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.
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. (more…)
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. (more…)
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. (more…)
Truth tables are an important tool for evaluating statements and arguments. We can create our own truth tables using following steps:
Translate statements of ordinary language.
Break all complex statements into smaller parts.
Determine how many columns are required.
Determine how many rows are required.
Determine the truth values of statement letters.
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. (more…)
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).
You can download a PDF ebook of this introduction to argument mapping here:
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. (more…)
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. (more…)
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. (more…)
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: (more…)
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…)
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. (more…)
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…)
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: (more…)
There is no uncontroversial “one size fits all” definition for good arguments that will tell us whether an argument is a good argument or not. The term is a bit vague and there is room for disagreement. We can’t give a list of necessary and sufficient conditions for when an argument is a good one that all philosophers will agree with. Even so, what constitutes good arguments involves rational criteria. In fact, arguments are good insofar as they are “rationally persuasive.” Consider the following six ways we can describe good arguments: (more…)
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…)
I have been working a lot more 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 should be improved or if I am still missing an important philosophy term. The new definitions I am planning on adding are the following: (more…)
I created a draft of The Comprehensible Philosophy Dictionary that is now available to the world. The motivation is to help people understand concepts related to logic, philosophy, and critical thinking. The definitions should generally be something you can understand, even if you have little to know education in these fields.
We all know that dictionaries can be valuable when we need to know what a term means while reading a book, but the philosophical dictionary isn’t just to help us understand the arcane language spoken by elitist intellectuals. The terminology used by philosophers often refer to concepts that are central to rational thought or that help us make important distinctions. Go here to take a look for yourself.
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Related:
There is a great deal of critical thinking concepts that can be both convenient to use and help improve our critical thinking skills. However, some critical thinking concepts should be considered to be indispensable to being a human being because it’s a requirement of having a minimal capacity to reason and argue properly. The list of critical thinking terminology listed here are used to refer to concepts that everyone should know about—and yet many people either haven’t been informed about them or they don’t understand them properly:
In this piece I will explain why philosophical terminology is important and I will present definitions for twenty important philosophical terms I think can help improve our thinking about various philosophical issues. (more…)
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