Modern philosophy and logic often make great use of small bite-sized papers and thought experiments. Usually, such papers are written as critical notices or replies to another author’s work, but sometimes they stand alone and make their point in a pithy and powerful way. Although far from an exhaustive list, these are five of my favourite standalone philosophy papers – taken together, they constitute less writing than half an undergraduate dissertation!
‘Is Justified True Belief Knowledge?’ By Edmund Gettier
Most philosophy students will be familiar with this paper, as well as the huge amount of discussion that it provoked. In just under three pages of writing, Edmund Gettier overturned one of the most enduring and widely held beliefs in philosophy: that knowledge could be thought of as justified true belief. In the paper (one of only three that he ever wrote), Gettier presents counterexamples against the ‘justified true belief’ analysis and appears to demonstrate that such a definition just isn’t up to the task. With over six times as many citations as it has words, ‘Is Justified True Belief Knowledge?’ is one of the most impactful papers ever to be published.
‘The Hardest Logic Puzzle Ever’ by George Boolos
‘The Hardest Logic Puzzle Ever’ was first published by George Boolos in 1996, although Boolos actually attributes it to the American logician and mathematician Raymond Smullyan. The puzzle goes something like this:
You are faced with three gods – A, B, and C – one of which always tells the truth, one of which always lies, and one of which randomises between telling the truth and lying. You must ask three yes-no questions (each to one god only) in order to determine the identity of each god. Whilst they understand your questions, they reply in their own language, in which the words for ‘yes’ and ‘no’ are ‘da’ and ‘ja’. The only problem is that you don’t know which word means which. What questions do you ask?
The beauty of the puzzle is that it seems so completely and utterly unsolvable at first, but many ways of approaching (and solving) it have since been discovered. Whilst Boolos’s solution was one of the first, this one is simpler and a bit easier to understand.
‘The Runabout Inference-Ticket’ by Arthur Prior
The belief that the meaning of language can be reduced to sets of rules that govern its usage was popular in the first half of the 20th century. The meaning of a connective like ‘and’, for instance, was said to be nothing more than the rules used for its introduction and elimination:
Introduction: If A is true and B is true, then A AND B is true (for any A and B).
Elimination: If C AND D is true, then C is true, and D is true (for any C and D).
Arthur Prior’s paper, ‘The Runabout Inference-Ticket’, cast this view (called inferentialism) into serious doubt. Creating a new connective called ‘tonk’, Prior demonstrates that following a set of well-defined rules is not all that’s needed to confer meaning. By demonstrating that the use of ‘tonk’ and the rules that govern it can take us from a true statement to a patently false one, Prior shows that defining a connective this way does not always ensure that its use is truth-preserving. The paper is probably the most complicated one on this list, but well worth a read anyway (especially considering it’s less than two pages long!).
‘A Demonstration of the Causal Power of Absences’ by Tyron Goldschmidt
It has long been argued that absences cannot be real causes. The death of a farmer’s crops can’t truly be said to have been caused by a lack of rain – after all, how can the nonexistence of one thing really cause another? Only real, existent entities could ever have the power to cause something else to happen, or so the argument goes.
Goldschmidt’s paper has by far the least words on this list and it’s more a novelty than anything else – but see if you have any sort of reaction when you read it. What caused this reaction?
‘What the Tortoise Said to Achilles’ by Lewis Carroll
Whilst Lewis Carroll isn’t best known as a logician, he did make some very interesting contributions to the field. This particular paper is presented in the form of a dialogue that takes place between Achilles and a tortoise (a partnership that will be familiar to anyone acquainted with Zeno’s paradoxes) and has come to be considered a classic text in the philosophy of logic.
In a terse (about three pages long) and entertaining exchange, the tortoise demonstrates that an infinite regress can be created by someone who accepts the premises of a valid argument but not the conclusion, as this person will always require the addition of another premise (namely, one that states that the conclusion of the argument follows from the pre-existing premises). The paradox appears to demonstrate that the conclusions of our arguments are always just out of reach, and we are left to explain the fact that – despite the tortoise’s example – we seemingly reach them all the time.
Disclaimer: the papers listed here are just a few of many short works in philosophy and logic and have been heavily influenced by my own interests within the subjects. If you want to read more papers like these, then Analysis is a good place to start.
Image: Patrick Tomasso on Unsplash