By Gary F. Marcus
An try and combine theories approximately how the brain works, one who says that the brain is a computer-like manipulator of symbols, and one other that claims that the brain is a big community of neurons operating jointly in parallel.
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Extra resources for Algebraic Mind: Integrating Connectionism and Cognitive Science
I do not mean to suggest that UQOTOM are the only mappings people compute. But UQOTOM are especially important to the arguments that follow because they are functions in which every new input has a new output. Because free generalization of UQOTOM would preclude memorization, evidence that people (or other organisms) can freely generalize UQOTOM would be particularly strong evidence in support of the thesis that people (or other organisms) can perform operations over variables. (A UQOTOM is not the only kind of mental operation that might reasonably be called an operation over variables.
1 could be represented as an expression of the universally quantified, one-to-one identity mapping, f(x) = x. We could then calculate the output that corresponds to the test item, f(1111) by substituting the instance 1111 into the variable x on the right-hand side of the equation. 4 We do not care which examples of that variable we have seen before; the operation over variables can be freely generalized to any instantiation. Looking something up in a table does not count as applying an abstract relationship between variables.
1 Can People Generalize UQOTOM? There is ample evidence, I think, that people can generalize universally quantified one-to-one mappings. 1 Input and output data. Training Item Input Output 1010 0100 1110 0000 1010 0100 1110 0000 Test Item 1111 ? artificial example. 1. If you are like other people whom I have asked, you would guess that in the test item the output that corresponds to input item  is . But that is not the only inference that you could draw. For example, in the training data, the rightmost column is always 0: there is no direct evidence that the rightmost column could ever be a 1.
Algebraic Mind: Integrating Connectionism and Cognitive Science by Gary F. Marcus