To introduce students to the language and methods of classical quantificational logic.

To enable students to use trees for both sentence logic and quantificational logic.

To relate quantificational logic to the philosophy of language.

(LO1) Students will be able to explain and apply the basic concepts of classical first-order logic.

(LO2) Students will consolidate their skill in translating from English into first-order logic and vice versa.

(LO3) Students will be able to construct proofs in natural deduction for valid sequents of first-order logic.

(LO4) Students will be able to test sets of formulas for consistency using trees and to assess sequents of truth-functional logic and sequents of first-order logic for validity using trees.

(S1) Students will enhance their abilities in reading and understanding texts and in comprehending abstract material.

(S2) Students will develop their skills in thinking critically, analysing problems and analysing and assessing arguments.

(S3) Students will enhance their ability to identify the issues that underlie debates.

(S4) Students will enhance their ability to marshal arguments and present them orally and in writing.

(S5) Students will develop their ability to work independently.

(S6) Students will develop their problem solving skills.

(S7) Improving own learning and performance; personal action planning.

(S8) Communication oral, written and visual; following instructions, protocols and procedures.

(S9) Communication oral, written and visual; influencing skills, argumentation.

(S10) Personal attributes and qualities; resilience.

Lecture 1 - The Language of Truth-Functional Logic (TFL): Syntax & Translations
Lecture 2 - TFL Semantics & Consistency: Basics
Lecture 3 - TFL Consistency Trees: Applications
Lecture 4 - The Language of First-Order Logic (FOL)
Lecture 5 - FOL Translations: Basics
Lecture 6 - FOL Translations: Advanced
Lecture 7 - FOL Consistency Trees
Lecture 8 - FOL Consistency Trees
Lecture 9 - TFL Derivations
Lecture 10 - FOL Derivations: Rules for the Quantifers
Lecture 11 - FOL Derivations: Identity & Strategy

In 2021-22, there will be no physical meetings for this module. (It is very likely that fewer than 20 students will be taking the module. It is not possible to conduct logic workshops in a socially distanced manner.) Instead, the module will be taught wholly online, using a mixture of synchronous and asynchronous methods.

Teaching Method 1 - Worked Example Videos (Asynchronous)
Description: around 1 hour per week, in small chunks, of screencasts with audio and closed captions. These concentrate upon -the explanation of work examples relating to the week's support notes.
Attendance Recorded: No

Teaching Method 2- Support Notes (Asynchronous)
The supporting notes explain key concepts and methods in succinct but intensive ways. Each set of notes is supplemented by a suite of worked examples and by an online formative quiz (both described above).
Attendance Recorded: No

Teaching Method 3 - Online Workshops (Synchronous)
Each week (exce pt Independent Study Week and Week 12), there will be 1 x 1 hour workshop for every 10 students taking GV15 Mathematics and Philosophy and 1 x 1 hour workshop for every 10 students on other programmes. Workshops will focus exclusively on material that has been set for, or that is directly relevant to, the worksheet that is due for submission in the following week. Students will be able to discuss drafts of their solutions to the exercises in the worksheet.
Attendance Recorded: Yes

Teaching Method 4 - Online Tutorials (synchronous)
Description: There will be 1 x 1 hour tutorial each week (except in Independent Study Week), for attendance by the whole class. These sessions offer opportunities for applied learning and formative feedback as tutors respond to questions and offer guidance and feedback. They will centre around material from, and exercises in, the textbook and the supporting online materials: unlike the workshops, they will not have an explicit focus on the wo rksheets.
Attendance Recorded: Yes

Teaching Method 5 - Summative Workshops (Asynchronous)
10 weekly worksheets, with a notional time allowance for each of 2 hours. (For further details, see ‘Assessment Strategy’ above.)
Attendance will be recorded automatically, via submission of the worksheet.
Attendance Recorded: Yes

Teaching Method 6 – Formative Quizzes (Asynchronous)
Around 10 weekly online formative quizzes, with a notional time allowance for each of 20 minutes. (For further details, see ‘Assessment Strategy’ above.)
Attendance Recorded: No