The Indian Tradition
In Indian logic it has long been traditional to claim that there are four kinds of claims. You can affirm that X is so, you can deny that X is so, you can neither-affirm-nor-deny that X is so, or you can both-affirm-and-deny that X is so. Each claim can also take one of four truth-values true, false, neither-true-nor-false, and both-true-and-false. However the tradition is clear that the four kinds of statements are distinct from the four values of statements. Nagarjuna is sometimes interpreted as teaching that there is a fifth logical quality besides the four typical of Indian logic, but there are disputing interpretations.
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