Combining Philosophers

All the ideas for Xenophon, Gerhard Gentzen and Wilhelm Dilthey

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10 ideas

1. Philosophy / H. Continental Philosophy / 3. Hermeneutics

5437	The claim of hermeneutics to give knowledge through understanding is challenged by positivism [Mautner on Dilthey]

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

11022

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

11065

The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]

11023

The logical connectives are 'defined' by their introduction rules [Gentzen]

11213

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

13832

Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10067

Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]

14. Science / D. Explanation / 1. Explanation / d. Explaining people

5436	Natural science seeks explanation; human sciences seek understanding [Dilthey, by Mautner]

22. Metaethics / B. Value / 2. Values / h. Fine deeds

5845	Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]

25. Social Practice / E. Policies / 5. Education / b. Education principles

5833	Education is the greatest of human goods [Xenophon]