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 cover (1) fallacies and intellectual virtues; (2) propositional logic, including symbolization and rules of inference; (3) categorical logic, including rules for categorical syllogism; and (4) methods for extracting and evaluating arguments, including evidence and probability.
Introduction to Logic
COGBOOKS COURSEWARE
ISBN: 978-1-913014-21-6
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This topic 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.
1.1 What is Logic? Reasoning is the process of moving from one thought to another. All of us engage in reasoning, but not all reasoning is good or “sound”
reasoning. Logic is the study of the general principles of sound reasoning. Learn what we mean by “reasons” and “conclusions”, observe that good reasoning neither concludes too much nor too little, and think about how studying logic can help us avoid “fallacies” – common mistakes in reasoning.
Learning Activities
● Reasoning
● Sound Reasoning
● How Do We Know Logic?
● Why Study Logic
1.2 Formal and Informal Logic: An argument is a structure of “premises”, or reasons, followed by a conclusion inferred from those premises. Informal Logic studies
general guidelines for good argumentation, the habits of a good reasoner, or “intellectual virtues”, and the tendencies we have to make mistakes in reasoning, or “fallacies”. Formal Logic studies abstract patterns of reasoning that meet the strictest standard for argumentation – validity. An argument is valid
when there is no possibility of the premises being true with the conclusion false.
Learning Activities
● Informal Logic
● Arguments
● Formal Logic
● Validity
● Tools of Formal Logic
1.3 The Standard View: This topic introduces key concepts that are part of the “Standard View” in philosophy, which form the foundations for logic. These concepts include representation, accuracy, facts, sentences, propositions, truth, negation, and logical connectives. Many people bring their own pre-conceived notions about what these words mean. Often, the way that these terms are used differs from the specialized meanings these words have among academics.
Learning Activities
● Representations
● Facts
● Sentences and Propositions
● Truth and Propositions
● Logical Connectives
1.4 Rational Opinions: A belief or opinion is an attitude towards a proposition. It must be either true or false, even if we don’t know whether it is true or
whether it is false. Whether an opinion is true or false is different from whether it is justified or unjustified by one’s evidence or reasons.
One can hold a true opinion for good reason, or for bad reasons; one can hold a false opinion for good reasons, or for bad reasons. One
should aim to hold justified beliefs, and this means avoiding forming beliefs through fallacious inferences.
Learning Activities
● Opinions and Beliefs
● Justifying Beliefs
● Non-Sequitur
● Begging the Question
2.1 Proper Regard: The three most basic intellectual virtues reasoners should aim to develop involve holding the proper degree of regard for themselves as
reasoners, for the truth, and for knowledge. Having too much or too little regard of each type tends to lead to fallacious reasoning.
Having intellectual self-respect is an important virtue, and having too little of it makes it easy to fall prey to appeals to ridicule or false
authority. Intellectual Humility is a virtue, too, however, and having too much self-regard can lead to hubris and dismissing legitimate
expertise. Similarly, it is a virtue to have enough desire for the truth that one seeks to be right, but also a virtue to have enough respect for the
truth that one is willing to have been wrong. Reasoners also need to seek a balance between skepticism and credulity, neither desiring knowledge so much that they accept falsehoods as knowledge, nor respecting knowledge so much that they are unable to know anything.
Learning Activities
● Intellectual Virtues and Fallacies
● Proper Intellectual Self-Regard
● Intellectual Humility
● Respect for the Truth
● The Desire for True Beliefs
● Knowing What You Know
● Knowing What You Don’t Know
2.2 Managing Subjectivity: Our own subjectivity is an inescapable and essential to who we are. It would be a mistake to ignore the role that our individual perspective
plays in shaping our judgments, and it would be a mistake to try to write off all emotions as unreasonable. At the same time, we can seek to reason more objectively than we tend to by default, by taking a step back from our particular circumstances, feelings, and interests, and trying to think of them
from the outside. Learning how to manage one’s own subjectivity is an important part of becoming a better reasoner.
