Interpretation is the conversion of a sentence in a formal language of a logical system into a natural language, which is primary done by providing a scheme of abbreviation for a symbolic sentence. The purpose of translation is generally to prove a sentence to be indeterminate, an argument to be invalid, a set of sentences to be logically consistent, or a set of sentences to be non-equivalent. (more…)
July 2, 2015
March 26, 2015
I have discussed a logical system called “propositional logic.” I will now discuss predicate logic, a system that is a bit more complex than propositional logic because it introduces predicates, quantifiers, constants, variables, and the universe of discourse. It also uses the elements of propositional logic (propositional letters and connectives). I recommend you learn about propositional logic before learning about predicate logic. (more…)
August 30, 2013
Manipulative tactics are those that can get people into believing something without giving any reason to think the belief is true. Informal fallacies are errors in reasoning that are often used as manipulative tactics, but sometimes we can use a manipulative tactic without actually committing an error in reasoning. Although informal fallacies are only one type of manipulative tactic, philosophers often treat all manipulative tactics as though they are fallacies. Just about every type of manipulative tactic has a corresponding fallacy. I will give examples of various manipulative tactics and corresponding fallacies. I hope to help make it clear that the difference between fallacies and potentially nonfallacious manipulative tactics is generally not important enough to worry about. Some people might defend a manipulative tactic by insisting it’s “not actually fallacious,” but that reply would usually miss the point. (more…)
July 16, 2013
Should we ever trust anyone’s expertise? The “appeal to authority” is a well-known fallacy (nonrational way to reason) and some people claim that all appeals to authority are fallacious. I was once told that my religion is science because I trust the expert opinion of scientists, so apparently that person doesn’t think scientists should be trusted. I will explain why we should often trust expert opinion and we have little choice but to often do so. (more…)
Critical thinking is an educational domain concerned with good reasoning. In the broad sense critical thinking includes both formal and informal logic. The narrow sense of critical thinking (as it is often taught in universities) is primarily concerned with (and often equated with) informal logic. Formal logic primarily involves the study of logical systems, logical axioms, logical consistency, and logical validity; and informal logic primarily involves argument identification, argument interpretation, unstated premise identification, and informal fallacies. (See “What is Logic?” for more information.) Critical thinking is generally not thought to be merely about memorizing logical facts. Instead, it is also thought to involve the development of critical thinking skills, the critical thinking attitude, and critical thinking virtues. The purpose of this paper is to briefly discuss critical thinking skills, the critical thinking attitude, and critical thinking virtues. (more…)
July 8, 2013
I will discuss what unstated premises are, how to identify them, and how to determine what they are.
What are unstated premises?
Unstated premises are premises that a deductive argument requires, but are not explicitly stated. Deductive arguments are popular and can be rationally persuasive, but people don’t always state all of the premises that their deductive arguments require. These premises can be called “unstated premises,” “missing premises,” or “hidden assumptions.” For example, consider the following argument: (more…)
June 13, 2013
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. (more…)
May 13, 2013
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 2, 2013
March 21, 2013
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.
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.
March 6, 2013
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…)
February 20, 2013
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.” (more…)
February 19, 2013
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…)
February 12, 2013
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…)
January 19, 2013
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…)
January 14, 2013
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).
December 31, 2012
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…)
December 6, 2012
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…)
October 22, 2012
‘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…)