Logic

Synopsis

Your complete introduction to logic
When you see black clouds looming and predict it's going to rain, you're using logic. When you decide that all swans are white because all the swans you've seen are white, that's logic too (even though the conclusion is false).

As humans we want to understand how things are connected and why, so that we can derive things we don''t know yet from what we do. Logic studies the methods and principles to distinguish good and bad reasoning.

This book introduces three basic logical systems: categorical logic, propositional logic and predicate logic. It identifies in each system essential methods to test arguments, and there are illustrations and exercises to enhance your mastery of these skills.

By the time you finish you will understand what logicians were thinking when they designed logical systems and start to think like them.

Whether you are preparing for an essay, studying for an exam or simply want to expand ypour knowledge, Logic: A Complete Introduction is your go-to guide.

Summary

Chapter 1: Introduction to Logic

* Defines logic as the study of reasoning and argumentation.
* Examines the importance of logic in everyday life and academic pursuits.
* Introduces basic logical terms such as propositions, arguments, and validity.

Example: A weather forecaster makes the proposition "It will rain tomorrow." To assess the validity of this proposition, we need to examine the evidence supporting it, such as weather forecasts and historical data.

Chapter 2: Propositional Logic

* Introduces the concept of propositions as statements that are either true or false.
* Presents logical connectives (e.g., and, or, not) and truth tables to evaluate compound propositions.
* Discusses the principles of deductive reasoning in propositional logic.

Example: Consider the compound proposition "(A or B) and not C." Using a truth table, we can determine that this proposition is true whenever either A or B is true and C is false, such as the situation where "A is Thursday" (true), "B is Friday" (false), and "C is raining" (false).

Chapter 3: Predicate Logic

* Extends propositional logic to include predicates and quantifiers.
* Introduces the concept of variables, which represent objects or individuals in a domain.
* Discusses the logical relationships between subjects, predicates, and quantifiers (e.g., all, some, none).

Example: Let "P(x)" represent the predicate "x is a student." The statement "All students are over 18" can be expressed in predicate logic as: ∀x(P(x) → x > 18), where ∀x means "for all x."

Chapter 4: Syllogistic Logic

* Examines deductive reasoning in the form of syllogisms, which consist of two premises and a conclusion.
* Identifies the four valid syllogistic forms and the four invalid forms.
* Presents rules for evaluating the validity of syllogisms.

Example: Consider the syllogism:
* All mammals are warm-blooded.
* All cats are mammals.
* Therefore, all cats are warm-blooded.
This syllogism is valid because it follows the valid syllogistic form: All A are B; all C are A; therefore, all C are B.

Chapter 5: Inductive Logic

* Contrasts deductive reasoning with inductive reasoning, which draws conclusions from observed evidence.
* Examines different types of inductive arguments, such as generalization, analogy, and causal inference.
* Discusses the limitations and strengths of inductive reasoning.

Example: A scientist observes that all swans they have encountered are white. They might inductively conclude that all swans are white, but this conclusion is not logically certain because they cannot observe all swans in existence.