Learning Activities
● Self-Awareness
● Objectivity
● Emotion and Morality
● Emotion within Reason
● Intellectual Courage
● Intellectual Caution
2.3 Realism: We all learn more over time. We can be cautiously optimistic that we will know more in the future than we know today, rather than falling into a cynical attitude that “no one will ever know” the answer to a question just because it is complicated or difficult.
Persistence despite frustration and failure is an intellectual virtue. At the same time, we should avoid excessive idealism about the future,
and recognize that there may be things we could only understand after we have learned much more than we already know. We should
avoid simplistic answers and develop the virtue of intellectual patience. When formulating theories about the world, we should
strike a balance between seeking comprehensive theories that explain as much as possible, and simple theories that have as few explainers as possible.
Learning Activities
● Tempered Optimism
● Patience
● Persistence
● Simplicity
● Comprehensiveness
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: (1) Charity: interpreting one’s opponent as rationally as possible; (2) Open-Mindedness: maintaining one’s own views while listening to disagreement; (3) Civility: making one’s contributions polite and respectful; (4) Sharing Assumptions: using but not abusing presuppositions to limit the conversation; (5) Justifying Exceptions: allowing for special cases but avoiding special pleading; (6) Quality: making one’s contributions true, and known to be true; (7) Quantity: making one’s contributions exactly as informative as required; (8) Relevance: making one’s contributions relevant to the issue being discussed; (9) Manner: making one’s contributions clear, and reducing vagueness and ambiguity.
3.1 Cooperation: Reasoning is a cooperative enterprise; even when people disagree, the aim of disagreement is weighing the reasons on each side, to
determine what is true. Disagreement can be a positive and constructive thing when both sides listen and try to understand what
the other is really saying. Reasoning cooperatively means interpreting others charitably and listening with an open mind. Someone who intentionally distorts what someone else says in order to make them seem wrong, or who simply dismisses anyone who doesn’t already agree with them, is more
interested in feeling like they are right rather than in actually being right.
Learning Activities
● The Cooperative Principle
● Interpreting Others Charitably
● Listening with an Open Mind
3.2 Disagreement: Disagreements can be good. Productive disagreements force us to test out and weigh our reasoning, and to justify our beliefs. Disagreements
tend to be most productive when both sides are able to disagree respectfully, when they allow for the possibility of justified exceptions
to general rules, and when they work from shared assumptions. On the other hand, attacks on someone’s character, or refusals to
work from shared common ground, tend to turn disagreements into power struggles. Insisting that no exceptions to a general rule can ever be justified, as well as insisting that an exception is special and doesn’t need to be justified, can also make disagreements
unproductive. Learning to have productive disagreements that are not sidetracked into power struggles is a useful skill to develop.
Learning Activities
● Disagreeing Respectfully
● Working from Shared Assumptions
● Allowing for Exceptions to the Rule
3.3 Contributing to the Conversation: H. P. Grice proposed that there were four maxims which we assume
everyone is following in a conversation. We can “flout” these rules openly, as a way of implicating something without saying it. Someone can also abuse or exploit these rules to produce fallacious reasoning, however, by making contributions which are not known to be true, too informative or not informative enough, irrelevant, or
deliberately ambiguous or vague. In general, we follow these four rules: (1) Quality: make your contribution something you know to be
true. (2) Quantity: make your contribution as informative as needed. (3) Relevance: make your contribution relevant to the conversation.
(4) Manner: make your contribution clear.
Learning Activities
● The Quality of a Contribution
● The Quantity of a Contribution
● The Relevance of a Contribution
● The Manner of a Contribution
Formal logic studies the abstract form of an argument rather than its content. This topic 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 unit include: (1) Applying Formal Logic only to statements; (2) Symbolizing Simple Positive and Negative Claims; (3) The Laws of Non-Contradiction and Excluded Middle; (4) The Rules of Reiteration and Double Negation; (5) Introduction to Basic Truth Tables; (6) Introduction to Basic Venn Diagrams; (7) Making Sentences more Precise; (8) Making Sentences more Concise; (9) Distinguishing the Explicit, Literal Meaning of Logical Connectives from Implicatures; (10) Testing the Validity of Rules of Inference; (11) Making use of formal tools to reason more methodically; (12) Making use of formal tools to more objectively approach controversial topics.
