Bit by bit
Backwards.
I recognise this scenario quite well – a class of slow, lazy pupils; threat of a test; sinking realisation that the whole thing will be a farce. (All right, I added the last part.) The teacher tells his class of retards that there's going to be a test some time before the end of term, and it's going to be a surprise.
Two of the pupils reason that it can't be on the very last day because then it wouldn't be a surprise. Nor could it be the day before that or before that or before that etc. for the same reason. (I think you get the picture.) Thus our two idiots conclude that the test is never going to happen because, according to their reasoning, it'll never be a surprise.
Nonetheless, the teacher does hold the test about a week later much to the dismay of the half-witted pupils who thought they'd realised what the teacher was up to. The question is whether their reasoning is flawed or the teacher is being a hypocrite.
This appears to be an instance where logic runs into gradience and falls flat on its face because the further it departs from the point at which an argument is valid, the less valid it becomes, although at each step it still seems valid. At least, that's how I see this problem. Obviously, if the test is left to the very end of the term, there can be no surprise. If this day is excluded for obvious reasons, then even the day before can also be discounted, but I'd say that any day prior to that may legitimately be regarded as a day for a surprise test. The less time the teacher leaves for the test, though, the less of a surprise it'll be.
I recognise this scenario quite well – a class of slow, lazy pupils; threat of a test; sinking realisation that the whole thing will be a farce. (All right, I added the last part.) The teacher tells his class of retards that there's going to be a test some time before the end of term, and it's going to be a surprise.
Two of the pupils reason that it can't be on the very last day because then it wouldn't be a surprise. Nor could it be the day before that or before that or before that etc. for the same reason. (I think you get the picture.) Thus our two idiots conclude that the test is never going to happen because, according to their reasoning, it'll never be a surprise.
Nonetheless, the teacher does hold the test about a week later much to the dismay of the half-witted pupils who thought they'd realised what the teacher was up to. The question is whether their reasoning is flawed or the teacher is being a hypocrite.
This appears to be an instance where logic runs into gradience and falls flat on its face because the further it departs from the point at which an argument is valid, the less valid it becomes, although at each step it still seems valid. At least, that's how I see this problem. Obviously, if the test is left to the very end of the term, there can be no surprise. If this day is excluded for obvious reasons, then even the day before can also be discounted, but I'd say that any day prior to that may legitimately be regarded as a day for a surprise test. The less time the teacher leaves for the test, though, the less of a surprise it'll be.
Query. What's wrong with the word "gradience"? It gets red-lined, yet it seems to be a perfectly feasible word derived from the adjective "gradient". The only other option would be to use "gradation", yet "gradience" seems the more natural term to use.
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