Combining Philosophers

All the ideas for Agrippa, Giuseppe Peano and Hans-Johann Glock

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17 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Analysis must include definitions, search for simples, concept analysis, and Kant's analysis [Glock]
2. Reason / A. Nature of Reason / 9. Limits of Reason
All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]
Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]
All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]
Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
German and British idealism is not about individual ideas, but the intelligibility of reality [Glock]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]
13. Knowledge Criteria / E. Relativism / 1. Relativism
Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]
18. Thought / D. Concepts / 4. Structure of Concepts / h. Family resemblance
The variety of uses of 'game' may be that it has several meanings, and isn't a single concept [Glock]
We might say that the family resemblance is just a consequence of meaning-as-use [Glock]