Friday, September 3, 2010

Who First Linked Epimenides to the Semantic Paradoxes?

As part of a philosophy of logic seminar on theories of truth I have developed an amateur interest in the history of discussions of logical and semantic paradoxes. As is well known, the Liar paradox can be traced to Epimenides and appears in the New Testament:
It was one of them, their very own prophet, who said, 'Cretans are always liars, vicious brutes, lazy gluttons.' That testimony is true. (Titus 1: 10-13, NRSV)
Russell makes allusions to this passage several times, including in "Mathematical Logic as Based on a Theory of Types" (see here.)

Given the discussion of these sorts of paradoxes in by medieval logicians, I was surprised to find this passage in Spade's article on Insolubles in the Stanford Encyclopedia:
One initially plausible stimulus for the medieval discussions would appear to be the Epistle to Titus 1:12: "One of themselves, even a prophet of their own, said, The Cretians [= Cretans] are always liars, evil beasts, slow bellies." The Cretan in question is traditionally said to have been Epimenides. For this reason, the Liar Paradox is nowadays sometimes referred to as the “Epimenides." Yet, blatant as the paradox is here, and authoritative as the Epistle was taken to be, not a single medieval author is known to have discussed or even acknowledged the logical and semantic problems this text poses. When medieval authors discuss the passage at all, for instance in Scriptural commentaries, they seem to be concerned only with why St. Paul should be quoting pagan sources.[5] It is not known who was the first to link this text with the Liar Paradox.
So, was Russell the first to make this link, or was he merely drawing on other sources?

My first thought was that Hegel or some other post-Kantian must have made the link, and Russell is merely repeating it. Through the power of Google Books I was able to find a passage in the English translation of Lotze's Logic:
One dilemma nicknamed Pseudomenos dates from Epimenides, who being a Cretan himself asserted that every Cretan lies as soon as he opens his lips. If what he asserted is true, he himself lied, in which case what he said must have been false; but if it false it is still possible that the Cretans do not always lie but lie sometimes, and that Epimenides himself actually lied on this occasion in making the universal assertion. In this case there will be no incongruity between the fact asserted and the fact that it is asserted, and a way out of the dilemma is open to us (Book II, Chapter IV).
This translation dates from 1884 and seems to be from the second edition of the Logic from 1880. I have not checked the German or the first edition.

It seems likely that Russell read Lotze's Logic, either in this very translation or the original German, as he notes Lotze's Metaphysik in his readings from 1897 and of course discusses Lotze's views on geometry in the fellowship essay. Still, it seems unlikely to me that Lotze was the first person to make the link. Any other candidates or evidence to consider?


Jonathan Livengood said...

The answer is that lots of other philosophers and logicians made this connection before Russell.

The earliest I could confirm for certain in ten minutes of looking on Google books was Pierre Bayle (1740) Dictionnaire historique et critique, vol. 2, pp. 414-415. Start at the bottom of the right-hand column on page 414. I suspect that the earlier edition of 1714 also made the connection, but I can't confirm it via Google books.

Other notables before Russell include De Morgan (1847) Formal Logic. See page 210: "Again, the Cretan, Epimenides, said that all the Cretans were incredible liars; is he to be believed or not? If we believe him, we must, he being a Cretan disbelieve him."

Fowler (1869) The elements of deductive logic makes the logic a bit plainer. See p. 163, number 69, which he calls the Fallacy of Mentiens: "Epimenides the Cretan says, "that all the Cretans are liars," but Epimenides is himself a Cretan; therefore he is himself a liar. But if he be a liar, what he says is untrue, and consequently the Cretans are veracious; but Epimenides is a Cretan, and therefore what he says is true; hence the Cretans are liars, Epimenides is himself a liar, and what he says is untrue. Thus we may go on alternately proving that Epimenides and the Cretans are truthful and untruthful."

Finally, Peirce (1878) The Probability of Induction gives it an odd twist by applying it to inductive logic. In Section IV, he writes, "Ninety-nine Cretans in a hundred are liars; But Epimenides is a Cretan; Therefore, Epimenides is a liar:-- I know that reasoning similar to that would carry truth 99 times in 100. But when I reason in the opposite direction: Minos, Sarpedon, Rhadamanthus, Deucalion, and Epimenides, are all the Cretans I can think of; But these were all atrocious liars, Therefore, pretty much all Cretans must have been liars; I do not in the least know how often such reasoning would carry me right. On the other hand, what I do know is that some definite proportion of Cretans must have been liars, and that this proportion can be probably approximated to by an induction from five or six instances."

So yeah, lots of people before Russell.

Chris Pincock said...


Thanks for tracking these down. I don't know if your Google Books skills are just better than mine or I was hampered by searching for sources that Russell might have drawn from.

I find the Bayle reference most promising. It is interesting that it comes from the entry for Euclid. It discusses "le menteur" and notes Diogenes (I think) and Cicero as ancient sources, and Gassendi as a modern source with "a good explication of all these sophisms supported by examples".

So maybe Gassendi will turn out to be the first?