4.1 The Form of an Argument: Symbolizing claims helps us focus on the form of an argument rather than its content. We begin by symbolizing simple statements and
negations of simple statements. The negation of a simple statement is false whenever the simple statement is true, and it is false whenever the simple statement is true.
Learning Activities
● Introduction to Formal Logic
● What to Symbolize
● Symbolization: Positive Claims
● Symbolization: Negative Claims
4.2 True and False: Classical Logic assumes that every proposition is either true or false and not both. We can use this to create a truth table for negated
statements, including those with multiple negations, and to prove valid the rule of double negation. This allows us to see how a truth table with multiple logical connectives works.
Learning Activities
● The Laws of Non-Contradiction and Excluded Middle
● Truth Tables: Positive and Negative Claims
● Negation and Double Negation
4.3 Clarifying Claims: A claim is a proposition which someone asserts, either so that you will believe the claim, or so that you will have a reason to believe some
other claim: it is the premise of an argument. In addition to being relevant to the conclusion, there are four other virtues that we want premises or claims to have in an argument. We want premises to be precise, concise, explicit, and to involve methodical reasoning.
Learning Activities
● More Precisely
● More Concisely
● More Explicitly
● More Methodically
4.4 Modeling Validity: We can model validity using truth tables when their form includes logical connectives, and using Venn Diagrams when their form
involves claims about categories. In both cases we first model the premises, and then confirm that the conclusion must be true on that model.
Learning Activities
● Validity and Truth Tables
● Validity and Venn Diagram
● Rules of Inference
● Controversy
This topic 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 Unit include: (1) Distinguishing disjunctive and conjunctive claims; (2) Symbolizing disjunctive and conjunctive claims; (3) Symbolizing “Neither-Nor” and “Not Both” sentences; (4) Truth tables for conjunctions and disjunctions; (5) Rules for creating truth tables of unlimited length; (6) The rules of conjunction introduction and elimination; (7) The rule of disjunction elimination; (8) The rules of Distribution and DeMorgan’s Law; (9) The rule of disjunctive syllogism and common fallacies.
5.1 Symbolizing Disjunctions and Conjunctions: This module introduces ways to symbolize disjunctive and conjunctive
claims. Symbolization helps us abstract away from the content of a
sentence to consider its form.
Learning Activities
● Disjunctive and Conjunctive Claims
● Symbolizing Disjunctions
● Symbolizing Conjunctions
● Symbolizing Neither-Nor and Not-Both
5.2 Truth Tables for Conjunctions and Disjunctions: This module discusses how to create truth tables for conjunctions,
disjunctions, and combinations of conjunctions, disjunctions, and negations, as well as how to create truth tables for any number of
atomic sentences and logical connectives.
Learning Activities
● Truth Tables for Disjunctions
● Truth Tables for Conjunctions
● Truth Tables for Complex Conjunctions and Disjunctions
● Truth Tables without Limits
5.3 Rules for Conjunctions and Disjunctions: This module presents the rules of conjunction introduction (&I) and
conjunction elimination (&E), disjunction introduction (vI), distribution
(DISTRIB), and disjunctive syllogism (DS). It also presents the fallacies
of affirming a disjunct, false dilemma, and alternative advance.
Learning Activities
● Conjunction Rules
● Disjunction Introduction
● Distribution
● Disjunctive Syllogism
● Fallacies with Disjunctions
5.4 Practice with Conjunctions and Disjunctions: This module contains activity pages which provide practice with
symbolizing, creating truth tables for, and applying rules of inference
for conjunctions and disjunctions. It also introduces DeMorgan’s law, and proves its validity.
