The understanding of man is paltry, but although it is paltry, it must rely on all those things that it does not understand before it can understand what is meant by Heaven.
Zhuangzi (p.396)

 Some Logical Investigations

1. Equality vs. Equivalence

Many differences exist between the logical relations "equality" and "equivalence". In this monograph I point out differences that concern definition, linguistics, computational gates and tables, denotation, application, negation of terms, negation of the relation, relations to other relations, the laws of symmetry, transitivity and reflexivity, the laws of commutation and permutation,the law of tautology, the law of distribution, the law of association, propositional meaning, and "genesis". I also point out a form of "symmetry breaking": the negation of some equality may yield some non-equality, while the negation of that non-equality might not yield the same equality.

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