The link for the paper is available here.
This is the case of the headmistress who says that next week, there will be a surprise exam one of the afternoons. The girl students argue that it is impossible for come Friday noon with no prior exam, the exam is no longer surprise later that afternoon. Arguing inductively backwards, they seek to show that no exam next week is possible.
In the above article, Jackson seems to break down his solution to the problem thus:
EC (Existence condition): An exam will be held one afternoon next week.
IC (Ignorance condition): You won't know until after noon on the day which afternoon it is.
D : One may be justified at t1 in believing p while acknowledging at t1 that should certain things happen between t1 and t2, one would not be justified at t2 in believing p
To the above, he adds the following:
BEC : At every noon prior to the exam, it is reasonable to believe EC.
BIC: At every noon prior to the exam, it is reasonable to believe IC.
Now, his solution to the problem states thus:
Once we have BEC and BIC, Friday afternoon exam is really not possible. (I can understand this.) But exam on any other prior afternoon would not violate any of the above. On any noon prior to Friday, the following are consistent (he claims):
(1) No exam has yet made its appearance (2) Girls are entitled to believe that the exam will occur at some future afternoon (3) Girls acknowledge that should Friday noon arrive without the exam having appeared, they would no longer be entitled to believe that the exam would occur within the specified period.
At this stage, he adds "It is important to see that Modus Tollens is beside the point here." He goes on to state that the girls would be arguing fallaciously if they argued at Wednesday noon "We are entitled to EC; if Friday noon should arrive without an exam, we would not; therefore Friday noon won't" He says that the first premise must be "We are entitled to EC at Wednesday noon" and the conditional premise must be "If Friday noon should arrive without an exam, we would not be entitled to EC at Friday noon. He claims that this follows from D, which is not controversial.
He then goes on to even more somewhat complex arguments to understand.
Can it be pointed out why these different assumptions are being used and what in particular the author is trying to convey by taking recourse to Modus Tollens and how he solves the paradox and not the hard version of the paradox? I am struggling to clearly see the connections.
I posted this over at /r/askphilosophy also but that site seems to prohibit newer posters from responding to posts from what I understand, hence the post here.