What is Propositional Logic?

Propositional logic, formal logic, truth tables, symbolic proofs, tableaux, and predicate logic are the main topics of this introductory video. Welcome to the first video in the Propositional Logic series. In this video, we place propositional logic within the broader map of formal logic. We discuss why formal logic uses formal languages, what propositions are, how truth-functional connectives work, why truth tables matter, and how propositional logic prepares us for predicate logic. Chapters: 00:00 Welcome and series overview 00:49 What is propositional logic? 01:05 What logic studies 01:47 Formal logic and formal languages 02:56 Symbolic logic as a mathematical model 03:57 Same form, different topics 05:03 Where propositional logic stands 05:38 What is a proposition? 06:15 Atomic propositions 07:15 Logical connectives 07:45 Truth-functional structure 08:28 Truth tables 09:44 Semantic and proof-theoretic methods 11:19 A practical map of logic 12:50 Propositional logic and first-order logic 14:44 Limits and value of propositional logic 15:35 Example: P implies Q, P, therefore Q 16:22 Validity and logical consequence 18:17 Working definition 18:53 What comes next in the series 19:47 Learning formal reasoning 20:17 Resources and closing This video is introductory. The later videos will move more slowly through arguments, premises, conclusions, propositions, atomic and compound formulas, the five basic connectives, truth tables, logical equivalence, logical consequence, symbolic proofs, tableaux, and finally the transition to predicate logic. Main topics in this video: - What logic studies - Formal logic and formal languages - Propositions and truth values - Atomic and compound propositions - Truth-functional connectives - Truth tables - Semantic methods and proof-theoretic methods - A practical map of logic - The relation between propositional logic and first-order predicate logic Main source: P. D. Magnus, Tim Button, Robert Trueman, Richard Zach, with contributions by J. Robert Loftis and Aaron Thomas-Bolduc, forall x: Calgary: An Introduction to Formal Logic. Official page: https://forallx.openlogicproject.org/ PDF: https://forallx.openlogicproject.org/forallxyyc.pdf License note: forall x: Calgary is licensed under a Creative Commons Attribution 4.0 license. This video is an original presentation prepared for this channel. It is informed by the sources listed here, but it is not a reading or reproduction of the textbook. Supplementary sources used for terminology, examples, and technical checking: - Herbert B. Enderton, A Mathematical Introduction to Logic. - Ian Chiswell and Wilfrid Hodges, Mathematical Logic. - Ali Nesin, Önermeler Mantığı. - Additional introductory logic notes and references may be used for comparison and terminology control. Resources for this video: For this introductory video, no separate worksheet is needed at this stage. If worksheets, notation lists, summary PDFs, or related files are prepared later, they will be linked here or in the pinned comment. Subtitles: This video is narrated in English. Turkish subtitles are available through YouTube captions. Questions and corrections: You can write your questions, correction suggestions, or remarks in the comments. #PropositionalLogic #FormalLogic #SymbolicLogic #TruthTables #PredicateLogic