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All the ideas for '', 'Sets, Aggregates and Numbers' and 'Philosophy without Intuitions'

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11 ideas

2. Reason / E. Argument / 7. Thought Experiments
So-called 'though experiments' are just philosophers observing features of the world [Cappelen]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
The word 'intuitive' often plays not role at all in arguments, and can be removed [Cappelen]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]