Good Arguments

What’s the point of a rational argument? To give someone a good reason to believe something. A sufficiently good argument gives us a good reason to believe something is true. It is better for us to have beliefs that are supported by good arguments in the sense that they are more likely true based on our limited understanding of the world, but it is possible for them to be false.

Logically Valid Arguments

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.

Cognitive Bias & Informal Fallacies

Daniel Kahneman wrote Thinking, Fast and Slow, which is about the psychological research concerning cognitive bias. Kahneman could very well be the leading expert concerning cognitive bias at this point in time. His research concerns how people reason and why people often reason poorly, and it has some important implications for critical thinking. I will describe three cognitive biases that he discussed in his book, and explain how they relate to logical fallacies.

What You Need From Propositional Logic Free Ebook (PDF)

Some of my key blog posts about propositional logic have been organized a free ebook. This ebook can greatly help people understand the importance of logically valid arguments and better understand logical form.

Abstract

The focus of this book is propositional logic. I discuss the meaning of “logic,” the importance of logic, logical connectives, truth tables, natural deduction, and rules of inference.

Why Logic is Important

Recommended reading: What is Logic?

Why is logic education important? The main question here is what the real point of logic education is. The real point of logic is not to teach people how to be logic professors, or to increase test scores, or to impress potential employers. Philosophers and mathematicians were very interested in understanding logic long before it was taught in universities precisely because of how important it is. Why is logic so important? The answer is that logic helps us better understand good arguments—it helps us differentiate between good and bad reasons to believe something. We should want to have well-justified beliefs. We want to know what we should believe. Understanding good argumentation helps us understand when we should believe something, and understanding logic helps us understand good argumentation.

Logic Part 6: Conditional & Indirect Proof

Part 1 | Part 2 | Part 3 | Part 4 | Part 5

This is part 6 of a series. Links to the other parts of the series are above.

The straightforward way to construct proofs using natural deduction is called the “direct method.” Every line of that type of proof is validly deduced from the premises and rules of inference. Every line of such a proof could be considered to be true as long as we consider the premises to be true. However, there are two other strategies: The conditional proof and the indirect proof. Both of these types of proofs introduce an additional premise that is assumed to be true “for the sake of argument.”

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.

Arguments Are Important

At some point you are likely to hear about how giving arguments is rude and we would all get along better without arguing. Arguing is often thought to be a shouting match or hostile disagreement of some sort. However, argumentation is central to thinking rationally and critical thinking. The success of natural science could not exist without it. Yes, some arguments are disrespectful, but not all of them are.

Logic Part 4: How To Make Truth Tables

• Part 1

• Part 2

• Part 3

Truth tables are an important tool for evaluating statements and arguments. We can create our own truth tables using following steps:

1. Translate statements of ordinary language.

2. Break all complex statements into smaller parts.

3. Determine how many columns are required.

4. Determine how many rows are required.

5. Determine the truth values of statement letters.

6. Determine the truth values of complex statements.

I will illustrate how to follow these steps by using an example. In particular, I will show how we can make a truth table of an argument to find out if the argument is logically valid.

Logic Part 3: Truth Tables

• Part 1
• Part 2

Truth tables are visual aids to help us determine all the truth value possibilities of various statements. Learning about truth tables can help us better understand logic. Truth tables are used to define logical connectives, and to help us identify various distinctions (such as tautologies, self-contradictions, consistent statements, equivalent statements, and valid arguments).

What is Argument Mapping?

You can download a PDF ebook of this introduction to argument mapping here:

• What is Argument Mapping?

Introduction

Argument maps are visual representations of arguments to help people better understand them. A meta-analysis of various studies found that classes with lots of argument map practice are the most effective type of critical thinking class to help improve critical thinking skills.

Argument Maps vs Other Argument Diagrams

I believe that argument maps as I understand them are superior to other types of argument diagrams. I will describe four different kinds of argument diagrams, then explain why argument maps seem to be the best.

Logic Part 2: Translation

This is Part 2. You should see What is Logic? and Logic Part 1: What is Propositional Logic? before reading this.

‘Translation’ refers to the act of converting statements of natural language to statements of a symbolic logical system. In this case I will discuss how to convert statements of English into statements of propositional logic. Translation requires us to know logical connectives used in propositional logic, and ways we use logical connectives in English.

Logic Part 1: What is Propositional Logic?

I have briefly discussed the meaning of “logic” and various parts of logic. I am now going to discuss the most important parts of propositional logic in greater detail. This will include the following chapters:

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 Philosophy Definitions Part 3

I worked more on the Comprehensible Philosophy Dictionary. What follows are several new definitions that will be added to it. Let me know if anything should be improved.

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 Philosophy Definitions Part 2

I have continued working on the Comprehensible Philosophy Dictionary. There will be many corrections coming soon in addition to many new definitions. You can let me know if any of these definitions can be improved or if I am still missing an important philosophy term. I decided to define a lot more terms used in logic, and many more can still be added. The new definitions I am planning on adding are the following:

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.