Course texts:

Michael Clark, Paradoxes from A to Z (London, Routledge, 2002).

Copies of this will be available from the bookstore after Chinese New Year. You should buy one. It contains excellent brief discussions of all the main paradoxes, and, for each, contains a guide to further reading.

R.M. Sainsbury, Paradoxes, second edition (Cambridge University Press, 1995).

Very clear presentation of five main areas of paradox.

Other introductory texts include:

Raymond Smullyan, What is the Name of this Book? (1978)

Some delightful puzzles created by a clever logician/magician.

William Poundstone, Labyrinths of Reason (1988)

A recreational work containing much interesting material.

Justin Leiber, Paradoxes (1993)

A very short and easy introduction.

Glen W. Erickson and John A. Fossa, Dictionary of Paradox (1998)

Useful brief discussions and suggestions for reading on each paradox.

Nicholas Rescher, Paradoxes: Their Roots, Range and Resolution (2001)

Aims to provide a unified way of handling paradoxes. Much interesting historical material.

Roy Sorensen, A Brief History of the Paradox (2003)

I’ve only just started reading this myself. Seems fun.

All of these texts are on short-term loan from the library. I shall also refer you, from time to time, to xeroxed articles that you can borrow via Mrs. Lau in the Department General Office.

Aim of the course

The study of paradoxes is one of the best routes into Philosophy, because the reasoning within each paradox quickly leads to contradiction or absurdity. Therefore the solving of a paradox requires us to question very basic assumptions and principles. In general Philosophy, it can often seem that we question commonsense beliefs, but that this is a rather pointless activity. However, with paradoxes, raising such questions is obligatory if we wish to escape inconsistency – and if you don’t want to escape inconsistency, that too requires a fundamental re-thinking of some common assumptions. Our aim is to get fascinated by the paradoxes and to solve some.

What is a paradox?

A paradox is a piece of reasoning that leads from apparently true premises, via apparently acceptable steps, to a conclusion that is contradictory or crazy.

In this course, we shall be searching for solutions to a number of paradoxes. Ultimately, we shall be looking for unified solutions. A solution is `unified’ if it shows there to be an underlying commonality between several paradoxes. It sometimes happens that some paradoxes which look entirely different from each other have deep similarities, such that a solution to one will almost automatically be a solution to all paradoxes in that group. So we need to first to get acquainted with a variety of paradoxes. Of course, getting acquainted with them is quite easy; solving them might be quite difficult. Here are four, to get us started. It should be obvious that the first two are closely related.

The Liar [Clark, Course text: p.99]

Somebody says `What I am now saying is false’. If what he says is true, then it is false. But if it is false, then it is true!

Epimenides the Cretan

It was a Cretan prophet, one of their own countrymen, who said `Cretans are always liars, vicious brutes, lazy gluttons' - and he told the truth!

( St. Paul, `Epistle to Titus, 1:12-13, The Holy Bible).

For a discussion of the biblical versions of this paradox, see A.R.Anderson's introduction to R.L. Martin (ed.), The Paradox of the Liar (Oxford, Oxford University Press, 1970). Note: As far as we know, the mediaeval logicians never used this variant of the Liar Paradox. See L.M. de Rijk, `Some notes on the mediaeval tract De Insolubilibus, with the edition of a tract dating from the end of the twelfth century', Vivarium 4 (1966), pp.83-115.

You might say `This is not a paradox: What the Cretan prophet said was simply false. Some statements made by Cretans are true.’ Yes, but notice that this means that the prophet’s statement requires that some Cretan made some true statement. But whether some Cretan did make a true statement is surely a matter for history (not logic) to decide.

The Paradox of Omnipotence [See also Course text: p.130 on the Paradox of Omniscience]

`God can create a stone so heavy that He cannot lift it'. That statement is either true or false. If it's true, then there is something that God cannot do (lift the stone); if it's false, there's something that God cannot do (create the stone). Now, the statement must be either true or false, so there must be at least one task that God cannot perform – but that contradicts our conception of God as omnipotent. The paradox here is that reflection on a rather simple sentence leads to a conclusion that shouldn't be obtained so cheaply - the conclusion that God doesn't exist (assuming that omnipotence is a necessary characteristic of God).

Achilles and the Tortoise [Clark, Course text: p.1]

`The slowest, in running, will never be overtaken by the fastest. For the pursuer must first reach whence the pursuit began, therefore it is necessary for the slower to be some distance ahead’

(Aristotle, Physics, Book Z, 239b14-18)

In other words, a fast runner can never catch a tortoise!