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Virtual Logic-Laws of Form and the Transfinite Ordinals

机译:形式和超常序的虚拟逻辑法则

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In this virtual logic column we discuss the transfinite ordinal numbers of Georg Cantor (Cantor, 1895/1941) and show how they are related to the expressions in the calculus of indications of George Spencer-Brown in his remarkable book Laws of Form (Spencer-Brown, 1969) and to infinite expressions and reentry forms as well. Cantor is the originator of the theory of sets. He said that a set is a multiplicity that can be seen as a unity. This dictum applies even to the empty set { } where there are zero elements in the multiplicity, and yet that nothing is drawn into a unity and becomes the one empty set. The dictum applies to a finity such as 3 where the set {{},{{}},{{},{{}}}} draws three distinct sets into a new set with three distinct members and so becomes one. The dictum applies to an infinity such as {1,2,3,...} where the set braces draw together all positive integers into a unity that can represent the one concept of positive integrality. The dictum applies to a self reference such as "I am the one who says I." where the act of saying articulates the self-relation of a self to itself, making a distinction and joining that distinction in the very act of apparent separation, and so coming to one.
机译:在这个虚拟逻辑专栏中,我们讨论了乔治·康托尔(Cantor,1895/1941)的超序数,并在乔治·斯宾塞·布朗(George Spencer-Brown)的非凡著作《形式定律》(Spencer-布朗(1969)以及无限表达和折返形式。康托尔是集合论的创始人。他说,集合是可以看作一个整体的多重性。该格言甚至适用于在多重性中有零个元素的空集{},但是没有任何东西被吸引到一个统一中而成为一个空集。该格律适用于诸如3的无穷大,其中集合{{},{{}},{{},{{}}}}将三个不同的集合吸引到具有三个不同的成员的新集合中,因此成为一个。该规定适用于无穷大,例如{1,2,3,...},其中集合括号将所有正整数汇集在一起​​,可以表示一个正整数概念。该格言适用于诸如“我是说我的人”之类的自我参照,其中说的行为阐明了自我与自身的自我关系,做出区分并将这种区分加入明显的行为中。分离,等等。

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