Epi­menides Para­dox Revisited

In response to our argu­ment that Paul’s fum­bling of the Epi­menides para­dox is proof that the ad-hoc ​“apos­tle” was not inspired after all, one Chris­t­ian has raised an objec­tion. The attempt­ed rebut­tal acknowl­edges the para­dox­i­cal nature of Epi­menides’ state­ment, but then makes the bizarre claim that Paul’s state­ment is true nonethe­less due to oth­er ele­ments attrib­uted to the Cre­tan ​“prophet” by the ​“apos­tle”.

While it is true that exter­nal fac­tors can some­times help us solve a para­dox, the ele­ments brought to wit­ness by the Chris­t­ian author of this defense of Paul fail to help us in any way, and worse, demon­strate that the crit­ic rais­ing this objec­tion does not under­stand log­ic. The crit­ic writes as follows :

We notice that Paul, who was prob­a­bly very aware of the PURE log­i­cal mean­ing­less sen­tence ​“Cre­tans are always liars” told by a Cre­tan, uses a more com­plex form of the sen­tence, ​“Cre­tans are always liars, evil brutes, lazy glut­tons.” We can now use the addi­tion­al FACTS to prove or dis­prove the testimony.

The crit­ic tries to fur­ther elu­ci­date this point by giv­ing the anal­o­gy of a per­son in a court of law tes­ti­fy­ing : ​“I always lie, I am an evil bul­ly and I am a lazy work­er.” The crit­ic’s point is that while the state­ment ​“I always lie” is para­dox­i­cal, the sen­tence over­all is true (or its truth can be deter­mined by check­ing the oth­er qual­i­ties not­ed). While some read­ers may not have caught it yet, the shock­ing real­i­ty is that in this dis­cus­sion on whether or not Paul under­stood log­ic, the defend­er has him­self exhib­it­ed deep log­i­cal defi­cien­cies. The prob­lem here is that the crit­ic does not real­ize that his state­ments involve log­i­cal con­juncts which he has not prop­er­ly interpreted.

In log­ic, for a con­junc­tive propo­si­tion to be true all its con­juncts must be true. So, what is a con­junc­tive propo­si­tion and what is a con­junct ? Well, if I say ​“my name is Mohd and I am a Mus­lim”, that is a con­junc­tive propo­si­tion. The propo­si­tion has two con­juncts, the first being ​“my name is Mohd”, the sec­ond being ​“I am a Mus­lim.” If my name is Mohd, but I am not a Mus­lim, the sen­tence is false, and if my name is not Mohd, but I am a Mus­lim, the sen­tence is again false. The sen­tence ​“my name is Mohd and I am a Mus­lim” can be true only if both con­juncts are true, i.e. if my name is Mohd and I am a Muslim.

So, if a man says ​“every­thing I say is a lie, I am lazy, and I am a bul­ly”, the state­ment can­not be true on the grounds that in order for it to be true, all three of its con­juncts must be true, but the first con­junct is clear­ly untrue. So, in response to the Chris­t­ian who defend­ed Paul, if we assume the sen­tence ​“all Cre­tans are liars” (or ​“Cre­tans are always liars”) is mean­ing­less, or even false, com­bin­ing it with oth­er state­ments in a con­junc­tion does not cre­ate a true sen­tence. This is because the orig­i­nal state­ment in ques­tion is still not true, thus it being a con­junct in a larg­er sen­tence results in the sen­tence also being untrue.

Inter­est­ing­ly, this exact sort of sen­tence was touched on by Dr. Lau­rence Gold­stein of the Uni­ver­si­ty of Hong Kong, in an arti­cle on Epi­menides, writ­ten for a schol­ar­ly jour­nal more than fif­teen years ago. An exam­ple of a sim­ple pseudomenon would be the propo­si­tion ​‘x’, where propo­si­tion ​‘x’ is ​“x is false”. Gold­stein, how­ev­er, brings in an extra propo­si­tion, cre­at­ing a con­junc­tion. Gold­stein gives the exam­ple of sen­tence ​‘E’, and sen­tence ​‘E’ is ​“E is not true and q” where ​‘q’ is some oth­er propo­si­tion. From there, he writes the following :

Here ​‘q’ is both con­joined with a state­ment about E, and also part of E (so, although ​‘q’ is arbi­trary, it is not inde­pen­dent of E). If ​‘q’ is not true, then, in virtue of E con­tain­ing ​‘q’ as a con­junct, E is not true, and this is con­sis­tent with what the first con­junct (the state­ment about E) says. How­ev­er, if ​‘q’ is true then we have the absurd (and thus to be reject­ed) impli­ca­tion that E is both true and not true.Lau­rence Gold­stein, ​“Epi­menides and Cur­ry,” Analy­sis, Vol. 46, 1986, p. 121

Thus we see that con­join­ing a para­dox­i­cal state­ment with oth­er state­ments (regard­less of their truth val­ue) does not result in the cre­ation of a true statement.

It should be fur­ther not­ed that this method­ol­o­gy still applies even if it is argued that the state­ment is not para­dox­i­cal, but mere­ly false. In biva­lent log­ic, state­ments are either true or false. In triva­lent and mul­ti-val­ued log­ics, state­ments can be true, false or have some oth­er truth-val­ue. Nonethe­less, in all realms of log­ic the rule of con­junc­tion is still the same : in order for a con­junc­tive propo­si­tion to be true, all its con­juncts must be true. If a con­junc­tive state­ment has some con­juncts that are true, and one that is mean­ing­less or false, the state­ment is not true ; rather it is mean­ing­less or false. Note that the state­ment ​“my name is Mohd Elfie and I like to ger­gle­plex with Jab­ber­wock­ies” can­not be con­sid­ered log­i­cal­ly true since one of the con­juncts is meaningless.

Thus either way, the fol­low­ing sev­en-point syl­lo­gism first pro­posed in Epi­menides Para­dox : Was Paul ​“Inspired”? still applies :

• Paul claims a Cre­tan uttered a cer­tain proposition. 
• The propo­si­tion is not true. 
• Paul claims the propo­si­tion is true. 
• Paul’s claim is an error. 
• Paul’s writ­ings are errant rather than inerrant. 
• Errant scrip­ture is not inspired scrip­ture (a com­mon assump­tion among Chris­tians and Muslims). 
• There­fore, Paul was not inspired (or at least not when he wrote the epis­tle to Titus). 

And only God knows best !