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In the subsection 4.3.4.2 The ‘odd number paradox’ of Cognitive Linguistics by W. Croft & D. A. Cruse

We read:

The ‘odd number paradox’ has also been put forward as a problem for prototype theory. Armstrong et al. (1983) found that people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features. Their proposed solution, the so-called ‘dual representation’ hypothesis, combines the prototype approach and the classical approach (Smith et al. 1974). The idea is that concepts have two representations, which have different functions. There is a ‘core’ representation, which has basically the form of a classical definition. This representation will govern the logical properties of the concept. The other representation is some sort of prototype system which prioritizes the most typical features, and whose function is to allow rapid categorization of instances encountered. With this set-up, the odd-number effect ceases to be a puzzle. However, this conjunction of two theories inherits most of the problems of both of them: in particular, it reinstates a major problem of the classical theory that prototype theory was intended to solve, namely, the fact that for a great many everyday concepts there is no available core definition.

It is clear for me that they speak about conjecture of the two representations of a concept. But I is unclear for me what do they mean in this sentence 'people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features.'

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"people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features" means that you can ask people things like "which is a better example of an odd number, 19 or 1001" and at least some of them will answer with one or the other (I'd guess most people will go with 19) rather than rejecting the question by saying something like "they're both odd numbers, since neither is divisible by two, so they're equally good examples". Presumably whatever sources Croft and Cruse cite would have details on the exact nature of the experiments that have been done.

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  • Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another? – Ana Vardosanidze Apr 11 '19 at 19:25
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    The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using. – melissa_boiko Apr 11 '19 at 23:15
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    Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though. – jlawler Apr 11 '19 at 23:54
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    With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting? – jk - Reinstate Monica Apr 12 '19 at 10:05
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    @jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :) – Luke Sawczak Apr 12 '19 at 12:42

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