Tyler Marghetis
(a)The 'Impossibility-of-a-Surprise-Test-on-Friday' as a Truth-in-Itself
--> The occurance of the test is not a causal event, but rather a rational event made under certain restrictions (i.e. it must be a surprise to the rational students). As such, the reality under consideration is an idealized one. Essentially, only a subset of the possible realities (as-if-MIRs) are being considered; the "Surprise" clause eliminates all possible as-if-MIRs which include a test on Friday. Thus, for the idealized subset of realities under consideration, FRIDAY IS NEVER THE DATE OF THE TEST; this universal restriction ("truth-in-itself") serves as the base assumption for the inductive argument. Therefore, if restrictions exist on the future rational choices to be made within an as-if-MIR (ie the Surprise Clause), universal restrictions exist on the possible future as-if-MIR constructions.
--> The only way to avoid the existence of truths-in-themselves is to deny the possibility of placing limitations on future rational choices -- in effect, claiming that the Surprise clause is only a construct, which has no absolute reality and is mutable. This, however, completely undermines the fundamental assumptions of the paradox, which state that the teacher WILL give a surprise test.
(b)The trivial role of backwards reasoning
--> If the falsity of the time-reversal assumption is at the core of the backwards-reasoning confusion, then in reasoning forward the paradox should disappear. HOWEVER, the possibility exists of formulating the Surprise Test Paradox in a form which reasons forward in time
--> It is announced that a surprise test is to be administered at the first possible opportunity. The forward reasoning proceeds as follows: the test cannot be administered at the next class (say Monday), since the class knows that is the first possible opportunity and so the test would not be a surprise. Neither can the test be administed on the following day (Tuesday), since once again the students are aware that the test is to be administered at the first possible opportunity for surprise. The same argument applies to every following day, ad infinitum. Therefore, reasoning forward in time, a surprise test can never be given as soon as possible. [Sorenson (1980) "Infinite 'Backward' Induction Arguments." PHILOSOPHICAL QUARTERLY 80, p.278]
--> Thus, time reversal is of no consequence to the Paradox. Feynman can turn positrons into electrons travelling backwards in time all he wants!
--> If Working Ontology denies the cogency of reasoning which extends infinitely into the future, then the time frame can be bounded (eg. one hour) but devided into an infinite number of time segments of decreasing size (similar to Zeno's paradox). Thus, it can be 'proved' that no surprise test can be given at the earliest opportunity in a bounded time segment.
(c) The Paradox remains!