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Basics of reasoning: deduction, validity, and soundness.

Updated on July 23, 2012

Two types of reasoning.

Philosophy, and reasoning in general, is all about arguments. No, not the kinds of arguments you and your spouse have about whose responsibility it was to take the garbage out last night - a more specialized kind of argument. In philosophy, an argument is a line of reasoning that takes us from propositions called premises to a conclusion. In other words, you aren't allowed to just make any old claim you want; you have to be able to back that sucker up with solid premises, and how you get from those premises to your conclusion makes a world of difference.

There are two basic ways of reaching a conclusion from a set of premises: deduction and induction. Understanding the difference between these methods and knowing how to spot them is crucial to being able to argue well. This guide will provide a very basic overview of perhaps the more straightforward of the two: deductive reasoning. It may help you to become a better philosopher, but I can't promise it will help you win that argument about taking the trash out!

(Image credit: detail from Francesco Hayez's Aristotle, 1811)

What is deductive reasoning?

Let's start with the simpler process, deduction. Deductive arguments are those in which the conclusion necessarily follows from the premises. That's really all there is to them. For this reason, deduction is considered the most rigorous form of argument, and is used whenever possible. Let's have a look at some examples.

Premise: All cats have four paws.

Premise: My pet Boots is a cat.

Conclusion: Therefore, Boots has four paws.

The argument above presents a fairly straightforward deductive argument. Why is it deductive? Because the conclusion that Boots has four paws necessarily follows from the two premises, meaning if the premises are true the conclusion must be true. If Boots is a cat, and all cats have four paws, then Boots must have four paws. Anyone who accepts the premises must accept the conclusion unless they are raving mad; this is what makes deduction such a strong argumentative tool.

For extra super-duper clarification, let's check that argument out as a Venn diagram:

The first premise shows us that all cats belong to the larger set of things that have four paws. The second premise shows us that Boots belongs to the larger set of things that are cats. Therefore, we can construct the following diagram as our conclusion:

Because the circle representing Boots is contained completely within the circle representing four-pawed things, we can conclude that Boots indeed has four paws. That's deduction!

What is validity?

Astute readers may have noticed something strange about the above argument. What if a cat loses a leg in an accident? Aren't three-pawed cats still cats? Of course they are, and this brings us to an important distinction: validity. The above argument was valid, which means that if the premises are true, the conclusion must also be true. To illustrate the point, let's keep our deduction valid but make it a little more absurd:

Premise: All cats are made from cheese.

Premise: My pet Boots is a cat.

Conclusion: Therefore, Boots is made from cheese.

This argument is still a valid deductive argument. If cats are made from cheese, and if Boots is a cat, then Boots must be made from cheese. Validity is important, because it ensures that the conclusion can safely be made given the premises; in a sense, validity is the very test of whether an argument is properly deductive at all! For instance, check out the following argument that is not valid:

Premise: All cats have four paws.

Premise: My pet Boots has four paws.

Conclusion: Therefore, Boots is a cat.

At a glance, this argument may seem rock solid. I mean, all three of those propositions could very well be true. But returning to the Venn diagrams will show that there is something very wrong here:

All the premises above tell us is that both cats and Boots belong to the larger set of things that have four paws. As the above chart shows, however, this doesn't mean that the groups "cats" and "Boots" overlap. For example, Boots may have four paws because he is a dog. The lesson is this: at the very least, your deductive argument had better be valid.

What is soundness?

Of course, validity can't be the only thing that matters if it lets us construct arguments concluding that our pets are made from cheese. This brings us to a second distinction: soundness. A deductive argument is sound if it is valid and if all of its premises are true. Soundness is the ultimate mark of an excellent deduction; sound deductions are virtually watertight. To demonstrate, let's return to our original argument:

Premise: All cats have four paws.

Premise: My pet Boots is a cat.

Conclusion: Therefore, Boots has four paws.

We have already demonstrated that this argument is valid. To check if it is also sound, we examine each of its premises to see if they are true. Consider the first premise: "All cats have four paws." It seems we can shoot this proposition down pretty easily - we objected above that three-pawed cats have been excluded. Therefore, this is not a sound deduction. Even if Boots is indeed a cat, he may have only three paws, and thus he has slipped between the cracks of our premises and our conclusion is untrue. So let's have a look at a sound deduction:

Premise: All cats are mammals.

Premise: My pet Boots is a cat.

Conclusion: Therefore, Boots is a mammal.

