Part 1: Introduction to Logic
Lesson 1: Why Study Logic?
Logic is all about argument and persuasion. It is the formal study of correct patterns of reasoning. Whenever we make a decision, pass a judgment, or express a position, we do so in a fairly patterned fashion. Whether explicitly or implicitly, we start from a set of assumptions and beliefs about something and we use them to arrive at some further belief.
Lesson 2: The Three Building Blocks of Logic
We will begin our study of logic by defining the three basic notions used in his system to characterize declarative sentences and the structure of the relations between them – terms, propositions, and syllogisms.
Part II: Term Logic
Lesson 3: Terms: What are they?
Terms are the basic building blocks of logic. In order to think and argue logically, we must fully understand and master the use of terms.
Lesson 4: Univocal Terms
In this lesson, we learn that terms can be categorized into genus and species. Many times, a term can be both. When two or more terms are species united by a genus, we call those terms univocal.
Lesson 5: Equivocal Terms
Terms which are equivocated can lead an argument with good premises to absurd conclusions. This is why it is crucial to recognize equivocation within arguments, so that faulty conclusions can be avoided.
Lesson 6: Derivative Terms
Aristotle distinguishes one final type of term: the derivative term. A derivative term is a term that derives its name from another term, and the two terms refer to different things.
Lesson 7: Universal, Particular, and Indefinite Terms
We must understand if a claim involves all of a given type of thing, one of a given type of thing, or some of a given type of thing. A misunderstanding of these ideas can lead to a myriad of logical fallacies where propositions are improperly converted.
Lesson 8: Definitions and Aristotle’s Categories
Aristotle’s 10 Categories for expressions is one of the most cited and famous logical tools in the history of philosophy. It has been the topic of much controversy. We can use it as a helpful system to better understand what terms are and how exactly to categorize them.
Lesson 9: Definitions and Ontology
We often use the word “attribute” to describe the characteristics of something. Aristotle writes quite extensively on attributes, and how they are important to understanding the way things are.
Lesson 10: Extension and Intension
A helpful method of understanding terms is the use of the properties of extension and intension. The notions of extension and intension are incredibly important because they ensure that we define terms correctly in any given circumstance.
Part III: Logic of Propositions
Lesson 11: The Elements of a Proposition
Simply speaking, propositions can be thought of as a sentence that can either be true or false. There are three parts to every proposition: subjects, predicates, and copulas.
Lesson 12: Universal Affirmative and Negative Propositions
The universal affirmative and universal negative are two of the four types of categorical propositions. Because of this, understanding the way that these two types of propositions function and relate to one another is very important to understanding what exactly it is that we are asserting about the world around us.
Lesson 13: Particular Affirmative and Negative Propositions
The particular affirmative and particular negative are the other two types of categorical propositions. Likewise, understanding them is helpful for a better understanding of our own assertions.
Lesson 14: The Square of Opposition
We previously learned about the four different types of categorical propositions. Now we will get to observe some interesting logical relations that exist among them: contradictories, contraries, subcontraries, and subalterns.
Lesson 15: Distributed versus not Distributed in Propositions
A term is distributed if we are using it to refer to its entire extension, while a term is not distributed if we are using it to refer only to a part of its extension. These notions are crucial for avoiding fallacies.
Lesson 16: Compound Propositions
In many cases propositions themselves may become elements of larger propositions. These larger propositions are known as compound propositions, and there are three types: conjunctive compound propositions, disjunctive compound propositions, and hypothetical compound propositions.
Lesson 17: Brief Introduction to Modality
A fourth element that can add itself onto a proposition is the operator – simply put, these are words that operate on the content of the proposition in certain ways. Here, we will look at the operators possibly, actually, and necessarily.
Part IV: Syllogistic Logic
Lesson 18: Types of Terms in a Syllogism
Out of everything Aristotle achieved in the field of logic, he is perhaps best known for his work on syllogisms. Here we examine the terminological and propositional components of his syllogisms.
Lesson 19: Modus Ponens and Modus Tollens
The rules of modus ponens and modus tollens can be used to provide valid arguments and are both incredibly useful within any form of argumentation or debate.
Lesson 20: Affirming the Consequent and Denying the Antecedent
In the prior lesson, we introduced the rules of inference known as Modus Ponens and Modus Tollens. In today’s lesson, we’ll be looking back at these rules of inference to see what happens when the wrong logical steps are taken during their use.
Lesson 21: Deduction, Induction, and Abduction
In this lesson, we will turn to two three forms of inference – deductive, inductive, and abductive. Notably, we will look at the differences between Aristotle’s time and modern times in the usage of ‘deduction’ and ‘induction’ and at the practical aims of each type of inference.
Part V: Logical Fallacies
Lesson 22: Ad Verecundiam and Ad Populum
Here we examine fallacies which can occur when a debater tries to make a point by claiming either that they themselves, or that some other relevant individual, knows what they are talking about, or by claiming that the thing is widely believed or common knowledge.
Lesson 23: Ignoratio Elenchi and Straw Man
These kinds of fallacies generally occur when an argument simply establishes an unrelated point or when an argument attacks a weaker position not held by an opponent.
Lesson 24: Genetic and Naturalistic Fallacies
Another important class of fallacies are causal fallacies. These errors involve some kind of improper use of cause in an argument. We will be looking at such errors: the genetic fallacy and the naturalistic fallacy.
Lesson 25: Slanting
In this lesson, we will be examining the fallacies which generally involve the deliberate withholding or unjust overemphasizing of information in order to slant the argument in one’s own favor.
Lesson 26: Circularity
One of the most common objections that we hear in public arguments is the claim, “you’re arguing in a circle!” or “you’re begging the question!” While these objections may be raised more often than the fallacy actually occurs, there is no doubt that circular reasoning fallacies are very important to understand and avoid.
Lesson 27: Composition and Division
In this lesson, we will focus on two more fallacies. This time they both have to do with a confusion of the part-whole relationship.
Part VI: Conclusion – Laws of Logic
Lesson 28: The Principle of Non-Contradiction
This lesson specifically shall focus on the principle of non-contradiction, which in itself was given in three separate forms by Aristotle: the metaphysical, the doxastic, and the semantic versions.
Lesson 29: The Principle of Identity
This principle tells us that each thing has all the same characteristics as itself. Why is this principle so crucial to logic? To start, it allows us to determine when two terms are equivalent.
Lesson 30: The Principle of Excluded Middle
The principle of excluded middle is one of the foundational principles of classical logic, widely employed in logical models in our own times, and somehow basic to our day-to-day reasoning.