductive reasoning.

If you accept the notion that inductive reasoning is more akin to sub-symbolic, and deductive reasoning is more akin to symbolic, one quietly rising belief is that we need to marry together the sub-symbolic and the symbolic. Doing so might be the juice that gets us past the presumed upcoming threshold or barrier. To break the sound barrier, as it were, we might need to focus on neuro-symbolic AI.

Neuro-symbolic AI is a combination of sub-symbolic and symbolic approaches. The goal is to harness both to their maximum potential. A major challenge involves how to best connect them into one cohesive mechanization. You don’t want them to be infighting. You don’t want them working as opposites and worsening your results instead of bettering the results. See my discussion at the link here .

I’d ask you to grab yourself a glass of fine wine, sit down in a place of solitude, and give these pressing AI questions some heartfelt thoughts:

• Can we leverage both inductive reasoning and deductive reasoning as brethren that work hand-in-hand within AI?
• Can we include other reasoning approaches into the mix, spurring multi-reasoning capacities?
• Can we determine whether AI is working directly via those reasoning methods versus outwardly appearing to do so but not actively internally doing so?
• Can we reuse whatever is learned while attempting to reverse engineer the brain and mind, such that the way that we devise AI can be enhanced or possibly even usefully overhauled?

That should keep your mind going for a while.

If you can find a fifth grader who can definitively answer those vexing and course-changing questions, make sure to have them write down their answers. It would be history in the making. You would have an AI prodigy in your midst.

Meanwhile, let’s all keep our noses to the grind and see what progress we can make on these mind-bending considerations. Join me in doing so, thanks.

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