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Logic Comes in Two Flavors

by Nathaniel Bluedorn

A Practical Introduction to Inductive and Deductive Reasoning

Through the ages, logicians have discovered two different types of reasoning: inductive reasoning and deductive reasoning. How these two differ lies at the heart of the philosophy of logic. I will attempt to show how these two ways of thinking are fundamentally different, and how both are useful in their own way.

Inductive Reasoning

Inductive reasoning is also called scientific reasoning. Since I'm a beekeeper, I will use an example with honey bees to explain what inductive reasoning is.

Honey bee hives are dying all across the country. This is an actual fact. I have experienced this in my own apiary. Let us suppose that the University of Illinois hired me to examine a thousand hives to see what was killing them. I observe that five hundred of these hives have varroa mites. However, the other five hundred hives do not have mites. I observe, in my very scientific way, that hives with mites usually die in a year, but hives without mites live. I conclude that varroa mites are killing honey bees.


Honey Bee with Varroa Mites

How did I form my argument? I had two groups of evidence:

1st Evidence: Most hives with mites die in one year.

2nd Evidence: Most hives without mites live.

. . . and a conclusion:

Conclusion: Mites kill hives.

If we assume that I was a good scientist, and my observations were correct, then, do I know for sure that my conclusion is true? No, something else might be killing the bees - a virus for instance - and mites are simply taking advantage of weak hives. But, barring my discovery of any new evidence, would you agree that the mites are probably killing the bees? We might be able to think of more experiments I could do to provide more evidence. Any new evidence could make my conclusion seem even more probable, or it might lead me to a different conclusion regarding what is killing the bees.

We might picture inductive reasoning as a police detective examining footprints around a crime scene, then making a good guess about where the criminal had gone. Or we might picture Mr. MacGregor seeing nibble marks on his lettuce leaves and concluding that Peter Rabbit had probably been in his garden again.

Technically, what is inductive reasoning? Inductive reasoning is the use of scientific principles to draw the most probable conclusion from evidence. Some methods of inductive reasoning are: Generalization, Mill's Methods for Experimental Inquiry, Hypothetical Scientific Reasoning, and the Laws of Probability.

Deductive Reasoning

Deductive reasoning is very different from inductive reasoning. It follows a different path. It begins from a different direction.

Suppose that I read an article in the American Bee Journal about the new varroa mite. The American Bee Journal says that if a beekeeper sees little red spots on his bees which look like varroa mites, then his hives will die within a year or two. Like a good beekeeper, I trust the ABJ. One day I visit my little apiary and I notice little red mites on the bees in my hives. In great anguish, I conclude that my bees have varroa mites, and my hives will die if I do not do something soon.

How did I form this argument? I began with two premises. These are statements which I know are true. These are the building blocks of a deductive argument.

1st Premise: If I see mites on my bees, then they will die.

2nd Premise: I see mites on my bees.

. . . my conclusion was:

Conclusion: Therefore, my bees will die.

Assuming that my premises are correct, do I know for sure that my conclusion is true? Yes, there are no other possibilities. If it is true that "if I see mites on my bees, then they will die," and if it is true that "I see mites on my bees," then the only possibility is that "they will die." However, with a valid deductive argument, the argument is only as sound as its premises. When the premises are true, then the conclusion follows necessarily. A necessary conclusion is called a deductive conclusion.

This time Mr. MacGregor sees Peter Rabbit scuttle under the fence of his garden. Mr. MacGregor knows that every time Peter Rabbit is in his garden, he always eats all his lettuce. Therefore, Mr. MacGregor resignedly walks to the shed for more lettuce seed. He knows for certain that he needs to replant his lettuce. As Sherlock Holmes would say, "Brilliant deduction, Dr. Watson."

With inductive reasoning we wanted to find probability, but with deductive reasoning we are seeking certainty. But to find certainty, we must begin with assumptions - these are the premises of our argument. Technically, what is deductive reasoning? Deductive reasoning is the use of necessary inference to draw sure conclusions from premises. Two methods of deductive reasoning are: Traditional Aristotelian Logic (Categorical Syllogisms), and Modern Symbolic Logic.

Comparing these two types of reasoning: inductive reasoning starts with many pieces of evidence and comes up with a probable conclusion, while deductive reasoning begins with a few trustworthy statements and ends with a necessary conclusion.

