A = B
A = B
While old Gottfried Wilhelm Leibniz held the logical principle of identity to be absolutely indemonstrable, and in that sense not primarily a logical but a metaphysical thesis, Bertrand Russell reasoned in the opposite direction, grounding his metaphysics in his particular view of logic. While the problem of universals is to explain how different things can have common properties, the problem of particulars is to show how objects with common properties can be different. Fundamental to these distinctions is Leibniz's principle of substitutivity. In his seminal work “über Sinn und Bedeutung” published in 1892, Gottlob Frege argued that sameness is a relation, but immediately added that sameness is not a relation between objects but a relation between the names or signs of objects. What logic and geometry share in common is that both modes of reasoning are forms of rhetoric, albeit a type of rhetoric which is so convincing that it is no longer called “rhetoric” but “logic” and “geometry.”
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