Further Logic
- Arts
- 400 level
- 3 credit units
- 97 pages
- 10 units
This course, Further Logic, deepens learners' skills in formal proof of validity and sharpens their understanding of mathematical logic. It covers the logic of quantification, analyzing the internal structures of simple propositions, and symbolizing propositions with quantifiers. Students will learn quantification rules, predicate calculus, conditional and indirect proofs, proofs of invalidity, and truth tree analysis. The course also explores rule of inference in truth trees and the application of truth tree to first order logic.
About this course
- Difficulty
- Intermediate
- Study hours
- 120 hours
- Maths
- Intermediate
- Content
- Theoretical, problem solving
- Practical work
- No
- PHL301: Introduction to Logic
- Assignments
- Tutor Marked Assessments
- Final Examination
What you'll read
The real module and unit structure of PHL431, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
PHL431 · Unit 1: Quantificational Logic
Quantificational Logic analyzes the internal structures of propositions into subject and predicate terms and symbolize them separately. It has a device for symbolizing propositions that contain words like ”All” and “Some”, that is propositions that have quantity or contain quantifiers; this device is called quantification.
What you should be able to do
- Analyze simple propositions into subject and predicate terms.
- Symbolize propositions containing quantification.
- Construct formal proofs of validity using quantification rules.
- Apply conditional and indirect proofs.
- Perform truth tree analysis of propositions and arguments.
- Prove invalidity in predicate logic.
What it prepares you for
- Logician
- Analyst
- Researcher
- Educator
- Critical Thinking Consultant
- Academia
- Research Institutions
- Government
- Consulting
- Artificial Intelligence
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 1: Quantificational Logic
Unit 3: Symbolizing Relational Propositions
Requires understanding of complex relationships between universal and existential quantifiers, and translating them into logical notation.
- Module 2: Formal Proof of Validity
Unit 1: Formal Proof of Validity in Quantificational Logic
Application of multiple rules of inference and replacement in complex derivations requires strong analytical and problem-solving skills.
- Module 3: Truth-Tree Tests
Unit 3: Proving Invalidity in Predicate Logic
Requires understanding of decomposition rules and strategic application to efficiently determine validity or invalidity.
A suggested way through it
13 weeks, about 39 hours in total. Yours will differ.
- Week 1Module 1: Quantificational Logic
Unit 1: Quantificational Logic · 3 hours
Read the introduction to Quantificational Logic.. Analyze simple propositions into subject and predicate terms.. Practice obtaining propositions from propositional functions.. Symbolize universal and particular propositions..
- Week 2Module 1: Quantificational Logic
Unit 2: Symbolization in Quantificational Logic · 3 hours
Study the techniques for symbolization in quantificational logic.. Translate expressions into logical notation.. Identify the scope of quantifiers.. Differentiate between free and bound occurrences of variables..
- Week 3Module 1: Quantificational Logic
Unit 3: Symbolizing Relational Propositions · 3 hours
Learn to symbolize relational propositions.. Analyze the internal structure of relational propositions.. Understand the types of relationships between propositions.. Practice using quantifiers in symbolizing relational propositions..
- Week 4Module 1: Quantificational Logic
Unit 4: Properties of Relations · 3 hours
Study the properties of relations: symmetrical, transitive, and reflexive.. Symbolize various categories of relational properties.. Distinguish between different types of relations.. Practice symbolizing relational propositions with appropriate predicates and variables..
- Week 5Module 2: Formal Proof of Validity
Unit 1: Formal Proof of Validity in Quantificational Logic · 3 hours
Understand the rules of quantification.. Recapitulate the rules of inference.. Apply rules of quantification and inference.. Construct formal proofs of validity for arguments in quantificational logic..
- Week 6Module 2: Formal Proof of Validity
Unit 2: Conditional Proof · 3 hours
Learn the method of conditional proof.. Construct formal proofs of validity using conditional proof.. Apply conditional proof in formal proof of validity.. Understand the strengthened rule of conditional proof..
- Week 7Module 2: Formal Proof of Validity
Unit 3: Indirect Proof · 3 hours
Study the method of indirect proof.. Construct formal proofs of validity using indirect proof.. Apply indirect proof in formal proof of validity.. Understand the rule of quantifier negation..
- Week 8Module 3: Truth-Tree Tests
Unit 1: Truth-Tree Tests of Propositions · 3 hours
Understand the general procedure for constructing truth trees.. Learn about decomposition of propositions.. Construct truth trees involving reduction of compound statements.. Apply truth tree tests to determine consistency and contradiction..
- Week 9Module 3: Truth-Tree Tests
Unit 2: Truth Tree Test of Validity in Propositional Logic · 3 hours
Apply truth tree tests to determine consistency and contradiction.. Practice testing groups of statements for consistency.. Construct truth trees for various propositional logic arguments..
- Week 10Module 3: Truth-Tree Tests
Unit 3: Proving Invalidity in Predicate Logic · 3 hours
Learn to prove invalidity in predicate logic.. Understand the rules governing proof of invalidity.. Construct truth tree tests of invalidity in predicate logic.. Practice applying truth tree method to test validity in Predicate Logic.
- Week 11Module 2: Formal Proof of Validity
Unit 1: Formal Proof of Validity in Quantificational Logic · 3 hours
Review Formal Proof of Validity in Quantificational Logic. Practice constructing formal proofs of validity for arguments in quantificational logic..
- Week 12Module 2: Formal Proof of Validity
Unit 2: Conditional Proof · 3 hours
Review Conditional Proof. Practice constructing formal proofs of validity using conditional proof..
- Week 13Module 2: Formal Proof of Validity
Unit 3: Indirect Proof · 3 hours
Review Indirect Proof. Practice constructing formal proofs of validity using indirect proof..
Preparing for the exam
- Create detailed concept maps linking key concepts from each module.
- Practice symbolization exercises from Units 1-4 weekly.
- Work through all examples of formal proofs in Units 5-7, focusing on rule application.
- Master truth tree construction techniques from Units 8-10, emphasizing strategic path selection.
- Review all exercises from the course guide, focusing on areas of weakness.
- Allocate specific time slots for focused study and practice each day.
- Form study groups to discuss challenging concepts and practice problem-solving.
- Prioritize understanding the underlying principles over memorization of rules.
- Simulate exam conditions by completing practice questions within time limits.
Questions students ask about this course
What is PHL431 about?
This course, Further Logic, deepens learners' skills in formal proof of validity and sharpens their understanding of mathematical logic. It covers the logic of quantification, analyzing the internal structures of simple propositions, and symbolizing propositions with quantifiers. Students will learn quantification rules, predicate calculus, conditional and indirect proofs, proofs of invalidity, and truth tree analysis. The course also explores rule of inference in truth trees and the application of truth tree to first order logic.
How many units does PHL431 have?
PHL431, Further Logic, has 10 units across 3 modules, over 97 pages of course material. You can read it one unit at a time.
How many credit units is PHL431?
PHL431 carries 3 credit units, at 400 level in Arts.
Is PHL431 hard?
PHL431 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical and problem solving work.
How long does PHL431 take to study?
About 120 hours of study, spread across its 10 units.
How is PHL431 assessed?
PHL431 is assessed by Assignments, Tutor Marked Assessments and Final Examination.
What do I need before starting PHL431?
PHL301: Introduction to Logic
What can I do with PHL431?
Logician, Analyst, Researcher, Educator and Critical Thinking Consultant.