Logic I
syllogisms : proofs : truth trees
Logic is the science and art of reasoning well. Join us as we dive into the study of logic starting with James Nance's introductory and intermediate logic books. Students will explore definitions, statements, syllogisms, fallacies, and formal logic study.
This course will emphasize the importance of memorizing the square of opposition, tests of validity, and logic rules.
- Materials:
- Introductory Logic by James B Nance and Douglas Wilson
- Intermediate Logic by James B Nance
How to navigate the course:
- enroll as math master
- purchase text
- download and print the syllabus *
- watch class lesson videos
- follow syllabus for course assignments
- email additional questions to tutor
- complete assessments
* syllabus, schedule, registration, etc can be found in the logistics unit below
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Course Content
Units
- LOGISTICS, RESOURCES, & REGISTRATION
- Unit 1 : Definitions Start logic by defining your terms 2 weeks
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Unit 2 : Statements
Statements and how to use them in logic 4 weeks
- § 6-10 : StatementsAll about statements: What are they and what kinds are there 45 min
- § 11-13 : Categorical StatementsCategorical statements and how to use them in logic 45 min
- § 14-16 : Square of OppositionMemorizing the square of opposition by understanding how it works 45 min
- § 17-18 : ImplicationsUse the square of opposition to study implications 45 min
- Unit 3 : Syllogism Learn how to create a true and valid argument 3 weeks
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Unit 4 : Logical Arguments I
Translate ordinary sentences to logic statements and analyze them for validity. 3 weeks
- § 27-28 : InferencesLearn to translate normal english sentences into logic statements 45 min
- § 29-30 : Inclusive & ExclusiveExplore what an inclusive and exclusive term means in a logical argument 45 min
- § 31-32 : Hypothetical SyllogismsLearn how to create a hypothetical statement and determine the validity 45 min
- Unit 5 : Fallacies Learn about informal fallacies, what are they and when do people use them and why 2 weeks
- Introductory Logic Review Do you know what to review for the semester assessment? 1 hr
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Unit 1 : Truth Tables
Get started with the special language of logic! 4 weeks
- § 1-3 : Propositional LogicLearn about the symbols used in propositional logic 45 min
- § 4-6 : Equivalence & ContradictionLearn about the terms used and how they are expressed in symbols 45 min
- § 7-9 : Truth TablesLearn about creating and using truth tables to determine validity of arguments 45 min
- § 10-12 : The DilemmaLearn about the dilemma and how to deal with it in logic 45 min
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Unit 2 : Formal Proofs
dive into the laws surrounding a formal proof 5 weeks
- § 13-14 : Rules of InferenceLearn the rules of inference that we use to prove formal arguments 45 min
- § 15-16 : Formal ProofsLearn how to use our rules to complete a formal proof 1 hr
- § 17 : Practice with ProofsPractice completing formal proofs 45 min
- § 18-19 : The ConditionalLearn how to use the conditional in a formal proof 45 min
- § 20-21 : Proving RulesExplore the necessity of rules, or are they? 45 min
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Unit 3 : Truth Trees
Work with paths to validity using truth trees 3 weeks
- § 22-23 : Truth TreesLearn the basics of breaking an argument down to its simple literals 45 min
- § 24-25 : Constructing Truth Treespractice working with truth trees to determine tautology and self-contradiction 45 min
- § 26 - 27 : Validity with Truth TreesUse truth trees to test an argument for validity 45 minn
- Unit 4 : Arguments II Practice using our logic tools in actual arguments 1 week
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Unit 5 : Digital Logic
Explore the world of digital logic and apply those thinking skills to the computer world 4 weeks
- § 29-31 : Number BasesLearn how to convert our base 10 numbers to base 2 and the electronic world 45 min
- § 32-35 : Logic GatesSee how computers use the logical operators to perform tasks 45 min
- § 35-37 : Simplification RulesLearn about applying our logic rules to our binary gates 45 min
- § 38-40 : Karnaugh MappingLearn how to create a circuit from a truth table 45 min
- Intermediate Logic Review Review intermediate logic by completing some practice problems in preparation for the assessment 1 week