Ugly duckling theorem

<p>The ugly duckling theorem is an <a href="/facts/Argument/1K1e3Xg4">argument</a> showing that classification is not really possible without some sort of <a href="/facts/Bias_(statistics)/Pql981K3">bias</a>. More particularly, it assumes finitely many properties combinable by <a href="/facts/Logical_connective/VkPhUs6M">logical connectives</a>, and finitely many objects; it asserts that any two <a href="/facts/Identity_of_indiscernibles/uaDTDeq8">different</a> objects share the same number of (<a href="/facts/Extension_(predicate_logic)/ruBkmsJ6">extensional</a>) properties. The theorem is named after <a href="/facts/Hans_Christian_Andersen/qV5t4NeP">Hans Christian Andersen</a>'s 1843 story "<a href="/facts/The_Ugly_Duckling/3tSn7sLF">The Ugly Duckling</a>", because it shows that a <a href="/facts/Duckling/lNhVvTRH">duckling</a> is just as similar to a <a href="/facts/Swan/gI6G1Ho5">swan</a> as two swans are to each other. It was derived by <a href="/facts/Satosi_Watanabe/k2s2mtha">Satosi Watanabe</a> in 1969.: 376–377 
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Ugly duckling theorem open-in-new

Ugly duckling theorem