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Ideas for 'works', 'Logic (Encyclopedia I)' and 'On the Question of Absolute Undecidability'

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6 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel]
     Full Idea: The law of excluded middle is ...the maxim of the definite understanding, which would fain avoid contradiction, but in doing so falls into it.
     From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], p.172), quoted by Timothy Williamson - Vagueness 1.5
     A reaction: Not sure how this works, but he would say this, wouldn't he?
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
     Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality.
     From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4
     A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional.
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
     Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)
5. Theory of Logic / L. Paradox / 3. Antinomies
The idea that contradiction is essential to rational understanding is a key modern idea [Hegel]
     Full Idea: The thought that the contradiction which is posited by the determinations of the understanding in what is rational is essential and necessary, has to be considered one of the most important and profound advances of the philosophy of modern times.
     From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48)
     A reaction: This is the aspect of Kant's philosophy which launched the whole career of Hegel. Hegel is the philosopher of the antinomies. Graham Priest is his current representative on earth.
Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel]
     Full Idea: The solution to the antinomies is as trivial as they are profound; it consists merely in a tenderness for the things of this world. The stain of contradiction ought not to be in the essence of what is in the world; it must belong only to thinking reason.
     From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem)
     A reaction: A rather Wittgensteinian remark. I love his 'tenderness for the things of this world'! I'm not clear why our thinking should be considered to be inescapably riddled with basic contradictions, as Hegel seems to imply. Just make more effort.
Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel]
     Full Idea: The main point that has to be made is that antinomy is found not only in Kant's four particular objects taken from cosmology, but rather in all objects of all kinds, in all representations, concepts and ideas.
     From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], §48 Rem)
     A reaction: I suppose Heraclitus and Empedocles, with their oppositional accounts of reality, are the ancestors of this worldview. I just don't feel that sudden flood of insight from this idea of Hegel that comes from some of the other great philsophical theories.