Learning Activities
● Practice Translating Conjunctions and Disjunctions
● Practice Using Truth Tables with Conjunctions and Disjunctions
● Practice with DeMorgan’s Law (DEM)
● Practice with Enthymemes for Conjunction and Disjunction
Categorical logic studies the logic of claims about all members (universals) or some members (existentials) of a category. This topic 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 Include: (1) Distinguishing Existential and Universal Claims; (2) Using Venn Diagrams to model claims and prove validity; (3) Basic rules for Existentials and Universals; (4) Relationships of contradiction and logical equivalence between categorical claims; (5) Constants, Variables, and Identity; (6) Categorical Syllogisms, including Standard Form, Mood, Figure, and the 15 Valid Forms.
6.1 Existentials and Universals with Venn Diagrams: Venn Diagrams can be used to represent Existential (SOME) and
Universal (ALL) claims. They can then be used to determine whether or not Categorical Syllogisms are valid.
Learning Activities
● Existential and Universal Claims
● Modeling Existentials with Venn Diagrams
● Modeling Universals with Venn Diagrams
● Using Venn Diagrams to Prove Validity
6.2 Rules for Universals and Existentials: In this module, we discuss some of the most basic rules available for dealing with Universals and Existentials. First, we introduce two very basic rules: the rule of existential generalization, and the rule of applied universal instantiation. These rules express the basic meaning
of what a “existential” or “universal” claim is. Next, we discuss some of the “immediate inference” which we can
easily see through looking at a truth table, through the rules of Contraposition, Obversion, and Conversion. We then turn to the law
of identity and the law of the indiscernibility of identicals. Lastly, we introduce the notion of an arbitrary variable, and see how it
is used in the rule of existential instantiation. By the end of this module, we should have enough of the basics in place to begin
considering the rules of categorical syllogism in the next module.
Learning Activities
● Basic Rules for Universals and Existentials
● Conversion, Obversion, and Contraposition
● Identities
● Variables
6.3 Categorical Syllogisms: This module presents the rules for valid categorical syllogisms, and the fifteen valid forms of categorical syllogism. We begin with three
clearly valid forms, then present the six rules and the fallacies which violate the six rules. We then show how to categorize categorical
syllogisms by mood and figure, and then present the 15 valid mood/figure combinations. Only these 15 forms of categorical syllogism are valid.
Learning Activities
● Three Valid Forms of Categorical Syllogism
● Fallacies and Categorical Syllogisms
● Mood and Figure for Categorical Syllogism
● Valid Categorical Syllogisms of the First Figure
● Valid Categorical Syllogisms of the Second Figure
● Valid Categorical Syllogisms of the Third Figure
● Valid Categorical Syllogisms of the Fourth Figure
6.4 Practice with Universals and Existentials: This module provides practice using Venn Diagrams to verify rules of
inference, and applying the rules for Categorical Syllogism. It also
introduces the Quantifier Negation law.
Learning Activities
● Practice with Venn Diagrams and Validity
● Practice with the Quantifier Negation Law
● Practice with Categorical Syllogism
This topic 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: (1) The structure of a conditional, with an antecedent and consequent; (2) Material conditionals; (3) Counterfactual conditionals; (4) Strict conditionals; and (5) Biconditionals. Topics reviewed from previous units include: (1) Intellectual Virtues; (2) Fallacies; (3) Symbolization; (4) Truth Tables; (5) Rules of Inference; (6) Venn Diagrams; and (7) Categorical Syllogisms.
7.1 Review of Prior Modules 1-6: This module provides a review of the topics covered earlier, including:
Intellectual Virtues, Fallacies, Symbolization, Truth Tables, Rules of
Inference, Venn Diagrams, and Categorical Syllogisms.
Learning Activities
● Review: Intellectual Virtues
● Review: Fallacies
● Review: Symbolizing
● Review: Truth Tables
● Review: Rules of Inference
● Review: Venn Diagrams
● Review: Categorical Syllogisms
7.2 Three Types of Conditionals: This module provides practice using Venn Diagrams to verify rules of
inference, and applying the rules for Categorical Syllogism. It also
introduces the Quantifier Negation law.
