This is an introductory course in both formal and informal logic. It provides you with the tools to evaluate and construct arguments in a more rigorous and precise way. Topics include fallacies and intellectual virtues, propositional logic, symbolization, and rules of inference, categorical logic and rules for categorical syllogism, and methods for extracting and evaluating arguments, including evidence and probability.

Modules

1. Introduction to Logic
2. Intellectual Virtues and Fallacies
3. Cooperative Principles and Fallacies
4. Foundations of Argumentation
5. Disjunctions and Conjunctions
6. Universals and Existentials
7. Conditionals
8. Material Conditionals
9. Constructing Valid Arguments
10. Conditional and Indirect Proof
11. Extracting Valid Arguments
12. Evidence
13. Probability
14. Causation
15. Intellectual Freedom & Responsibility

1. Introduction to Logic

This module gives an overview of the topics in logic and some foundational vocabulary for the course. This includes informal logic, such as intellectual virtues and fallacies. It also includes formal logic, such as tools like truth tables, rules of inference, symbolization, and Venn Diagrams.

2. Intellectual Virtues and Fallacies

Fallacies are common mistakes that people tend to make when arguing. Intellectual virtues are qualities of good reasoning that one can develop to help reduce the likelihood of committing a fallacy. In this module, we will discuss 9 pairs of intellectual virtues that someone can develop, as well as the various fallacies that failing to develop those virtues may tend to produce. These virtues are:

Intellectual self-regard and intellectual humility,
Respect and desire for the truth,
Knowing what you know, and knowing what you don’t know,
Self-awareness and objectivity,
Reasonable emotions and intellectual temperance,
Intellectual courage and intellectual caution,
Realism and optimism about intellectual progress,
Intellectual patience and intellectual persistence, and
Simplicity and comprehensiveness.

3. Cooperative Principles and Fallacies

Reasoning is something we do cooperatively with others as part of an ongoing conversation, as we identify disagreements and weigh one another’s reasons. We make certain assumptions when communicating that are important to make our conversations cooperative and productive, and to avoid fallacies. These assumptions can be expressed as nine specific principles:

Charity: interpreting one’s opponent as rationally as possible;
Open-Mindedness: maintaining one’s own views while listening to disagreement;
Civility: making one’s contributions polite and respectful;
Sharing Assumptions: using but not abusing presuppositions to limit the conversation;
Justifying Exceptions: allowing for special cases but avoiding special pleading;
Quality: making one’s contributions true, and known to be true;
Quantity: making one’s contributions exactly as informative as required;
Relevance: making one’s contributions relevant to the issue being discussed;
Manner: making one’s contributions clear, and reducing vagueness and ambiguity.

4. Foundations of Argumentation

Formal logic studies the abstract form of an argument rather than its content. This module studies the assumptions of classical logic, how to clarify claims in order to symbolize them, and how to use very basic truth tables and Venn Diagrams to model validity. Topics studied in this module include:

Applying Formal Logic only to statements;
Symbolizing Simple Positive and Negative Claims;
The Laws of Non-Contradiction and Excluded Middle;
The Rules of Reiteration and Double Negation;
Introduction to Basic Truth Tables;
Introduction to Basic Venn Diagrams;
Making Sentences more Precise;
Making Sentences more Concise;
Distinguishing the Explicit, Literal Meaning of Logical Connectives from Implicatures;
Testing the Validity of Rules of Inference;
Making use of formal tools to reason more methodically;
Making use of formal tools to more objectively approach controversial topics.

5. Disjunctions and Conjunctions

This module presents the rules for symbolizing disjunctions (‘or’ sentences) and conjunctions (‘and’ sentences), how to create truth tables for conjunctions and disjunctions, and the rules which apply to conjunctions and disjunctions. Topics studied in this module include:

Applying Formal Logic only to statements;
Symbolizing Simple Positive and Negative Claims;
The Laws of Non-Contradiction and Excluded Middle;
The Rules of Reiteration and Double Negation;
Introduction to Basic Truth Tables;
Introduction to Basic Venn Diagrams;
Making Sentences more Precise;
Making Sentences more Concise;
Distinguishing the Explicit, Literal Meaning of Logical Connectives from Implicatures;
Testing the Validity of Rules of Inference;
Making use of formal tools to reason more methodically;
Making use of formal tools to more objectively approach controversial topics.

