## PP3LOG-Logic

Module Provider: Philosophy
Number of credits: 20 [10 ECTS credits]
Level:6
Terms in which taught: Spring term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Module version for: 2016/7

Module Convenor: Mr George Mason

Summary module description:
This course follows on from the Part 1 Reason and Argument module, taking some of the ideas introduced there further and covering some additional formal ways of thinking about arguments, consistency and validity. Students will learn to prove results in a formal language, and some of the theoretical underpinnings of such proofs.

Aims:
1.To further develop your awareness of the structure of arguments and to enable you to use additional methods to analyse that structure;
2. To understand the formal and mathematical underpinnings of a formal logical system.
3. To develop a more extensive familiarity with this logical notation so that you will be able to understand it and use it in philosophical writing.

Assessable learning outcomes:
By the end of the module you will understand (how to):

1.spot ambiguous sentences and rewrite the different readings without ambiguity.
2.recognise declarative sentences.
3.recognise premises and conclusions of arguments.
4.say when an argument is valid and when an argument is sound, and apply these definitions.
5.say what a sentence-functor is, and what a truth-functor is, and draw truth-tables for sentence-functors.
6.draw truth-tables for the five standard truth-functors.
7.recognise when the truth-functors above can correctly translate English connectives, and when they cannot.
8.recognise when a connective takes wide or narrow scope in a sentence.
9.translate sentences into propositional logic, or say why they cannot be translated.
10.write down the standard rules of the formal system.
11.write down a suitable interpretation for a complex sentence or set of complex sentences.
12.translate English sentences into logical notation (propositional calculus) using an interpretation.
13.explain the link between consistency and validity.
14.use a formal system to test arguments for validity.
15.construct a counterexample for an invalid argument.
16.draw truth-tables for complex sentences.
17.test a set of sentences for consistency using truth-tables.
18.test an argument for validity using truth-tables, and write down a counterexample for an invalid argument.
19.say what it means for a sentence to be tautologous, contingent or inconsistent, and apply these definitions.
20.say what it means for two or more sentences to be logically equivalent and apply these definitions.
21.write arguments and sets of sentences in sequent notation, and explain what it means for a sequent to be correct.
22.use either truth-tables or a formal system to test a sequent for correctness.
23.translate English sentences containing ‘ifs’, ‘only ifs’, ‘unless’ and necessary and sufficient conditions into logical notation correctly.
24.analyse English sentences into their constituent designators and predicates.
25.recognise quantifiers and their domains in English sentences.
26.write down a suitable predicate interpretation for a sentence or set of sentences.
27.translate simple English sentences containing universal or existential quantifiers into logical notation using a predicate interpretation.
28.paraphrase English sentences to enable their translation into logical notation.
29.translate more complicated English sentences containing universal or existential quantifiers into logical notation using a predicate interpretation.
30.for a given argument, either prove its validity using a formal system or produce a counterexample;
31.translate English sentences involving the quantifiers ‘at least’, ‘at most’ and ‘exactly’ into predicate calculus.
32.translate English sentences involving singular definite descriptions into predicate calculus
33.prove basic meta-theoretic results such as that if A entails B, then A entails (B or C).
34.state the completeness and consistency results, and explain their significance.

Outline content:
Schedule of topics to be covered:

1 Introduction and recap of some themes from critical thinking; introduction to logical analysis in propositional logic.
2 Truth-functors and translation; truth-tables, consistency, validity
3 Formal proofs in propositional logic
4 Predicate logic
5 Finding formal proofs or counter-examples in predicate logic
6 Some meta results

Brief description of teaching and learning methods:
You will be set passages of the assigned textbook to read each week before the next lecture. Doing this reading will help you get the most out of each lecture.
•The lectures will explain each week’s material, including worked examples.
•At each lecture, you will be given a set of exercises. These are to be submitted to the seminar leader at the start of each seminar. You will also be set additional exercises from Hodges for further practice.
•Seminars will be used to practise the material covered in lectures, offer further explanation and help as required, and discuss the homework exercises.

Contact hours:
 Autumn Spring Summer Lectures 20 Seminars 10 Guided independent study 170 Total hours by term 200.00 Total hours for module 200.00

Summative Assessment Methods:
 Method Percentage Written exam 50 Set exercise 50

Other information on summative assessment:

Formative assessment methods:
In-class problem sets, and ‘further practice’ weekly exercises.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Length of examination:
Two hours

Requirements for a pass:
A mark of 40% overall

Reassessment arrangements:
By written examination only.