logic1

UNIVERSITY OF EDINBURGH :: PHIL08004

course summary. This course is an introduction to what is known as formal or symbolic logic, requiring no prior knowledge of philosophy or mathematics. Logic is the science of reasoning—the systematic study of the principles of good and bad reasoning, and has been a central and foundational part of philosophy, stretching back over 2000 years to the earliest investigations of logic in Ancient Greece. Logic is both an historically important area of philosophy and an indispensable tool used in philosophy. Understanding philosophical texts without any knowledge of basic logic is typically very difficult and a general grasp of the meaning of various key concepts is absolutely essential if one is to evaluate the strength of a philosophical position or philosophical claim. Virtually every area of philosophy—be it ethics, metaphysics, or epistemology—relies extensively on concepts from logic. The aim of this course is not to communicate results about logical systems per se but instead to impart a skill—the ability to recognize and construct correct derivations and countermodels. We will proceed via a graduated but unified development of logic from the basics of the sentential logic up to predicate logic. Along the way we will take short diversions into the historical issues that led to various developments (e.g. the insights of Aristotle, the Stoics, Leibniz, Frege, Jaskowski, and Tarski, among others).

course text: An Exposition of Symbolic Logic, Terrence Parsons

Weekly homework excersises will be assigned on the web application ∃LOGIC: this program is essential to the course. Instructions for getting started are here.

For help see ∃LOGIC tutorial videos.

Week 1 [ homework ]

- What is logic? (slides) [Parsons 0: 5-13]
- Formal languages and systems (slides) [Hunter, "Formal languages": 4-13]
- System MIU (slides) [Hofstadter: "The MU-puzzle"; Homework: MIU exercises]

Week 2 [ homework ]

- L1 (The language of `if' and `not') (slides) [Parsons 1: 1-6]
- Symbolisations (slides) [Parsons 1: 7-10] [A note on 'if' and 'only if']
- Inference rules (slides) [Parsons 1: 11-12]

Week 3 [ homework ]

- Introduction to derivations (slides) [Parsons 1: 13-18]
- Direct, Conditional, and Indirect Derivations (slides) [Parsons 1: 18-30]
- Sub-derivations (slides) [Parsons 1: 30-44]

Week 4 [ homework ]

- L2 (The language of `if', `not', `and', `or', `iff') (slides) [Parsons 2: 1-11]
- Inference rules (slides) [Parsons 2: 12-14]
- Derivation strategies (slides) [Parsons 2: 15-18]

Week 5 [ homework; study guide ]

- Box and cancel (slides) [Parsons 2: 19-21]
- More derivations (slides) [Parsons 2: 25-33]
- Midterm Exam, Feb. 16th [ answers ]

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BREAK Week -- no classes -- 20-24 February 2017

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Week 6 [ homework ]

- Truth tables (slides) (exersices) [Parsons 2: 34]
- Truth tables and tautologies (slides) [Parsons 2: 34-37]
- Validity and countermodels (slides) [Parsons 2: 37-39]

Week 7 [ homework ]

- Introduction to quantifiers (slides) [Parsons 3: 1-3]
- Names, variables, and predicates (slides) [Peters & Westerståhl]
- L3 symbolisations (slides) [Parsons 3: 3-7]

Week 8 [ homework ]

- Quantifier inference rules (slides) [Parsons 3: 8-19]
- Derivations with quantifiers (slides) [Parsons 3: 19-24]
- Derivations (slides) [Parsons 3: 25-28]

Week 9 [ homework ]

- More Derivations (slides) [Parsons 3: 28-33]
- Quantifier negation rules (slides) [Parsons 3: 34-38]
- Derivations (slides) [Parsons 3: 39]

Week 10 [ homework ]

- Models (slides) [Parsons 3: 40-42]
- Invalidity and countermodels (slides) [Parsons 3: 42-44]
- Countermodels (slides) [Parsons 3: 45-48]

Week 11 [ Exam study guide ] [answers]

- Review
- Review
- Conclusion (slides)