Combining Philosophers

All the ideas for Cardinal/Hayward/Jones, Jean Calvin and Gerhard Gentzen

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13 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
The logical connectives are 'defined' by their introduction rules [Gentzen]
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
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
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
The phenomenalist says that to be is to be perceivable [Cardinal/Hayward/Jones]
Linguistic phenomenalism says we can eliminate talk of physical objects [Cardinal/Hayward/Jones]
If we lack enough sense-data, are we to say that parts of reality are 'indeterminate'? [Cardinal/Hayward/Jones]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
Primary qualities can be described mathematically, unlike secondary qualities [Cardinal/Hayward/Jones]
An object cannot remain an object without its primary qualities [Cardinal/Hayward/Jones]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
My justifications might be very coherent, but totally unconnected to the world [Cardinal/Hayward/Jones]
25. Social Practice / E. Policies / 2. Religion in Society
Only when working people are poor do they remain obedient to God [Calvin, by Weber]