If we examine each of our premises this time, we find them to be true (well, you'll just have to trust me that Boots is a cat). In fact, the first premise is a special kind of proposition called an analytic proposition, meaning it is true by definition. Being a mammal is part of the very definition of being a cat. This argument is both valid and sound!

Another pattern of deduction.

The examples above deal with only one particular pattern of deduction - specifically, they all deal in an object's properties (for example, having four paws or being made from cheese). Another major way to reason from one proposition to the next is through conditionals, meaning statements containing "if". For example, consider the following argument:

Premise: If it rains, the roof will leak.

Premise: If the roof leaks, my spouse will complain.

Conclusion: Therefore, if it rains, my spouse will complain.

Is this a deductive argument? To determine that, we need to see if the conclusion must follow once we accept the premises. Let's turn to our diagrams again:

The diagrams make it easier to trace the chain of events that emerges from our premises. It seems that this is in fact a deductive argument, and we can show this by constructing the following diagram as our conclusion:

From this chart we can see clearly that we can "cancel out" the middle term, therefore supporting our conclusion that my spouse will complain if it rains.

Avoiding ambiguities.

As a final note, I want to point out the monumental importance of precisely wording your arguments. For example, consider the argument below:

Premise: Every time I have observed it raining, the roof has leaked.

Premise: Every time I have observed the roof leaking, my spouse has complained.

Conclusion: Therefore, if it rains, my spouse will complain.

At a glance, this argument appears to be the same as the one above. But take a closer look. In this argument, we are specifically forming a conclusion based on past observations. This makes the argument inductive rather than deductive. We can tell the argument is not deductive because the conclusion does not necessarily follow from the premises. All our premises state is that we have observed complaining and leaking many times when it has rained. There is no logically necessary reason why we must then conclude that complaining always follows rain. Let's have a look at one last argument:

Premise: Every time it rains, the roof leaks.

Premise: Every time the roof leaks, my spouse complains.

Conclusion: Therefore, every time it rains, my spouse complains.

This argument is the weakest of the three wordings. In this form, our meaning is ambiguous. Those two premises look an awful lot like universal declarations, but in fact what we probably mean is that we have observed those pairs of occurrences many times. An argument of this form should either be reworded using conditionals, or fleshed out to clarify that the premises are based on past observations.

As a side note, in this case the inductive form of the argument should be preferred. If you advance an argument about your spouse complaining when it rains, your critics will know that you are basing that argument on past observations. They will be able to easily shoot down the argument using conditional statements, but will be more willing to accept your conclusion as a probable result if worded as an inductive argument.

Further reading.

If you're looking to do some further reading on the basic elements of reasoning, you can check out this entry in the Internet Encyclopedia of Philosophy. For a more in-depth look, I would suggest checking out the books below. Both of them cover the basics of premises and conclusions, and both go into some detail regarding deductive and inductive reasoning.

The Philosopher's Toolkit: A Compendium of Philosophical Concepts and Methods
The Philosopher's Toolkit: A Compendium of Philosophical Concepts and Methods

This book is incredibly accessible, and sets out the basics of reasoning in the simplest terms possible.

 
An Introduction to Philosophical Logic
An Introduction to Philosophical Logic

Grayling's book is a little heavier, but is still accessible for newcomers to philosophy. It gives a fuller and more nuanced account of deduction and induction than Baggini's book.

 

Did you know what deductive reasoning was before reading this page? Did I help you understand it? Your questions and comments are welcome!

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    • savateuse profile image

      savateuse 5 years ago

      My cat did indeed have three paws ;)

    • profile image

      anonymous 5 years ago

      Mu uncle always told me to never "follow blindly" the ideas of others. One needs to seek out the facts, the truths, the information on their own. One needs to test them and contemplate them, like you are showing how to do in this article. The best class I ever took in college was Aesthetics -- which I failed twice, exactly because I was always asking and testing and could never pin down what I believed. I was the hamster on the wheel, which was very frustrating. HOWEVER, my way of thinking changed dramatically and I'm much better for it. My writing is now more dimensional and I also approach problem-solving differently. Okay ... I'll shush now. Awesome article.

    • DrBillSmithWriter profile image

      William Leverne Smith 5 years ago from Hollister, MO

      I love the Venn diagrams! ;-)

    • Thrinsdream profile image

      Thrinsdream 5 years ago

      I think my cat may have been made from cheese! It is definitely one I have to read through again but another one understood and enjoyed! Cathi x