Learning Activities
● Antecedents and Consequents
● Material Conditionals
● Counterfactual Conditionals
● Strict Conditionals
● Biconditionals
This topic 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: (1) Using Material Conditionals to make an argument valid; (2) Symbolizing Material Conditionals; (3) Symbolizing multiple material conditionals and biconditionals; (4) Truth Tables for Material Conditionals and Biconditionals; (5) Modus Ponens and Modus Tollens; (6) Material Contraposition, Implication, and Negated Conditional; (7) The Fallacies of Denying the Antecedent, Affirming the Consequent, and Commutation of Conditionals; and (8) Completing Proofs and Enthymemes
8.1 Symbolizing Material Conditionals: This module introduces ways to symbolize conditional claims.
Conditional claims play a role in many valid forms of argument.
Learning Activities
● Why Material Conditionals?
● Symbolizing Material Conditionals
● Symbolizing Material Conditionals with Negation
● Symbolizing Complex Material Conditionals
8.2 Truth Tables for Material Conditionals: This module discusses how to create truth-tables for material
conditionals, including multiple, embedded material conditionals, and biconditionals.
Learning Activities
● Truth Tables: Material Conditionals
● Truth Tables: Material Conditionals with Negation
● Truth Tables: Complex Material Conditionals
● Truth Tables: Multiple Material Conditionals
8.3 Rules for Material Conditionals: This module introduces the rules of modus ponens and modus tollens,
as well as the fallacies of affirming the consequent and denying the antecedent. It also introduces the rule of implication, to convert
between conditionals and disjunctions. Modus ponens is especially useful for representing an argument that one claim follows from another, and modus tollens is especially useful for representing an argument that one claim should be rejected because it would lead to something false.
Learning Activities
● The Rule of Modus Ponens
● Complex Uses of Modus Ponens
● Using Modus Ponens to Produce Validity
● The Rule of Material Contraposition
● The Rule of Modus Tollens
● Using Modus Tollens to Reject a Claim
● The Rule of Material Implication
8.4 Practice with Material Conditionals: This module offers practice with symbolizing material conditionals,
creating and interpreting truth tables, applying the rules of modus ponens and modus tollens, and completing proofs and enthymemes.
Learning Activities
● Practice with Symbolizing Material Conditionals
● Practice with Material Conditionals and Truth Tables
● Practice with Modus Ponens and Modus Tollens
● Practice with Proofs
● Practice with Enthymemes
This topic 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: (1) Applications of valid arguments; (2) Recognizing Valid Arguments; (3) Applied Truth Tables; (4) Applied Venn Diagrams; (5) Proofs with Propositional Rules; (6) Proofs with Categorical Rules; (7) Recognizing Applications of a Rule; (8) Complex Enthymemes; (9) Translating Back into English; (10) Choosing Propositional Rules; (11) Choosing Categorical Rules; (12) Extracting arguments.
9.1 Testing Validity for Complex Arguments: Nothing in this module should be new, but you will have to apply what you have learned to more difficult problems. Most of the valid arguments we encounter in ordinary language rely on a hybrid of propositional and categorical rules. Most of the invalid
arguments we encounter in ordinary language seem intuitively invalid, but it takes work to prove to those who make them that they are
invalid. The goal of this module is to give you a method for proving that an argument which seems valid is valid, or proving that an argument
which seems invalid is not valid, at least within the rules of propositional or categorical logic.
Learning Activities
● Applications of Valid Arguments
● Recognizing Valid Arguments
● Applied Truth Tables
● Applied Venn Diagrams
9.2 Proving Validity for Complex Arguments: The purpose of this module is to give you practice taking arguments written in English, translating them, and them proving them valid using our existing rules of inference. Make sure you have with you notes with the valid propositional rules of inference and the valid
categorical inference forms before you begin this module.
