The below is pilfered from a 11+ sample paper on non-verbal reasoning. For the benefit of those outside of the UK, the 11+ is a test some unfortunate children have to take to determine if they are fit to go to the higher stream 'Grammar' schools.
It's an element in paper which asks children to analyse the relationship between the first pair of shapes, and then make a pair with the same relationship.
So here the answer the answer is 'b' – the smaller of the two shapes appears as am even smaller, filled in shape inside the bigger shape. What are we learning through doing such tests? Surely it's how certain relations, certain principles, can be cross-applied from one context to another. One way of viewing this might be to say that it's teaching the principle of analogy, another that of universal law.
Now this one excites the philosophy student in me:
The correct answer, according to the sample paper, is 'e', where the shape is left unchanged bar acquiring a chequered pattern. However, we could also make a case for 'c', where the. Why? Because with the two images on the left, the shape which changes is symmetrical along the horizontal (and vertical) plane, and so we cannot tell if it has been flipped upside-down or not. How can we possibly go for 'e' over 'c' then? Well, it appears that this problem is a visual application of Occam's Razor, the principle which states that given any number of equally likely possibilities, we should always go with the simplest. We do not know that the shape has been flipped upside-down, so we should assume it hasn't.
But what's more interesting is this question contains within the potential for creating a test for paralogical reasoning. By paralogical reasoning, I mean forms likes jokes, sophistry and wordplay. These forms which can bring out amazing possibilities without subscribing to our normal notions of logic and sense. All we have to do for this question is say the answer is 'c' – that we should assume, if nothing is there to the contrary, that objects have been transformed, that we should subscribe to the wildest notions that are available to us.
Perhaps it would be possible to compose an entry paper to a radical and subversive academy, which turns normals notions of sense on their head. But could such a paper ever be marked – wouldn't the most talented students subvert even the modest assumptions such papers must be founded on?
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"Perhaps it would be possible to compose an entry paper to a radical and subversive academy, which turns normals notions of sense on their head. But could such a paper ever be marked – wouldn't the most talented students subvert even the modest assumptions such papers must be founded on?"
Perhaps the entry test would consist of a challenge --namely to set an entry test for a radical and subversive academy. . . .
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