Combining Philosophers

All the ideas for Herodotus, Curt Ducasse and Peter Koellner

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15 ideas

2. Reason / D. Definition / 2. Aims of Definition
A correct definition is what can be substituted without loss of meaning [Ducasse]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
26. Natural Theory / C. Causation / 2. Types of cause
Causation is defined in terms of a single sequence, and constant conjunction is no part of it [Ducasse]
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
We see what is in common between causes to assign names to them, not to perceive them [Ducasse]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Causes are either sufficient, or necessary, or necessitated, or contingent upon [Ducasse]
When a brick and a canary-song hit a window, we ignore the canary if we are interested in the breakage [Ducasse]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
A cause is a change which occurs close to the effect and just before it [Ducasse]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Recurrence is only relevant to the meaning of law, not to the meaning of cause [Ducasse]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
We are interested in generalising about causes and effects purely for practical purposes [Ducasse]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]