Combining Philosophers

All the ideas for Agrippa, Gerhard Gentzen and Averroes (Ibn Rushd)

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13 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason

1815	Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]

1812	All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]

1811	Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]

1813	All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]

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 / e. Being and nothing

16587

Prime matter is halfway between non-existence and existence [Averroes]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma

8850	Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]

13. Knowledge Criteria / E. Relativism / 1. Relativism

1814	Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]