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.

The Problem of Evil & Objective Morality

The problem of evil refers to the fact that certain traditional views of theism involve contradictory beliefs. The problem is that God should be willing and able to make sure evil doesn’t exist, but evil exists. Some theists argue that atheists can’t reject the existence of God based on the problem of evil because atheists would then have to assume objective morality exists, but objective morality requires God. I will argue that the theist’s argument is irrelevant in consideration of one argument against one type of traditional theism, but it is somewhat relevant against another. Even so, both arguments are unsound.

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.

Can We Know Anything About Philosophical Issues?

Many people think philosophers aren’t experts, that we can’t really know anything about philosophical issues, or that everyone’s opinion is equal concerning philosophical issues. Philosophical issues are often narrowly understood to be those concerned with the nature of reasoning, knowledge, morality, or reality; and many people say we can’t know anything about such issues.  I will argue that we can know something about philosophical issues, which implies that there can be expert philosophers, and that not everyone’s philosophical opinion is equal. We do seem to know something about philosophical domains and it is plausible to think we can give meaningful philosophical arguments within these domains. Such a position is actually more consistent with how people think about the world.

I will introduce the plausible view that we can know about scientific issues, and the common view that many people have that we can’t know about philosophical issues. I will explain why we can’t reject philosophy without being inconsistent, and I will give examples of various plausible philosophical beliefs and reasonable philosophical arguments.

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.

Do Extraordinary Claims Require Extraordinary Evidence?

Do extraordinary claims require extraordinary evidence? Is there a burden of proof against extraordinary claims? Should we literally assume that something extraordinary doesn’t exist until it is proven to exist?

Many people say that those who claim that bigfoot, ghosts, and gods exist are making “extraordinary claims” and we should reject the existence of these things because we don’t have enough evidence for them.

What’s “extraordinary” mean? It refers to claims that conflict with what we think we know about the world. Many claims are extraordinary because they are extreme (likely false) or potentially impossible.

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.

Is Atheism or Theism The Default Position?

Many atheists say that atheism is the default position, so theists have the burden of proof. I will consider the best argument I can come up with that theism is the default position and the best argument I can come up with that argument that atheism is the default position. I believe that the argument that atheism is the default position seems a little more plausible, but I am not yet convinced that either of the arguments are rationally compelling. Even so, the arguments I will present are merely food for thought and could be considered to be a starting point when considering whether atheism or theism is the default position (or perhaps neither).

How to Have a Rational Debate

It can be difficult to find anyone willing and able to engage in rational debate, but it is something I think we should aspire to having. Many people refuse to engage in rational debate because they find it offensive or they would rather engage in name calling. I believe that rational debate has a lot to offer. It can help us better understand how to reason properly and to develop critical thinking skills. Rational debate is important to everyone who wants to know what they should believe about a controversial issue because we need to know if there’s a good argument in favor of a belief.

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).

The Top 10 Posts on Ethical Realism from 2012

2012 was Ethical Realism’s most successful year and I believe that is partially because some of my new articles were much more popular than usual. Other people linking to my material was a great help, and was greatly appreciated. What were Ethical Realism’s ten best articles in 2012? I suggest the following:

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.