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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.1
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!
- Laurence Goldstein, “Epimenides and Curry,” Analysis, Vol. 46, 1986, p. 121 [⤺]