Here is the answer according to logic.
Suppose the (material) conditional statement 'If it is Thurs. and we have not had the surprise quiz, then we cannot have it on Friday' is true. This does not allow us to infer the consequent, viz., that we cannot have it on Friday. For, in order to infer that by an application of modus ponens, we need to assume the antecedent. But it's not Thursday yet, so we can't. The rest of the argument breaks down here, but we can make the whole argument explicit according to the following.
1. If it's Thurs and no surprise quiz, then it's not on Fri.
2. If it's not on Fri., then if it's Wed. and no surprise quiz, then it's not on Thurs.
3. If it's not on Thurs., then if it's Tues and ....
Each of the premises of the argument is a nested conditional statement, each of which requires, for the conclusion to follow, a supposition of the antecedent of the last conditional in the nesting of the preceding conditional (premise). (Sorry, that is extremely wordy.) It suffices then to show that there are no grounds to suppose the antecedent of (1) - i.e, the antencedent of the first conditional - in order to show that the conclusion does not hold simpliciter, that is, not on condition of all of the premises. Well, this is easy to show, since it is supposed by the statement of the surprise quiz paradox that it is not yet Thurs.