6. Universals and Existentials

Categorical logic studies the logic of claims about all members (universals) or some members (existentials) of a category. This module discusses the distinction between existentials and universals, some of the basic rules which apply to each, and the fifteen valid forms of categorical syllogism. Specific Topics are:

Distinguishing Existential and Universal Claims;
Using Venn Diagrams to model claims and prove validity;
Basic rules for Existentials and Universals;
Relationships of contradiction and logical equivalence between categorical claims;
Constants, Variables, and Identity;
Categorical Syllogisms, including Standard Form, Mood, Figure, and the 15 Valid Forms.

7. Conditionals

This module offers a review of the prior modules, and then introduces conditional (“if.. then”) sentences, and the three types of conditional sentences. Topics covered in the discussion of conditionals include:

The structure of a conditional, with an antecedent and consequent;
Material conditionals;
Counterfactual conditionals;
Strict conditionals; and
Biconditionals.

Topics reviewed from previous units include:

Intellectual Virtues;
Fallacies;
Symbolization;
Truth Tables;
Rules of Inference;
Venn Diagrams; and
Categorical Syllogisms.

8. Material Conditionals

This module explains how to symbolize and create truth tables for material conditionals and biconditionals. It also introduces the rules of modus ponens, modus tollens, and other rules and fallacies for conditionals. Topics include:

Using Material Conditionals to make an argument valid;
Symbolizing Material Conditionals;
Symbolizing multiple Material Conditionals and Biconditionals;
Truth Tables for Material Conditionals and Biconditionals;
Modus Ponens and Modus Tollens;
Material Contraposition, Implication, and Negated Conditional;
The Fallacies of Denying the Antecedent, Affirming the Consequent, and Commutation of Conditionals; and
Completing Proofs and Enthymemes.

9. Constructing Valid Arguments

This module aims to help you polish many of the skills needed to construct valid arguments. This includes testing the validity of arguments, proving the validity of arguments, filling in missing premises or rules of inference, and other proof strategies. By the end of this module, you should have the preparation you need to begin composing arguments on your own. Topics studied in this module include:

applications of valid arguments;
Recognizing valid arguments;
Applied Truth Tables;
Applied Venn Diagrams;
Proofs with Propositional Rules;
Proofs with Categorical Rules;
Recognizing applications of a rule;
Complex Enthymemes;
Translating back into English;
Choosing Propositional Rules;
Choosing Categorical Rules;
Extracting arguments.

10. Conditional and Indirect Proof

This module introduces three new rules for propositional logic which make use of temporary or provisional assumptions: conditional proof, indirect proof, and disjunction elimination. It also proves the validity of two other rules, hypothetical syllogism and exportation. These rules work together to make it easier and quicker to complete proofs.

11. Extracting Valid Arguments

It is time to apply what you have learned! Extracting an argument is a way of using the formal methods and rules of inference we have studied in order to present, explain and evaluate the reasoning in a real-world argument. Real arguments are rarely pre-packaged in perfect deductive form. So, we have to charitably re-interpret their arguments and reconstruct them so that every premise is explicit and every inference is valid. Once we do that, it is clear exactly what in the argument needs to be defended, and what in the argument could be challenged.

12. Evidence

Up to this point, we’ve studied how to determine whether an argument is valid or invalid, and how to reconstruct invalid arguments to make them valid. We haven’t discussed how to determine whether or not an argument is sound: that is, how to determine whether or not the premises are true. For that, we need evidence about the way the world is. This module studies the types of evidence available to us. First, we’ll study sources of direct evidence: perception, testimony, and memory, and the ways each can fail. Then, we’ll study indirect sources of evidence, including arguments from analogy, induction, abduction, and inference to the best explanation.

13. Probability

When we look at our evidence to weigh the truth of a premise in an argument, it is rarely certainly true or certainly false. The rules of probability allow us to calculate degrees of certainty and uncertainty. Learn a few basic principles that sound reasoners should understand: how we come up with probabilities, how to determine the probability of a disjunction, conjunction, or conditional, and common mistakes that people make with probabilities.

14. Causation

This module presents four different types of explanation: definitional explanations, compositional explanations, functional explanations, and causal explanations. A number of fallacies result from mixing up these types of explanation. It then presents methods for determining whether or not causal explanations hold, including necessary and sufficient conditions, counterfactuals, and Mill’s Methods. The importance of not mistaking causation for correlation is emphasized.

15. Intellectual Freedom & Responsibility

Many people have not developed their capacity to reason to the same degree which students of logic have. This gives a logic student certain advantages, but also brings with it certain ethical responsibilities. The responsibilities of sound reasoners include:

The social responsibilities of scholarship, ethics, and understanding;
The epistemic responsibilities of curiosity, critical judgment, and openness to change; and, lastly,
The individual responsibilities of fairness, keeping perspective, and imagination.

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