Combining Philosophers

All the ideas for Anaxarchus, Melissus and Gerhard Gentzen

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11 ideas

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]

7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being

12270

Being is one [Melissus, by Aristotle]

13. Knowledge Criteria / D. Scepticism / 1. Scepticism

3061	Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]

27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement

3059	There is no real motion, only the appearance of it [Melissus, by Diog. Laertius]

27. Natural Reality / C. Space / 1. Void

5100	The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus]

27. Natural Reality / E. Cosmology / 2. Eternal Universe

456	Nothing could come out of nothing [Melissus]