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2: First Order Logic

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    16848

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    • 2.1: Names and predicates
      This page focuses on the significance of predicates and their arity in first-order logic, emphasizing the importance of precise definitions for names and predicates to form valid arguments. It explains how to determine arity and underscores the distinction between natural and logical language to prevent ambiguity. Additionally, it covers sentence construction in first-order logic using prefix notation and provides a framework for translating these constructions to enhance clarity.
    • 2.2: “All” and “some”
      This page addresses the complexities of translating quantifiers in logical arguments, focusing on Aristotle's claim about mortality and the distinctions between "all" and "some." It introduces universal (∀) and existential (∃) quantifiers while defining free and bound variables within well-formed formulas.
    • 2.3: Reasoning with quantifiers
      This page covers reasoning with quantifiers, including universal and existential forms, and introduces inference rules like universal instantiation and existential generalization. It illustrates the construction of valid arguments in first-order logic and presents examples, including the Design Argument for an intelligent designer. The text critiques the Design Argument's soundness, contrasting it with Darwin's evolutionary theory as an alternative explanation for biological complexity.
    • 2.4: Universal derivation
      This page explores concepts from Plato's *Meno*, illustrating how Socratic dialogue fosters understanding of geometric principles and universal truths through specific instances. It discusses first-order logic, emphasizing the importance of arbitrary instances and the distinction between tautologies and logically true sentences.
    • 2.5: Relations, functions, identity, and multiple quantifiers
      This page explores relations, functions, and identity in first-order logic, providing examples and illustrating properties like reflexivity and symmetry. It discusses identity through examples such as Malcolm X and Leibniz’s Law, emphasizing its logical implications. Bertrand Russell's theories on existence and reference are examined, addressing challenges in assigning properties to non-existent entities and introducing quantifiers.
    • 2.6: Summary of first order logic
      This page covers first-order logic, detailing its components like names, variables, and predicates, along with syntax and semantics. It explains the structure of arguments, validity, and inference rules for deriving conclusions. Universal proofs are highlighted as ordered lists of sentences proving specific formulas, with examples of translating everyday phrases into first-order logic, including the translations for universal statements and negations.

    This page titled 2: First Order 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.