Learning Activities
● Propositional Rules: Proofs
● Propositional Rules: More Proofs
● Categorical Rules: Proofs
● Categorical Rules: More Proofs
9.3 Filling in the Missing Pieces: In addition to the ability to work through the steps of a proof to reach the conclusion, if is often helpful to be able to recognize other missing pieces of an argument: which rule has been applied, what the premises ought to be, or how to translate everything back into
English. This module offers suggestions and practice on doing those three things.
Learning Activities
● Recognizing Applications of a Rule
● Complex Enthymemes
● Translating Back into English
9.4 Argumentative Strategies: This module offers you some strategies when trying to figure out how to move forward with a proof when it isn’t obvious how the conclusion follows. First, it discusses some strategies within propositional logic for each of the three two-place main connectives: disjunction, conjunction, and conditionals. Second, it discusses some strategies within categorical logic for creating a valid categorical syllogism when the sentences available do not fit into the rules required by standard form. Lastly, it presents the idea of “extracting an argument”, which is taking an informal argument and reconstructing it as a formal argument.
Learning Activities
● Choosing Propositional Rules
● Choosing Categorical Rules
● Preview of Extracting Arguments
This topic 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.
10.1 Conditional Proof: The rule of conditional proof allows us to prove that a conditional claim is true, by proving that the consequent follows when we assume the antecedent. It is also known as “conditional introduction”.
Learning Activities
● Provisional Assumptions
● Method of Conditional Proof
● Practice with Conditional Introduction
10.2 Hypothetical Syllogism and Exportation: Two useful rules which we can prove using Conditional Proof are
Hypothetical Syllogism (HS) and Exportation (EXPO). We can also present another rule for dealing with disjunctions, Disjunction
Elimination.
Learning Activities
● Disjunction Elimination Rule
● The Rule of Hypothetical Syllogism
● The Rule of Exportation
10.3 Indirect Proof: The last set of rules we will study are also the most powerful: the method of indirect proof gives us the rules of negation introduction and elimination.
Learning Activities
● Principle of Indirect Proof
● Negation Introduction
● Negation Elimination
10.4 Applications of Conditional and Indirect Proof: This module discusses how to use conditional proof and indirect proof to model arguments, and some proof strategies.
Learning Activities
● Modeling Arguments as Conditional Proofs
● Modeling Arguments as Indirect Proofs
● Three Proof Strategies
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.
11.1 The Extraction Method: Extracting arguments is the culmination of the skills which we have studied up to this point in the course. ‘Extracted’ or ‘reconstructed’ arguments are easy to understand, make every premise explicit, and make clear which premises need to be defended.
Learning Activities
● Overview of Extractions
● Identifying Premises and Conclusions
● Repairing Arguments
11.2 Tricks and Shortcuts: There are a number of tricks or shortcuts to repairing arguments in order to make them valid. These tricks involve employing many of the
rules of inference.
Learning Activities
● Disjunctive Strategies
● Conditional Strategies
● Categorical Strategies
11.3, Evaluating Arguments: Extracted arguments must be valid, but should have no more premises than are actually used to obtain the conclusion. They should avoid
obvious fallacies. When an extraction meets these criteria, it can then be evaluated for soundness.
Learning Activities
● Evaluating for Validity
● Evaluating for Fallacies
● Evaluating for Soundness
11.4, Practice with Extractions: The only way to get better at extracting arguments is practice. This module offers practice in extracting arguments.
Learning Activities
● Extractions from Simple Prose
● Extractions from Complex Prose
● Extracting your Own Arguments
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.
12.1 Direct Evidence: Perceptual evidence can give us direct acquaintance with the facts which make a claim true. Testimony or memory can also make us
acquainted with the facts perceived at another time or by another person. All these forms of evidence can be wrong at times, however.
Learning Activities
● What is Evidence?
● Using Evidence to Defend a Premise
● Perceptual Evidence
● Testimonial Evidence
● Evidence From Memory
12.2 Supporting Evidence: Even when we don’t have direct evidence about a claim, evidence about similar or related cases can support the claim. Arguments by analogy and induction rely on this principle.
