PP2IL-Introductory Logic

Module Provider: Philosophy
Number of credits: 20 [10 ECTS credits]
Terms in which taught: Spring term module
Pre-requisites: PP1RA Reason and Argument
Non-modular pre-requisites:
Modules excluded:
Module version for: 2014/5

Module Convenor: Dr Alice Drewery

Email: a.e.drewery@reading.ac.uk

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.

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 develop a more extensive familiarity with logical notation so that you will be able to understand it and use it in philosophical writing.

Assessable learning outcomes:
After completing this module, you should be able to:
•spot ambiguous sentences and rewrite the different readings without ambiguity.
•recognise declarative sentences.
•recognise premises and conclusions of arguments.
•say when an argument is valid and when an argument is sound, and apply these definitions.
•say what a sentence-functor is, and what a truth-functor is, and draw truth-tables for sentence-functors.
•draw truth-tables for the five truth-functors ‘¬’, ‘?’, ‘?’, ‘?’ and ‘?’.
•recognise when the truth-functors above can correctly translate English connectives, and when they cannot.
•recognise when a connective takes wide or narrow scope in a sentence.
•translate sentences into propositional logic, or say why they cannot be translated.
•derive the tableau rule for any truth-function from its truth-table.
•write down a suitable interpretation for a complex sentence or set of complex sentences.
•translate English sentences into logical notation (propositional calculus) using an interpretation.
•use the tableau method to test sets of sentences for consistency.
•explain the link between consistency and validity.
•use the tableau method to test arguments for validity.
•use the tableau method to write down a counterexample for an invalid argument.
•draw truth-tables for complex sentences.
•test a set of sentences for consistency using truth-tables.
•test an argument for validity using truth-tables, and write down a counterexample for an invalid argument.
•say what it means for a sentence to be tautologous, contingent or inconsistent, and apply these definitions.
•say what it means for two or more sentences to be logically equivalent and apply these definitions.
•write arguments and sets of sentences in sequent notation, and explain what it means for a sequent to be correct.
•use either truth-tables or tableaux to test a sequent for correctness.
•translate English sentences containing ‘ifs’, ‘only ifs’, ‘unless’ and necessary and sufficient conditions into logical notation correctly.
•analyse English sentences into their constituent designators and predicates.
•recognise quantifiers and their domains in English sentences.
•write down a suitable predicate interpretation for a sentence or set of sentences.
•translate simple English sentences containing universal or existential quantifiers into logical notation using a predicate interpretation.
•understand the quantifier equivalences on p. 208 of Hodges.
•paraphrase English sentences to enable their translation into logical notation.
•translate more complicated English sentences containing universal or existential quantifiers into logical notation using a predicate interpretation.
•show an argument is valid using a predicate tableau.
•translate English sentences involving the quantifiers ‘at least’, ‘at most’ and ‘exactly’ into predicate calculus.
•translate English sentences involving singular definite descriptions into predicate calculus.

Additional outcomes:

Outline content:
Week 1Introduction and recap of some themes from critical thinking; introduction to logical analysis in propositional logic.
Week 2Truth-functors and translation
Week 3Sentence tableaux.
Week 4Consistency and validity.
Week 5Truth-tables and what they show.
Week 6Sequents and further translation.
Week 7Introduction to predicate calculus.
Week 8More quantifiers.
Week 9Predicate tableaux.
Week 10Further translation into predicate calculus.

The set text is W. Hodges, Logic, Penguin, 2001. Students will be required to bring their own copy of this book to all lectures and seminars.

Brief description of teaching and learning methods:
•You will be set passages of Hodges 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 100

Other information on summative assessment:
Weekly exercises will be done throughout this module, both in class and outside.

Relative percentage of coursework: 0%

Formative assessment methods:

Penalties for late submission:
The Module Convener 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:
    There will be one examination, of two hours in length, worth 100% of the module mark. Students must answer all questions.

    Requirements for a pass:
    A mark of 40% overall.

    Reassessment arrangements:
    Re-examination in August by written examination only.

    Last updated: 8 October 2014

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