Year
2024Credit points
10Campus offering
No unit offerings are currently available for this unit.Prerequisites
PHIL100 Philosophy: the Big Questions or PHIL102 Theories of Human Nature or PHIL104 Introduction to Ethics or PHIL107 Philosophy of World Religions or PHCC102 Being Human or PHCC104 Ethics and the Good Life
Incompatible
PHIL219 Basic Symbolic Logic
Teaching organisation
This unit involves 150 hours of focused learning, or the equivalent of 10 hours per week for 15 weeks. The total includes formally structured learning activities such as lectures, tutorials and online learning. The remaining hours typically involve reading, research, and the preparation of tasks for assessment.Unit rationale, description and aim
This unit provides an introduction to formal logic, including both propositional and quantificational (predicate) calculus. Particular attention is given to applications to natural language reasoning. The unit aims not only to introduce students to a major field of philosophy in its own right - logic - but also to equip them with essential tools for comprehending various kinds of complex arguments made in contemporary philosophy across a wide range of fields, from metaphysics to ethics. Further, the unit provides students with the philosophical background for understanding developments in other fields such as mathematics, computer science and linguistics.
Learning outcomes
To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.
Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.
Explore the graduate capabilities.
| Learning Outcome Number | Learning Outcome Description |
|---|---|
| LO1 | Correctly manipulate the symbols of propositional calculus and quantificational calculus |
| LO2 | Competently calculate truth tables, Venn diagrams, semantic tableaux and elementary algebraic models |
| LO3 | Translate natural language sentences into the symbolism of propositional calculus and quantificational calculus |
| LO4 | Write proofs in these logical languages, and apply the tools of propositional calculus and quantificational calculus to analyse and criticise arguments in natural language |
Content
Topics will include:
Propositional Calculus (PC):
- basics of syntax and semantic structures of PC;
- sentential form in natural language and translation between it and PC;
- truth tabular methods testing validity and other logical notions;
- proofs in PC and application in natural language argumentation.
Quantificational Calculus (QC):
- basics of syntax and elementary semantic techniques for QC;
- quantificational structure and other logical forms in natural language and translation between it and QC; QC and syllogistic logic;
- proofs in QC and application to natural language argumentation;
- topics such as nested quantifiers, scope distinctions and elementary theory of relations and identity.
In addition, topics such as the following may be briefly touched upon:
- introduction to modal logics;
- introduction to many-valued logics;
- introduction to classical metatheory;
- elementary issues in philosophical logic.
Learning and teaching strategy and rationale
This unit involves 150 hours of focused learning, or the equivalent of 10 hours per week for 15 weeks. The total includes formally structured learning activities such as lectures, tutorials and online learning. The remaining hours typically involve reading, research, and the preparation of tasks for assessment.
Given the pre-requisite requirement, students will have some experience with philosophical analysis and the construction of logical arguments in natural language. This unit has been designed to introduce students to symbolic logic through a blend of direct instruction and extensive scaffolding for student mastery of concepts and operations in symbolic logic, and competency in their application. The formally structured learning activities explain the concepts, demonstrate the methods, and enable students to practice the application, extension and critical use of those concepts and methods.
Assessment strategy and rationale
The assessment strategy for this unit is a combination of regular exercises that double as formative consolidation, and summative tasks at mid and end semester. The regular exercises are designed to facilitate deepening engagement with the concepts, methods and skills of symbolic logic while also providing the occasion for regular feedback. The mid semester writing task tests for a maturing competence in logical skills of analysis, translation from natural language, writing proofs, evaluating arguments semantically and syntactically, and manipulating the symbols of logical languages in ways that illuminate natural language reasoning. The Final Exam examines students’ competence and skill levels in identifying what logical language or method to use and how best to use it in the analysis and evaluation of natural language reasoning.
Overview of assessments
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes |
|---|---|---|
Regular Exercises Requires students to demonstrate their developing competence in the understanding and application of the basic concepts and methods of symbolic logic | 20% | LO1, LO2, LO3, LO4 |
Mid Semester written task Requires students to demonstrate their competence in understanding, application and critical use of the concepts and methods of symbolic logic | 40% | LO1, LO2, LO3, LO4 |
Final Exam Requires students to demonstrate their competence in understanding, application and critical use of the concepts and methods of symbolic logic | 40% | LO1, LO2, LO3, LO4 |
Representative texts and references
Barker-Plummer, D., Barwise, J. & Etchemendy, J. (2011). Language, Proof and Logic. 2nd ed. Stanford, CA: Centre for the Study of Language and Information Publications.
Copi, I. & Cohen, L. (2010). Introduction to Logic. 14th ed. New York: Macmillan.
Gensler, H. (2010). Introduction to Logic. London: Routledge.
Klenk, V. (2007). Understanding Symbolic Logic. 5th ed. Sydney: Prentice-Hall.
Pollock, J.L. (1990). Technical Methods in Philosophy. London: Westview Press.
Priest, G. (2008). An Introduction to Non-Classical Logic. Cambridge: Cambridge University Press.
Restall, G. (2006). Logic: An Introduction. London: Routledge.
Sainsbury, M. (2001). Logical Forms: An Introduction to Philosophical Logic. 2nd ed. Oxford: Wiley-Blackwell.
Sider, T. (2010). Logic for Philosophy. Oxford: Oxford University Press
Smith, P (2003). An Introduction to Formal Logic. Cambridge: Cambridge University Press