The Gettier Problem

Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition:

(d) Jones is the man who will get the job, and Jones has ten coins in his pocket.

Smith’s evidence for (d) might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones’s pocket ten minutes ago. Proposition (d) entails:

(e) The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is then true, though proposition (d), from which Smith inferred (e), is false.

In our example, then, all of the following are true: (i) (e) is true, (ii) Smith believes that (e) is true, and (iii) Smith is justified in believing that (e) is true. But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith’s pocket, while Smith does not know how many coins are in Smith’s pocket, and bases his belief in (e) on a count of the coins in Jones’s pocket, whom he falsely believes to be the man who will get the job. [Does Smith know that the man who will get the job has ten coins in his pocket?]

— Edmund L. Gettier, “Is Justified True Belief Knowledge?”, Analysis, 1963

| Science & Math

Unquote

“The natural flights of the human mind are not from pleasure to pleasure, but from hope to hope.” — Samuel Johnson

“If it were not for hopes, the heart would break.” — Thomas Fuller

“Always leave something to wish for; otherwise you will be miserable from your very happiness.” — Baltasar Gracián

| Quotations

The End of the Road

http://commons.wikimedia.org/wiki/File:Napoleon_sainthelene.jpg

The following anagram on the original name of Napoleon I, the most renowned conqueror of the age in which he lived, may claim a place among the first productions of this class, and fully shows in the transposition, the character of that extraordinary man, and points out that unfortunate occurrence of his life which ultimately proved his ruin. Thus: ‘Napoleon Bonaparte’ contains ‘No, appear not on Elba.’

— Kazlitt Arvine, Cyclopaedia of Anecdotes of Literature and the Fine Arts, 1856

| History · Language

Asleep at the Gate

In 1996, in order to demonstrate the undiscerning trendiness of postmodernism, NYU physicist Alan Sokal submitted an article “liberally salted with nonsense” to the academic journal Social Text:

As Althusser rightly commented, ‘Lacan finally gives Freud’s thinking the scientific concepts that it requires.’ More recently, Lacan’s topologie du sujet has been applied fruitfully to cinema criticism and to the psychoanalysis of AIDS. In mathematical terms, Lacan is here pointing out that the first homology group of the sphere is trivial, while those of the other surfaces are profound; and this homology is linked with the connectedness or disconnectedness of the surface after one or more cuts.

It was published even though Sokal refused to make any changes.

In 2005, MIT student Jeremy Stribling submitted a paper of computer-generated gibberish to the technology conference WMSCI:

One must understand our network configuration to grasp the genesis of our results. We ran a deployment on the NSA’s planetary-scale overlay network to disprove the mutually largescale behavior of exhaustive archetypes. First, we halved the effective optical drive space of our mobile telephones to better understand the median latency of our desktop machines. This step flies in the face of conventional wisdom, but is instrumental to our results.

It was accepted when none of three reviewers rejected it.

French twins Igor and Grichka Bogdanov insist that their papers on the Big Bang are genuine contributions to physical cosmology, but mathematician John Baez calls them “a mishmash of superficially plausible sentences containing the right buzzwords in approximately the right order.” That battle is still raging.

| Hoaxes

Limerick

There was a young man from Darjeeling
Who got on a bus bound for Ealing;
It said at the door:
“Don’t spit on the floor,”
So he carefully spat on the ceiling.

— Anonymous

| Humor

King Bed

http://commons.wikimedia.org/wiki/File:Drawn_by_Bt_Henry_Shaw_in_the_year_1832.jpeg

Shakespeare, Byron, and Ben Jonson all refer to the Great Bed of Ware, an enormous luxury bed built by Hertfordshire carpenter Jonas Fosbrooke at the end of the 16th century. Measuring 10 feet by 11, it was said to fit 12 comfortably; Sir Henry Chauncy tells how six couples once contrived to sleep in it so that no man lay next to any woman but his wife: “six should lie at one End of the Bed and six at the other, after this Manner, first a Man and his Wife, next a Woman and her Husband, next him a Man and his Wife; then the other three Couple should lie in the same Order at the Feet.”

After centuries as an “inn wonder,” it resides today in the Victoria and Albert Museum in London.

| Oddities

A Logic Oddity

Opinion polls taken just before the 1980 election showed the Republican Ronald Reagan decisively ahead of the Democrat Jimmy Carter, with the other Republican in the race, John Anderson, a distant third. Those apprised of the poll results believed, with good reason:

— If a Republican wins the election, then if it’s not Reagan who wins it will be Anderson.
— A Republican will win the election.

Yet they did not have reason to believe

— If it’s not Reagan who wins, it will be Anderson.

— Vann McGee, “A Counterexample to Modus Ponens,” Journal of Philosophy, September 1985

| Science & Math

Home Again

Unprepossessing English town names:

  • Bishop’s Itchington
  • Brokenborough
  • Great Snoring
  • Mockbeggar
  • Turners Puddle
  • Pett Bottom
  • Twelveheads
  • Ugley
  • Nether Wallop
  • Nasty
  • Wetwang
  • Blubberhouses
  • Yelling

Charles Dickens called the chipper-sounding Chelmsford “the dullest and most stupid spot on the face of the earth.”

| Language

Pi Squared

pi magic square

This curiosity was discovered by T.E. Lobeck. The square on the left is a conventional magic square — each row, column, and long diagonal totals 65. Replacing each number with the corresponding digit of pi (for example, replacing 17 with the 17th digit of pi, which is 2) yields the square on the right, in which the rows and columns yield equivalent sums.

| Science & Math