Learning Activities
● Arguments by Analogy
● Arguments by Induction
● Scientific Laws
12.3 Suggestive Evidence: We have already studied the evidence we get directly, such as through observation, and the evidence we get through inductive inferences
based on similar cases. A third category, the weakest sort of evidence, occurs when a hypothesis would explain the other evidence we have.
Learning Activities
● Abduction and Hypothesis
● Disanalogies and Exceptions
● Inference to the Best Explanation
● Moral Arguments
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.
13.1 Weighing the Evidence: Probability is a tool we can use to mathematically describe the outcome of weighing the evidence for and against a claim. Probabilities can be obtained from theoretical models, statistical generalizations, or subjective judgments.
Learning Activities
● What is Probability?
● Statistical Probability
● Statistical Significance
● Subjective Probability
● Fallacies and Probability
13.2 Probability and Logic: This module discusses how to apply probabilities to individual cases, and now to compute the probability of a conjunction of events or a
disjunction of events. It is important to pay attention to whether events are independent of one another, and whether events are mutually exclusive.
Learning Activities
● Making and Applying Generalizations
● Probability and Conjunctions
● Probability and Disjunctions
13.3 Conditional Probabilities: We can calculate conditional probabilities, or the probability of one event given another event. This allows us to evaluate the strength of inductive arguments and to calculate how much new evidence should impact our previous beliefs.
Learning Activities
● Probability and Conditionals
● Probability of a Conclusion Given the Premises
● Probability and Symmetry Over Time
This topic 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.
14.1 Review of Topics 8-13: Walk through a series of review exercises on Material Conditionals, Proving Validity, Conditional and Indirect Proof, Extracting Arguments, Evidence, and Probability.
Learning Activities
● Review of Material Conditionals
● Review of Proving Validity
● Review of Conditional and Indirect Proof
● Review of Extracting Arguments
● Review of Evidence
● Review of Probability
14.2 Types of Explanation: Explanations are used to support the premises of an argument, in an attempt to establish why something is the case. Learn the different kinds of explanation and how to evaluate causal explanations.
Learning Activities
● What is an Explanation?
● Definitional Explanations
● Functional Explanations
● Compositional Explanations
● Causal Explanations
● Mill’s Methods
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: (1) the social responsibilities of scholarship, ethics, and understanding; (2) the epistemic responsibilities of curiosity, critical judgment, and openness to change; and, lastly, (3) the individual responsibilities of fairness, keeping perspective, and imagination.
15.1 Social Freedoms and Responsibilities: Being a critical thinker affords certain freedoms, but also brings with it certain responsibilities, in one’s intellectual interactions with others. First, there is the freedom to be critical of appeals to irrelevant authority of social status, when they are used as substitutes for
genuine expertise. With this, however, comes the responsibility to track sources carefully and cite legitimate expertise when making
arguments. Second, there is the freedom to be critical of social conventions, and to rethink how things are typically done. With this, however, comes
the responsibility to develop an understanding of ethics, and to apply ethics to everyday life. Third, there is the freedom to maintain one’s own beliefs even in the face of sharp disagreement. With this, however, comes the responsibility to genuinely listen to and seek to understand opposing views and the arguments behind them.
Learning Activities
● Scholarship
● Practical Ethics
● Understanding
15.2 Epistemic Freedoms and Responsibilities: Studying logic brings a number of freedoms and responsibilities in the beliefs one forms. This includes applying critical judgment by rejecting claims which, even if they can’t be proven false, are not necessary to explain anything known to be true. It includes the freedom to be
intellectually curious, and the responsibility to insist on deeper and more comprehensive explanations. It includes the freedom to change one’s mind, and the responsibility to do so when appropriate.
Learning Activities
● Critical Judgment
● Curiosity
● Change
15.3 Individual Freedoms and Responsibilities: Students of logic have the opportunity to reconsider biases that say that we ourselves, our present time, and the way our world happens to be, are especially privileged over other people, times, or ways things could be.
Learning Activities
● Fairness
● Perspective
● Imagination