Natural deduction is the use of rules of inference and assumptions in order to reach a conclusion, and they are used to prove argument forms to be logically valid. The entire reasoning process is made entirely explicit, and is known as a ‘proof’ or ‘derivation.’ I will assume here that you already know how to use natural deduction in propositional logic, and natural deduction in predicate logic is done in the same way as in propositional logic, except some additional rules of inference are needed. (more…)
July 20, 2015
July 2, 2015
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…)
May 10, 2015
This is part 2. You should see part 1 before reading this. This is also written with the assumption that you already know propositional logic. Translation is the conversion of natural language into the formal language of some type of logical system. Every statement in predicate logic is either symbolized as a single letter (just like propositional logic), or it requires (1) a predicate letter, and (2) an individual. (more…)
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…)
February 23, 2015
I am wondering if the debates we have over certain words are often confused because we assume the word has one correct definition when it doesn’t. For example, does the word ‘atheist’ refer to someone who believes gods don’t exist or someone who just doesn’t actively believe in a god? Why would anyone think we have to define it one of these two ways, and that the other definition has to be wrong? Other examples include debates over the definition of ‘free will’ and ‘knowledge.’ The question is, “Is there really a correct way to define these terms?” We might think that debates over definitions isn’t really substantive because there is no essence corresponding to the words (at least some of the time). Words could also have a tendency to make use of family resemblance concepts that lack necessary and sufficient conditions, so it might be hopeless to try to define words based on how we actually use them using exact specifications. If there isn’t a single definition, then the debate could end up having various opposing views of how people should talk about things. (more…)
December 29, 2014
Philosophy essays are a bit different from other types of essays, but there aren’t necessarily any strict rules about how to write them best, and there are a variety of different types of philosophy essays. I will discuss three main types of philosophy papers: (a) argumentative, (b) speculative, and (c) interpretative. I will also discuss some important elements of philosophy essays, such as the idea of philosophical content and what the introduction should be like. I hope that thinking about various types of philosophy essays and various elements of philosophy essays will help people improve their philosophical writing. (more…)
May 5, 2014
I believe that one source of confusion can be solved by the distinction between normative and descriptive ethics. Whenever people talk about cultural relativism or evolutionary theories of ethics, I think they have descriptive ethics in mind, but they often jump to the conclusion that whatever they are talking about has certain obvious normative implications. In particular, some people claim that morality comes from evolution and others claim that morality is relative. What they have in mind often doesn’t actually make sense, as I will discuss in detail. (more…)
December 23, 2013
December 20, 2013
A lot of people are saying ‘atheism’ is what we call it when people don’t believe in gods.1 The more traditional meaning of ‘atheism’ is the belief that no gods (or certain types of gods) exist. This newer (nontraditional) type of atheism is sometimes called ‘soft atheism’ as opposed to ‘hard atheism.’ I will describe atheism, consider reasons that the newer definition of ‘atheism’ can lead to confusion, and I will consider reasons why people might prefer this newer definition. (more…)
November 1, 2013
September 30, 2013
I have defined several new philosophically-related terms for the Comprehensible Philosophy Dictionary (a work in progress). Some of these are words I’ve already defined before but have been significantly improved. You can let me know if you think any of the terms need further clarification or if any need improvement for any other reason. (more…)
September 22, 2013
I will discuss two related philosophical questions related to death: One, is death bad? Two, how should we feel about death? (more…)
September 6, 2013
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…)
August 23, 2013
The most popular page on this site has been Philosophy is Important for quite some time, but that page has now been replaced with a new piece I recently wrote (that uses the same name). I was not convinced that the old piece deserved all the attention it got, but it is certainly an important issue.
The older piece that used to be there is now a PDF and can be seen here: 11 Reasons Philosophy is Important.
August 20, 2013
A lot of people accuse those who are dismissive of non-scientific fields of study of having scientistic views. This raises important questions—Is science always the only legitimate source of knowledge? Could philosophy ever be a source of knowledge?
The main issue concerning scientism that I’m interested in is the scientistic view that philosophy has little to nothing it can contribute. For example, in 2011 Stephen Hawking said, “[P]hilosophy is dead… philosophers have not kept up with modern developments in science. Particularly physics.”1 And in 2012 Lawrence Krauss said, “[S]cience progresses and philosophy doesn’t.”2
Even so, anti-philosophical views are not the only types of scientism, and I believe that some types of scientism can be explicitly favorable to philosophy. What exactly is scientism? I will define and categorize various types of scientism. (more…)
August 13, 2013
I have defined several new philosophically-related terms for the Comprehensible Philosophy Dictionary (a work in progress). You can let me know if you think any of the terms need further clarification or if any need improvement for any other reason. (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…)