11: Logical Form and Sentential Logic
- Page ID
- 22026
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Abstracting from the content of an argument reveals the logical form of the argument. The initial sections of this chapter show that logical form is the key to the validity of deductively valid arguments. The chapter then explores sentential logic, the logic of sentences. Finally, the chapter investigates the tricky terms only, only if and unless. To understand reasoning that uses these terms—in contracts and legal documents—many persons are forced to hire a lawyer. You, however, will be one step closer to becoming their lawyer.
- 11.1: What is Logic?
- This page outlines the prescriptive nature of logic, emphasizing the ideal processes of reasoning. It distinguishes between deductive reasoning, which provides certain conclusions based on premises, and inductive reasoning, which yields probable conclusions. The importance of understanding the logical structure, or "logical form," is highlighted over merely collecting effective arguments. Future discussions will delve into these logical forms.
- 11.2: Logical Equivalence
- This page explains logical equivalence, highlighting that different sentences can convey the same logical meaning, such as active and passive voice examples. It defines logical equivalence as a mutual implication of two statements and stresses context's role in determining equivalence.
- 11.3: Logical Forms of Statements and Arguments
- This page explores the logical form of arguments, emphasizing its role in assessing validity in deductive reasoning. It provides examples, including a diamond argument that exemplifies the fallacy of affirming the consequent, and stresses that valid arguments follow identifiable patterns.
- 11.4: Sentential Logic
- This page covers the fundamentals of Sentential Logic, including the use of symbols for logical operations such as "or," "and," and negation. It explains how to create well-formed logical sentences and underscores the significance of syntax in complex structures, providing an example of incorrect grammar. The content also notes that, despite their complexity, logical sentences must remain finite.
- 11.5: Review of Major Points
- This page discusses the logical form of sentences and logical equivalence, vital for assessing deductive argument validity. It focuses on Sentential Logic, using connectors such as and, or, not, and if-then, and clarifies confusing terms. Additionally, it introduces 3-valued logic and the history of logic, emphasizing the necessity of multiple logical tools since no single one is suitable for all reasoning types.
- 11.6: Glossary
- This page covers basic concepts in logic, including conditionals, logical relationships, and key terms like antecedent and consequent. It explains logical fallacies, logical forms (contradictions and equivalences), and introduces deductive arguments such as modus ponens and modus tollens. The focus is on Sentential Logic, which examines complex sentences connected by logical operators.
- 11.7: Exercises
- This page covers logical equivalence and argument validity in sentential logic, including concepts like self-equivalence, deductibility, and logical fallacies. It provides examples and exercises on identifying logical forms, analyzing deductive arguments, and evaluating the implications of complex premises. Key terms such as "only if" and "unless" are introduced, along with scenarios that assess conditional statements.