A formal logic class or textbook should teach us ways to know when an argument has a valid argument form, and that can take a significant amount of time to learn. I encourage everyone to learn formal logic one way or another because it is of central significance to rational argumentation, and it is not something we spontaneously understand instinctively or through personal experience. Perhaps the first philosopher to understand formal logic and the importance of validity was Aristotle, and philosophers would have liked to understand it sooner. It was a great achievement because it can be so difficult to figure out on our own. Even so, we can learn a lot about valid argument form very quickly. I will explain why we need to make sure our deductive arguments are valid, give examples of valid argument forms, and explain how we can improve our arguments. (more…)

## May 13, 2013

## February 19, 2013

### Logic Part 5: Natural Deduction

Part 1 | Part 2 | Part 3 | Part 4

This is part 5 in a series. There are links to the other parts of the series above.

Natural deduction is used to give proofs of validity by showing all the steps in reasoning required. In this case natural deduction uses rules of inference to allow us to reach conclusions from statements of propositional logic. (more…)

## October 10, 2012

### What is Logic?

Logic is a domain of philosophy concerned with rational criteria that applies to argumentation. Logic includes a study of argumentation within natural language, consistent reasoning, valid argumentation, and errors in reasoning. It is divided into two main domains: Formal and informal logic. (more…)

## September 9, 2012

### My Reply to Neo of The Skeptic Arena: Are All Good Arguments Logically Sound?

Neo of The Skeptic Arena read two of my posts: “Not All Good Arguments Are Logically Sound Part 1” and “Not all Good Arguments Are Logically Sound Part 2.” (At first he only read Part 2, which might have led to confusion.) We had an email conversation that he decided to post on his website for educational reasons. Go to his website to see for yourself. He concludes the following:

Against my better judgment I went ahead and read part 1. As I expected, it was pretty much the same drivel I put up with in Part 2. It was a waste of time. Since he is obviously unable to defend his assertions, continuing the email exchange would also be a waste of time.

### 10 Myths About Logic

Logic is greatly misunderstood. Not only do very few people understand logic properly, but even critical thinking educators believe false things about logic. I will discuss ten myths (false beliefs) I believe many people have about logic. (more…)

## August 22, 2012

### Not All Good Arguments Are Logically Sound Part 2

See Part 1 here. (I advise you to read part 1 first.)

One reason that not all good arguments are logically sound is because good arguments used in science are inductive, and inductive arguments are not meant to be logically sound. However, not all good deductive arguments are logically sound either. There is a sense that deductive arguments would ideally be logically sound, but some deductive arguments have sufficiently justified premises, even if those premises aren’t known to be true for certain. A good deductive argument must be logically valid, and it must have sufficiently justified premises. Even so, not all good deductive arguments are logically sound. (more…)

## August 13, 2012

### Not All Good Arguments Are Logically Sound

More than one person has believed that all good arguments are logically sound, but this is a mistake. Not all good arguments are logically sound. Even so, understanding why not all good arguments are logically sound can help us better understand what good arguments are. I will discuss what good arguments are, I will explain what it means for an argument to be logically sound, explain the distinction between deductive and inductive arguments, and present an argument that proves that not all good arguments are logically sound. (more…)

## June 19, 2011

### Proving an Argument Is Logically Valid

I have discussed the importance of understanding logical form and how to create formal counterexamples. Understanding logic well is a lot easier when we know something about logical validity, and one way to better understand logical validity is to consider an argument that proves an argument to be valid. If we can know *why* an argument can be valid, then we can know more about logical validity in general. I will now produce a proof of logical validity here. It can take some time to understand the proof, so you might want to take your time to read it carefully. (more…)

## June 17, 2011

### Examples of Valid & Invalid Logical Reasoning

I have described formal logic, said a little about why it’s important for proper reasoning, and described how we can prove arguments to be logically invalid through counterexamples. I will now give examples of valid and invalid logical arguments to help illustrate the difference and help us learn how to identify the difference in everyday life. I will give 10 examples of arguments that could be either valid or invalid, but I won’t give the answers to the examples right away to give you a chance to think about the answers on your own. Then I will give the answers in another section below and justify my answer using counterexamples when possible. I will also prove that various argument forms are valid. It’s possible that the arguments below make use of poor reasoning that is unrelated to logical validity, but logical validity is my only concern here. (more…)

### Logical Validity & Counterexamples

I have already described formal logic and explained why it’s important for proper reasoning. One of the best ways to learn formal logic is to take a logic class. However, we don’t have to take a class just to learn the basics and improve our intuitive grasp of formal logic. What I want to do here is explain how to use counterexamples to prove an argument to be logically invalid. This can help improve our understanding of logic and help us prove arguments to be logically invalid. (more…)

## February 22, 2010

### What You Need From Formal Logic

It can be extremely helpful to know some formal logic in order to visualize how arguments work. Formal logic shows how the form of an argument can be valid or invalid. Assuming that the premises of an argument are true, a valid argument form guarantees that the conclusion is true. An invalid argument doesn’t. In other words, a valid argument can give us a complete reason to agree to a conclusion and an invalid argument can’t. Knowledge about argument form helps us achieve clear thinking and relevant arguments. (more…)