Centre for Continuing Education

Philosophy Course: Formal Logic and Arguments

Philosophy. Study the fundamental nature of knowledge, reality and existence.

COVID-19 update: arrangement of our courses

We are now delivering courses online and in-person. Please check the delivery format of each class before enrolling.

Please note that course materials (excluding prescribed texts) are shared electronically within 48 hours of course commencement. Printing is not available.

This course offers a basic introduction to symbolic logic and deductive arguments, truth-tables and truth-trees. Formal logic is a powerful tool that can be used to evaluate an argument’s validity for proper form. Deductive arguments are found in philosophy, ethics and other disciplines where precision and rigour are required.

Join us to learn how to translate arguments from English into propositional logic, and to determine if arguments are valid or fallacious.


This course aims to teach the main concepts, techniques and skills in deductive argument evaluation using the proof methods of truth-tables and trees. It teaches the five basic logical connectives, and how to translate an argument from natural language into formal language for testing.


By the end of this course, you should be able to:

  • identify propositions and deductive arguments in texts, in order to apply formal logical techniques
  • translate arguments from English into formal (symbolic) language using variables and the five logical operations: negation, disjunction, conjunction, conditional, and bi-conditional
  • use and apply proof methods: truth-tables and truth-trees to these formal arguments
  • decide whether an argument is deductively valid or invalid
  • consider the importance of deductive validity as a value in argumentation over the pathology of formally invalid arguments.


Introduction to logic and deductive arguments

  • The big picture: how to translate, test, and evaluate a complex argument for deductive validity
  • The definition of deductive validity and soundness
  • Standard form of arguments: premises and conclusions

Propositions and propositional logic

  • Understanding propositions – simple and complex
  • The concept of truth-value
  • Classical logical laws: non-contradiction, excluded-middle, bivalence

The semantics of the five logical operators

  • The ‘meaning’ or semantics of the logical operators. Negation, conjunction, disjunction, material- conditional and bi-conditional
  • The material-conditional. Identifying antecedent and consequent
  • Alternative conventions for the symbolisation of the five logical operators

Proof technique 1: Truth-tables

  • How to construct a truth-table for an argument
  • Testing an argument using truth-tables
  • How truth-tables do (and do not) demonstrate deductive validity
  • Criticisms of using the truth-table method

Proof technique 2: Truth trees

  • The concept of indirect method of proof and the superiority of using truth trees over truth tables
  • Tree rules for each logical operator (Handout)
  • How to test an argument for validity using trees

Translating from English to formal language

  • Examples and practice of translating arguments into formal language

Common argument forms and fallacies

  • Common valid argument forms
  • Formally invalid arguments

Intended audience

This workshop is designed to give an overview of logic for anyone interested in formally analysing deductive arguments in philosophy. The course may also be relevant for anyone with an interest in maths, computer science or linguistics.



Delivery style

Delivery options:

  • presenter-taught workshop on University premises
  • online workshop via the platform Zoom.

Topics are roughly divided into hour-long segments which includes practise time to work on exercises in each topic area.


Handouts are provided electronically.

Recommended reading


For pre-reading about propositions and arguments, it is recommended to read the chapter indicated from any one of the following texts:

Nolt, J et al. 2011, Schaum’s Outline of Logic, 2nd Edition, McGraw-Hill Education. (Chapter 3)

Restall, G 2005, Logic: An Introduction (Fundamentals of Philosophy), Oxford: Routledge. (Chapter 1)

Smith, NJJ 2012, Logic: The Laws of Truth, Princeton University Press. (Chapter 1)

Optional purchase:

Lamenated logic card/reference guide:

BarCharts 2002, Logic: Propositional Logic, Quick Study Academic.


  • Expert trainers
  • Central locations
  • Course materials – yours to keep
  • CCE Statement of Completion

Philosophy Course: Formal Logic and Arguments

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