Combining Philosophers

Ideas for John Mayberry, Georg W.F.Hegel and Thales

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14 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
17786 The mainstream of modern logic sees it as a branch of mathematics [Mayberry]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
17788 First-order logic only has its main theorems because it is so weak [Mayberry]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
17791 Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
21595 Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
21777 Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
17787 Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17790 No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17779 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]
17778 Axiomatiation relies on isomorphic structures being essentially the same [Mayberry]
17780 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry]
5. Theory of Logic / K. Features of Logics / 6. Compactness
17789 No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
5. Theory of Logic / L. Paradox / 3. Antinomies
15628 The idea that contradiction is essential to rational understanding is a key modern idea [Hegel]
15629 Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel]
15630 Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel]