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I took a math course that contained an entire chapter about 2 verses in the Holy Book of Titus. Verses 12 and 13 say, "One of them, a prophet of their own, said, 'Cretans are always liars, evil beasts, lazy gluttons.' This testimony is true." My professor says that since a Cretan prophet is saying that all Cretans are always liars, being a Cretan himself, the prophet cannot tell the truth, therefore all Cretans cannot be liars. I know that the Holy Bible is infallible. Although I don't quite understand how this fits into the category of "math" but how would you respond to this?

These two verses in the Holy Bible are known to mathematicians and are sometimes called 'Cretan Paradox' or the 'Epimenides Paradox'. They are used to teach students logical reasoning. Given any statement, by the use of reason and known facts we should be able to determine the truth or falsehood of that statement. Mathematicians teach how to recognize a paradox when we see it. It is equally important not to see one when there are none. The case of Titus 1:12,13 is used to prove the law of the excluded middle: either a statement is true or its denial is true.

St. Paul quotes this line from a Cretan prophet, Epimenides, a religious teacher who lived around 600 B.C. The ground for Epimenides' conviction of his fellow Cretans was their popular claim that the tomb of Zeus, the head of the Greek pantheon of gods, was located on their island. This claim was considered false, since Zeus, as a god, could not be dead. By St. Paul's time, Epimenides' words had become a popular slogan, expressing the widespread reputation of Cretans as untruthful. The verb "to Cretize" became slang for lying or cheating, just as the city of Corinth's reputation for sexual immorality led to the slang verb "to Corinthianize."

The context in which St. Paul refers to Epimenides' words is one of crisis. St. Paul was angry at the enemies of the truth in the Cretan churches, and he responded to their deceptions by using the typical device of overstatement. What St. Paul intended to communicate forcefully is clear; namely, in the case of these teachers who peddle false teaching, Epimenides' saying is in fact shown to be true..That St. Paul's words are not to be understood in an absolute sense (that is, that every Cretan is a liar!) is confirmed by the fact that his appeal to Epimenides would otherwise involve a contradiction. For since Epimenides is a Cretan, his statement that "Cretans are always liars" would include him. And that would lead to the conclusion that he always lies and that his statement is therefore false. It is clear then that neither Paul nor Epimenides intended the statement to be understood in an all-inclusive general sense.

To read more about the mathematical reasoning of these verses you can check this website: http://216.239.53.104/search?q=cache:JtTfSC1iOp8J:tavernini.com/arc/mat3013note1.pdf+titus+liars+cretans&hl=en&start=13&ie=UTF-8.