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1: Propositional Logic

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    16847

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    • 1.1: Developing a Precise Language
      This page covers the foundation of propositional logic, emphasizing clarity in truth values and avoiding vagueness and ambiguity. It introduces atomic sentences and their representation using capital letters, distinguishing between syntax and semantics. Truth tables are presented as a tool for evaluating the truth conditions of these sentences.
    • 1.2: “If…then….” and “It is not the case that….”
      This page covers conditionals in logic, focusing on "if...then..." structures represented as P→Q. It explains truth conditions through truth tables, discusses the principle of bivalence, and compares English phrases related to conditionals. Negation and its recursive application are introduced, with alternative symbols provided.
    • 1.3: Good Arguments
      This page explores the concept of logical arguments, focusing on validity and soundness through Ignaz Semmelweis’s historical example of handwashing. It distinguishes valid arguments—where conclusions follow from premises regardless of their truth—from sound arguments, which require true premises. The use of truth tables for analyzing argument validity is emphasized, along with the importance of scientific reasoning and hypothesis testing in empirical research.
    • 1.4: Proofs
      This page explores the limitations of truth tables for validating logical arguments, advocating for syntactic proofs using inference rules like modus ponens. It details direct proofs and their importance in ensuring conclusions follow from true premises. Additionally, it covers semantical validations through modus tollens and double negation, introducing the "repeat" rule for clarity in proofs.
    • 1.5: “And”
      This page covers the concept of logical conjunction "and" in propositional logic, including its use in translating English sentences and its equivalence to "but." It explains rules of adjunction and evaluates complex sentences with truth tables, highlighting key points like negation and logical equivalence. The text also touches on evidence-based reasoning through a narrative involving Inspector Tarski and Dr. Kronecker, illustrating how logical deductions are drawn from available evidence.
    • 1.6: Conditional Derivations
      This page outlines Hobbes's argument in "Leviathan" that without government, humanity faces constant conflict and insecurity, advocating for a social contract where individuals trade freedoms for safety. It also delves into logical concepts like conditional derivation and the construction of valid arguments, emphasizing the transition from assumptions to conclusions.
    • 1.7: “Or”
      This page explores important philosophical concepts from Plato's Euthyphro argument, focusing on the relationship between ethics and theology, and the nature of piety. It distinguishes between divine command theory and moral objectivity. The page also delves into logical disjunctions, explaining exclusive versus inclusive "or," and introduces rules for reasoning with disjunctions.
    • 1.8: Reductio ad Absurdum
      This page explores "reductio ad absurdum" through Galileo's argument against actual infinities, demonstrating contradictions related to natural and square numbers. It explains indirect proofs, emphasizing their role in propositional logic, and discusses the evolution of infinity concepts, referencing Georg Cantor.
    • 1.9: “… if and only if …”, Using Theorems
      This page covers key philosophical and logical concepts, beginning with David Hume's skepticism and empiricism concerning the validity of knowledge. It introduces biconditionals, highlighting their logical structure and reasoning rules. The discussion expands to De Morgan's Laws and the classifications of logical sentences: tautologies, contradictions, and contingent sentences.
    • 1.10: Summary of Propositional Logic
      This page introduces the basics of propositional logic, detailing its components, reasoning processes, and proof techniques. It emphasizes the principle of bivalence, which states that statements are strictly true or false, and explores the syntax and semantics of propositional sentences using truth tables.

    This page titled 1: Propositional Logic was last modified on Sun, 13 Sep 2026 17:21:18 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Craig DeLancey (OpenSUNY) via source content that was edited to the style and standards of the LibreTexts platform.