A striking thing about language is that is composable in certain ways. I can make an argument in which each step of the argument is self-evident, yet the conclusion is a surprising (but true) consequence of the premises.
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Perhaps the best analogue is jokes, which often rely on the same kind of multiple inverse inferences about the meaning of words.
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Or certain kinds of cognitive bias - like the Group Attribution Error - which also rely on faulty inverse inference.
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Maybe when we sum small amounts? E.g. if a put .1g of sugar in a cup of coffee, the taste doesn't change from before. If now I put .1g is doesn't change. Every step is correct, but in the end the taste is different. It happens when we discretize continuous things, maybe?
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Interesting example. I don't know how discrete the response of taste receptors and the olfaction system are.
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Also related to search algorithms; for example, a greedy algorithm (at each point, take the best local step/option available, and repeat from there.) This often does not produce the best overall outcome, and your example of shortest route is one case of that!
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I think there is an important distinction between inference and optimization. Truth does not “leak” or diminish between steps of pure logical inference, whereas optimality can.
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I really like this thread. The reference to the fascinating work of MC Escher is quite interesting. One could derive several possible mappings between each of those visuals and its linguistic interpretations. Doug Hofstadter's Godel, Escher, Bach: ... is highly recommended.
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