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indiscernibles : ウィキペディア英語版
indiscernibles
In mathematical logic, indiscernibles are objects which cannot be distinguished by any property or relation defined by a formula. Usually only first-order formulas are considered.
==Examples==
If ''a'', ''b'', and ''c'' are distinct and is a set of indiscernibles, then, for example, for each binary formula φ, we must have
: (\varphi (a, b) \and \varphi (b, a) \and \varphi (a, c) \and \varphi (c, a) \and \varphi (b, c) \and \varphi (c, b) ) \or (\lnot \varphi (a, b) \and \lnot \varphi (b, a) \and \lnot \varphi (a, c) \and \lnot \varphi (c, a) \and \lnot \varphi (b, c) \and \lnot \varphi (c, b) ) \,.
Historically, the identity of indiscernibles was one of the laws of thought of Gottfried Leibniz.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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