Centre for Continuing Education

Philosophy Course: Formal Logic and Arguments

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

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.


1. 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

2. Propositions and propositional logic

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

3. 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

4. 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

5. 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

6. Translating from English to formal language

  • Examples and practice of translating arguments into formal language

7. Common argument forms and fallacies

  • Common valid argument forms
  • Formally invalid arguments

Intended audience

This one-day 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

This is a one-day workshop. Topics are roughly divided into hour-long segments where there will be practise time to work on exercises in each topic area.


Handouts are provided in class.

Recommended reading


For prereading 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, N.J.J. (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
  • Small class sizes
  • Free, expert advice
  • Student materials – yours to keep
  • Statement of completion