Explore philosophical logic through comprehensive lectures covering propositional logic, predicate logic, modal logic, and their applications in philosophy, discrete mathematics, computing science, and linguistics. Master the translation of English statements into logical notation, construct and analyze truth tables for simple and complex formulas, and learn to identify tautologies, contradictions, and contingencies. Develop proficiency in truth tree methods for testing validity and entailment, and practice natural deductive proofs using various inference rules including modus ponens, conditional proof, reductio ad absurdum, and quantifier rules. Study the syntax and structure of well-formed formulas, understand scope relationships and variable binding in predicate logic, and work with Boolean algebra concepts including conjunctive and disjunctive normal forms. Apply logical reasoning to determine argument validity and soundness, practice translating complex English expressions involving quantifiers like "no" and "not all," and explore modal logic proofs with necessity and possibility operators. Gain hands-on experience through numerous exercises and practice problems that reinforce theoretical concepts with practical applications in digital logic and formal reasoning systems.

Syllabus

Introduction to Propositional Logic Translations
Four Exercises in TRANSLATING ENGLISH into PROPOSITIONAL LOGIC - LOGIC
Propositional Logic Syntax and Structure
Three Exercises in WELL-FORMED FORMULAS in PROPOSITIONAL LOGIC - LOGIC
Propositional Logic Truth Tables
Two Exercises in drawing TRUTH TABLES in PROPOSITIONAL LOGIC
Propositional Logic Challenging Truth Tables
Two Exercises in Drawing TRUTH TABLES for COMPLEX WFFS in PROPOSITIONAL LOGIC
Propositional Logic Tautologies, Contradictions, and Contingencies
Three Exercises in TAUTOLOGIES, CONTRADICTIONS, and CONTINGENT WFFS - Logic
Propositional Logic Validity, Soundness, and Entailment
How to determine whether an argument is VALID - Logic
Propositional Logic Indirect and Partial Truth Tables
Two Exercises in using PARTIAL TRUTH TALBES to determine VALIDITY - Logic
Propositional Logic Truth Trees (and, or, not)
Two exercises in TRUTH TREES for negation, conjunction, and disjunction - Logic
Propositional Logic Truth Trees (conditionals)
Two exercises in TRUTH TREES with Negation, Conditional, and Biconditional - Logic
Exercises in COMPLEX TRUTH TREES - Logic
Propositional Logic Truth Trees Tautologies and Contradictions
Two exercises in how to prove TAUTOLOGIES and CONTRADICTIONS with TRUTH TREES - Logic
Propositional Logic Truth Trees Validity
Two exercises in proving VALIDITY and ENTAILMENT using TRUTH TREES - Logic
Natural Deductive Logic: RULES #1 (R, &E, &I, MP, CP)
Two Exercises in Natural Deductive Logic: RULES #1 (R, &E, &I, MP, CP) - Logic
Natural Deductive Logic: RULES #2 (vI, vE, DN, RAA)
Two exercises in Natural Deductive Logic: RULES #2 (vI, vE, DN, RAA) - Logic
Natural Deductive Logic: RULES #3 (=I, =E)
Two practice exercises in Natural Deductive Logic: RULES #3 (=I, =E) - Logic
Natural Deductive Proofs - TrevTutor's Propositional Logic Workbook
Natural Deductive Logic: DERIVABLE RULES (MT, HS, DS, DeM)
Four Exercises in Natural Deductive Proofs: DERIVABLE RULES (DeM, Contra, Impl)
Natural Deductive Proofs: THEOREMS
Three Exercises in Natural Deductive Proofs: THEOREMS - Logic
Boolean Algebra in 13 Minutes
Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF)
Syntax of PREDICATE LOGIC and WELL-FORMED FORMULAS (wffs)
SCOPE and FREE and BOUND Variables in Predicate Logic
Translating ENGLISH into PREDICATE LOGIC
Translating NO and NOT ALL into Predicate Logic
TRUTH TREES for QUANTIFIERS in Predicate Logic
VALIDITY and ENTAILMENT in Truth Trees for Predicate Logic
Truth Trees for the IDENTITY Operator
Natural Deductive Logic - Universal and Existential Rules
Natural Deductive Proofs in Modal Logic (Box In, Box Out)
Natural Deductive Proofs in Modal Logic (Diamond Out)