Part Ten X › Division I I › Section 10/12 10/12

Formal Logic, Metalogic, and Applied Logic

Subject Outline

AFormal logic
- 1The propositional calculus: the logic of unanalyzed sentences in combination
  - aGeneral features of the propositional calculus: symbols employed for propositional connectives or operators (i.e., "not," "and," "or," "if. . . then," "is equivalent to"), propositional variables
  - bSpecial systems of the propositional calculus
- 2The predicate calculus: the logic of quantified functions of terms
  - aGeneral features of the predicate calculus: individual variables and predicate variables, universal and existential quantifiers (i.e., "any" or "all," "some" or "one")
  - bThe lower predicate calculus: the logic of individual variables
  - cHigher order predicate calculi: the logics of classes of variables
- 3Syllogistic: the theory of the syllogism
- 4Modal logic: the logic of necessity, possibility, and contingency; systems of and validity in modal logic
- 5Set theory and natural-number arithmetic
BMetalogic: the study of the syntax and the semantics of formal languages, formal systems, and logical calculi
- 1The nature and elements of metalogic
- 2The nature of a formal system and of a formal language
- 3Discoveries about formal mathematical systems: completeness and consistency, decidability and undecidability
- 4Discoveries about logical calculi
- 5Model theory: the study of the interpretations, or models, that satisfy the axioms of a given formal system
CApplied logic
- 1The critique of forms of reasoning
  - aTheory of argumentation: the new rhetoric
  - bAnalysis of logical fallacies: material, verbal, and formal fallacies
- 2Epistemic logic: logic dealing with the concepts of belief, knowledge, assertion, doubt, and question
- 3Practical logic: logic dealing with the concepts of choosing, planning, commanding, and permitting
- 4Logics of physical application