How to Reason Deductively
Think Again: How to Reason and Argue
Reasoning is important. This series of four short courses will teach you how to do it well. You will learn simple but vital rules to follow in thinking about any topic at all and common and tempting mistakes to avoid in reasoning. We will discuss how to identify, analyze, and evaluate arguments by other people (including politicians, used car salesmen, and teachers) and how to construct arguments of your own in order to help you decide what to believe or what to do. These skills will be useful in dealing with whatever matters most to you.
Courses at a Glance:
All four courses in this series are offered through sessions which run every four weeks. We suggest sticking to the weekly schedule to the best of your ability. If for whatever reason you fall behind, feel free to re-enroll in the next session.We also suggest that you start each course close to the beginning of a month in order to increase the number of peers in the discussion forums who are working on the same material as you are. While each course can be taken independently, we suggest you take the four courses in order.
Course 1 – Think Again I: How to Understand Arguments
Course 2 – Think Again II: How to Reason Deductively
Course 3 – Think Again III: How to Reason Inductively
Course 4 – Think Again IV: How to Avoid Fallacies
About This Course in the Series:
Imagine that a friend denies that modus ponens is a valid form of argument. Can you prove that it is valid without using modus ponens itself and thereby assuming that it is valid? If so, how? If not, what does this show about the validity of modus ponens?
How can phrases like “and”, “or”, “if”, and “not” work as “truth-functional connectives”?
In this course, you will learn how to evaluate deductive arguments for validity. In particular, you will learn new ways of representing the information that is contained in the premises of a deductive argument. Using these new representational devices (devices that we call “truth tables” and “Venn diagrams”), we will be able to apply rules to determine whether or not a particular deductive argument is valid.
Students who want more detailed explanations or additional exercises or who want to explore these topics in more depth should consult Understanding Arguments: An Introduction to Informal Logic, Ninth Edition, Concise, Chapters 6 and 7 by Walter Sinnott-Armstrong and Robert Fogelin.
Each week will be divided into multiple video segments that can be viewed separately or in groups. There will be short ungraded quizzes after each segment (to check comprehension) and a longer graded quiz at the end of the course.
Welcome to the Course
<p>Welcome to <b>Think Again: How to Reason Deductively</b>! This course is the second in a series of four courses jointly titled <em>Think Again: How to Reason and Argue</em>. We are excited that you are taking this course, and we hope that you will stick around for all four courses in the series, because there is a great deal of important material to learn.In the series as a whole, you will learn how to evaluate deductive arguments.</p> <p>What is it for a deductive to be “valid”? And how can you tell the difference between deductive arguments that are valid and those that aren’t? In this course, we will answer these questions.</p><p>The first part of this course introduces the series and the course. It also clarifies some peculiarities you may find with this course. We encourage you to watch the "<b>Introduction to the Course</b>" video first as it will help you learn more from the materials that come later. </p>
Propositional Logic and Truth Tables
<p><b>CONTENT</b>: This week we will teach you how such phrases as “and”, “or”, “if”, and “not” can work to guarantee the validity or invalidity of the deductive arguments in which they occur. It will also teach you to understand the functioning of these phrases using a device called a “truth-table”, which shows how the truth or falsity of propositions that use these phrases depends upon the truth or falsity of the propositions contained within it. We highly recommend that you practice the skills that you will learn in this week by doing the puzzles at betapuzzle.sonjara.com.</p><p><b>LEARNING OUTCOMES</b>: By the end of this week’s material you will be able to :<ul><li>define what a deductive argument is</li><li>define what it is for a deductive argument to be valid</li><li>identify truth-functional operators and connectives</li><li>build a truth-table for any truth-functional operator or connective</li></ul></p><p><b>OPTIONAL READING</b>: If you want more examples or more detailed discussions of these topics, we recommend <em>Understanding Arguments, Ninth Edition</em>, Chapter 6. </p>
Categorical Logic and Syllogisms
<p><b>CONTENT</b>: This week will teach you how such phrases as “all”, “some”, and “none” can work to guarantee the validity or invalidity of the deductive arguments in which they occur. It will also teach you to understand the functioning of these phrases using a device called a “Venn Diagram”, which shows how the truth or falsity of propositions that use these phrases depends upon the truth or falsity of other propositions that use these phrases. We highly recommend that you practice the skills that you will learn in this week by doing the puzzles at http://philgames-neta.apps.unc.edu</p><p><b>LEARNING OUTCOMES</b>: By the end of this week’s material you will be able to : <ul><li>understand the information conveyed by a truth-table</li><li>use truth-tables to determine whether a deductive argument is valid</li><li>identify quantifiers and categories</li><li>build a Venn Diagram for any statement using quantifiers or categories</li></ul><p><b>OPTIONAL READING</b>: If you want more examples or more detailed discussions of these topics, we recommend <em>Understanding Arguments</em>, Ninth Edition, Chapter 7. </p>
<p><b>CONTENT</b>: This week we will teach you how to use the tools that you’ve learned about in the preceding modules in order to represent information. Information can be communicated in very different ways – by means of different languages or signaling systems – but no matter how that information is communicated, it can be important to use that information in reasoning. In this week, you will learn how to reason from information that is communicated directly by means of truth-tables or Venn Diagrams.</p><p><b>LEARNING OUTCOMES</b>: By the end of this week's material you will be able to: <ul><li>understand the information conveyed by a Venn Diagram</li><li>use Venn Diagram to determine whether a deductive argument is valid</li></p>
Catch-Up and Final Quiz
<p>This week gives you time to catch up and review, because we realize that the previous weeks include a great deal of challenging material. It will also be provide enough time to take the final quiz as often as you want, with different questions each time. </p><p>We explain the answers in each exam so that you can learn more and do better when you try the exam again. You may take the quiz as many times as you want in order to learn more and do better, with different questions each time. You will be able to retake the quiz three times every eight hours. You might not need to take more than one version of the exam if you do well enough on your first try. That is up to you. However many versions you take, we hope that all of the exams will provide additional learning experiences. </p>