Combining Philosophers

All the ideas for Hans Reichenbach, Giordano Bruno and Giuseppe Peano

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12 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Contextual values are acceptable in research, but not in its final evaluation [Reichenbach, by Reiss/Sprenger]
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]
12. Knowledge Sources / B. Perception / 5. Interpretation
Kant showed that our perceptions are partly constructed from our concepts [Reichenbach]
26. Natural Theory / C. Causation / 5. Direction of causation
A theory of causal relations yields an asymmetry which defines the direction of time [Reichenbach, by Salmon]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
The direction of time is grounded in the direction of causation [Reichenbach, by Ladyman/Ross]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
Bruno said that ancient Egyptian magic was the true religion [Bruno, by Yates]