Combining Philosophers

All the ideas for Eubulides, Peter John Olivi and Gerhard Gentzen

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13 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
The logical connectives are 'defined' by their introduction rules [Gentzen]
Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
5. Theory of Logic / L. Paradox / 1. Paradox
If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
8. Modes of Existence / A. Relations / 1. Nature of Relations
Relations do not add anything to reality, though they are real aspects of the world [Olivi]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
Quantity is the quantified parts of a thing, plus location and coordination [Olivi]
Quantity just adds union and location to the extension of parts [Olivi]
27. Natural Reality / G. Biology / 5. Species
Things are limited by the species to certain modes of being [Olivi]