Offered through the University of Melbourne

PHIL20030: Meaning, Possibility and Paradox is a University of Melbourne undergraduate subject. The idea that the meaning of a sentence depends on the meanings of its parts is fundamental to the way we understand logic, language and the mind. In this subject, we look at the different ways that this idea has been applied in logic throughout the 20th Century and into the present day.

In the first part of the subject, our focus is on the concepts of necessity and possibility, and the way that ‘possible worlds semantics’ has been used in theories of meaning. We will focus on the logic of necessity and possibility (modal logic), times (temporal logic), conditionality and dependence (counterfactuals), and the notions of analyticity and a priority so important to much of philosophy.

In the second part of the subject, we examine closely the assumption that every statement we make is either true or false but not both. We will examine the paradoxes of truth (like the so-called ‘liar paradox’) and vagueness (the ‘sorites paradox’), and we will investigate different ways attempts at resolving these paradoxes by going beyond our traditional views of truth (using ‘many valued logics’) or by defending the traditional perspective.

The subject serves as an introduction to ways that logic is applied in the study of language, epistemology and metaphysics, so it is useful to those who already know some philosophy and would like to see how logic relates to those issues. It is also useful to those who already know some logic and would like to learn new logical techniques and see how these techniques can be applied.

The subject is offered to University of Melbourne undergraduate students (for Arts students as a part of the Philosophy major, for non-Arts students, as a breadth subject). Details for enrolment are here.

Rosza Peter
The writing down of a formula is an expression of our joy that we can answer all these questions by means of one argument. — Rózsa Péter, Playing with Infinity

I make use of video lectures I have made freely available on Vimeo. If you’re interested in this sort of thing, I hope they’re useful. Of course, I appreciate any constructive feedback you might have.


The course is divided into four major sections and a short prelude. Here is a list of all of the videos, in case you’d like to follow along with the content.

Classical Logic

Meaning, Sense, Reference

Basic Modal Logic

Normal Modal Logics

Double Indexing


Three Values

Four Values


What to do with so many logical systems

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I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.



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