The Liar Paradox

Medieval philosophers categorized several logic puzzles as insolubilia, unsolvable things. Probably the most common of these was (and still is*) the Liar Paradox.

Consider the statement "I am lying." If I am truly lying at that moment, then what I just said was true. If the statement is therefore true, however, then to say "I was lying" would be a lie. So which is it?

One 20th century philosopher used Jean Buridan (c.1300-c.1361, mentioned elsewhere in this blog) to claim that it wasn't really a paradox. Arthur Prior said it wasn't really paradoxical because every statement includes an assertion of its own truth. The statement "I am lying." is therefore taken as true—it carries its own truth independent of other sentences or context— and considering it a paradox is an unnecessary complication.

Buridan actually used the Liar Paradox to prove the existence of God. He put forth two statements:
"God exists."
"None of the sentences in this pair is true."

The only consistent way to assign truth values, that is, to have these two sentences be either true or false, requires making “God exists” be true. In this way, Buridan has “proved” that God does exist. [Internet Encyclopedia of Philosophy]

This particular paradox first appears in the middle of the 4th century BCE. Eubulides of Miletus made a list of seven puzzles, one of which was “A man says that he is lying. Is what he says true or false?” His commentary on whether it is true or false is lost to time.

*Those readers of a certain vintage will remember the Star Trek: The Original Series episode "I, Mudd" in which a controlling super-robot is rendered useless by its inability to process the two statements "Everything Harry Mudd says is a lie." followed by Mudd saying "I am lying."

The Black Death, Part 3 (of 4)

Concerning Nursery Rhymes

Ring around the rosie
A pocket full of posies
Ashes, Ashes
We all fall down!

"Everybody knows"* that the preceding nursery rhyme was composed about the Bubonic Plague. It covers it all: the red ring around the flea bite, the flowers carried constantly to help the bearer avoid the stench of death, the ashes from the mass burning of bodies, and the inevitable death of everyone. It's all about the Black Death, clearly.

Except that it isn't.

Bottom line: this poem appears in the 1880s and no earlier. Aha! (you say) But "everybody knows" that our illiterate forebears transmitted their knowledge orally, and so this rhyme was probably around for centuries before that! Hmmm. Ever played the parlor game (do we even call them "parlor games" anymore?) called "Telephone"? Now imagine a game of telephone that extends for generations ... centuries ... and winds up in Modern English saying exactly what we would expect it to say about an event that hit the cultural consciousness hundreds of years earlier. I doubt anyone could compute the odds of this, but I'm willing to bet that they would be on a par with the odds of a royal fizzbin, ie., astronomical.

It turns out that Snopes has an excellent entry dealing with this rhyme, its various nonsensical versions, and the tendency of people to ascribe meaning to random collections of words.


*If you have ever studied a subject thoroughly, then you know that this phrase from a lay person usually kicks off a conversation that will not end well for someone.