Reasoning with the Bible

Let us look at examples of reasoning using the Bible. First, inductive reasoning using evidence I found in Genesis:

1st Evidence: God created Adam.

2nd Evidence: God created the moon and the stars.

3rd Evidence: God created the oceans.

4th Evidence: God created insects, like the locust and the caterpillar.

5th Evidence: God created big animals like elephants, and little ones like the mouse.

Conclusion: God probably created me too.

Do I know for sure that my conclusion is true? How do I know that Zeus or some other pagan god did not create me when I was born? I have not logically excluded that possibility. Logicians know that inductive reasoning can never prove anything for sure.

But inductive reasoning is not useless. If it were not for inductive reasoning, you would not be reading this. Paper and ink would not have been invented. Developments in our understanding of inductive reasoning have made possible the spectacular advances of modern science and technology.

Also, you use inductive reasoning on an everyday basis. You made judgments based on probability in order to fry an egg for breakfast. You know from past experience that when you crack an egg something gooey plops out on the frying pan and starts to sputter. After a while, that gooey stuff turns hard and it tastes good when you put it into your mouth. However, you can't prove that you will never meet an egg which will act differently. But everyone thinks that eggs will probably continue to be good for breakfast.

Now let us see if deductive reasoning using the Bible can prove something:

1st Premise: The Bible says God created all things – John 1:3.

2nd Premise: I am a thing – We'll assume this is true.

Conclusion: Therefore, God created me.

This form of deductive argument is called a syllogism.

The issue of abortion provides another example of deductive Bible reasoning. The Bible nowhere explicitly says that abortion is wrong, but we can prove that it is wrong by putting two and two together. Here are some statements which we can derive from the Bible:

Murdering a living person is sin. – Exodus 20:13. Matthew 19:18.

To unlawfully kill a person with premeditation is murder. – Deuteronomy 19:4, 11.

Pre-born children are living persons. – Jeremiah 1:5; Luke 1:41.

Abortion is killing a living pre-born child. This is the definition of abortion.

Therefore, abortion is murder and a sin.

Do I know my conclusion for sure? Yes, each point in this argument builds on the last point until we come to the conclusion which has been necessarily deduced from the premises. This is an example of deductive reasoning from the Bible. The only prerequisite for agreeing with this argument is that a person must believe the Bible. All the premises come from the Bible, or from the definition of abortion. Only those who do not believe the Bible could disagree with the conclusion.

How to Tell them Apart

There are a few ways of telling an inductive argument from a deductive argument. Here is one simple test which often works:

If an argument can be made more convincing by adding more evidence, then it is an inductive argument. If we discovered more evidence about how varroa mites kill honey bees, then our argument that mites are killing hives would seem even stronger.

On the other hand, if an argument cannot be improved by adding more to it, then it is a deductive argument. If we found a hundred more Bible verses which said that God created all things, that would not make the conclusion that God created me any more true. Once a sound deductive argument is made, nothing can make it better. Someone may be able to state the argument in clearer terms, but none of the reasoning changes.

Uses of Deductive and Inductive Reasoning

Both forms of logical reasoning are useful in their own way. Inductive reasoning has energized the developments of modern science and technology, such as discoveries about how to treat honey bees for varroa mites. We use this type of reasoning to make practical choices in our life, such as which washing machine to buy, or how to get rid of a headache.

Deductive reasoning is useful for proving things for sure - prove your doctrines from the Bible.

These [of Berea] were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so. Therefore many of them believed . . . – Acts 17:10-12.

Prove all things; hold fast that which is good. – 1 Thessalonians 5:21.

The simple believeth every word: but the prudent man looketh well to his going. – Proverbs 14:15.

Inductive reasoning is useful, deductive reasoning is indispensable. And as you can see, logic is about raising our standards of thinking.

Learn More

There is much more to learn about inductive and deductive reasoning which cannot be said in one little article. For instance, there are types of inductive reasoning other than what I have described here, which we use all the time. And do you know how to quickly detect errors in a deductive argument using circle diagrams? To learn more about inductive and deductive reasoning, study the materials which I recommend in my article, Suggested Course of Study for Learning Logic at Home.

Copyright September 01, 2000, all rights reserved. 23879 views


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