List, Jon, Francesco: > On Sep 11, 2018, at 8:14 PM, Jon Alan Schmidt <[email protected]> > wrote: > > He also wrote later that the three different forms of thought--corresponding > to Icons, Indices, and Symbols--are best explained by positing three > different "modes of metaphysical being." > > CSP: You will observe that each kind of sign serves to bring before the mind > objects of a different kind from those revealed by the other species of > signs. The key to the solution of this question is that what we think of > cannot possibly be of a different nature from thought itself. For the thought > thinking and the immediate thought-object are the very same thing regarded > from different points of view ... We must conclude, then, that the reason why > different things have to be differently thought of is that their modes of > metaphysical being are different. (CP 6.339; 1908) >
I believe that this quote, coming late in his lifetime, reveals a critical aspect of the connections between natural sorts and kinds and logic. In simpler language, it recalls Gregory Bateson, “the difference that makes a different.” In this context, the reasoning about the experience of signs is not merely to form propositions. It is necessary to reason such that the differences between signs distinguish the metaphysical differences between the Immediate objects. Another way of stating this conclusion is that of identity of objects. The signs emanating from an object are causally connected to the mode of meta-physical being of the whole. The logics of the natural sciences necessarily derive themselves from this notion of comparison. The term “species” may refer to any natural species of any scope or scale. In the natural sciences, the scope and scale of objects are arrived at by compositions of parts of wholes (mereology) using the logic of comparisons of qualisigns. What is the difference between this view of the meta-physical origins of logic and First Order Logic? Or, Propositions of Predicate Logic? In other words, what is the role of identity in first order logic? Or, predicate logic? In short, the mathematical notion of an identity is a construct of logical operations within the mathematical symbol system, NOT OF SIGNS emanating from the particular mode of metaphysical being of a particular natural object. Jon: Why do you associate this excerpt with Icons, Indices and Symbols? The actuality of the logic of sets does not uses three different terms, such as Icons, Indices and Symbols in constructing arguments about mathematical species. Indeed, only one term, “set” is used and does not have a “mode of meta-physical being”. Cheers Jerry
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