Combining Texts

All the ideas for 'works', 'Sets, Aggregates and Numbers' and 'The Logic of Scientific Discovery'

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16 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Scientific objectivity lies in inter-subjective testing [Popper]
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]
14. Science / A. Basis of Science / 6. Falsification
Give Nobel Prizes for really good refutations? [Gorham on Popper]
Falsification is the criterion of demarcation between science and non-science [Popper, by Magee]
We don't only reject hypotheses because we have falsified them [Lipton on Popper]
If falsification requires logical inconsistency, then probabilistic statements can't be falsified [Bird on Popper]
When Popper gets in difficulties, he quietly uses induction to help out [Bird on Popper]
14. Science / B. Scientific Theories / 2. Aim of Science
Good theories have empirical content, explain a lot, and are not falsified [Popper, by Newton-Smith]
14. Science / C. Induction / 3. Limits of Induction
There is no such thing as induction [Popper, by Magee]
14. Science / C. Induction / 4. Reason in Induction
Science cannot be shown to be rational if induction is rejected [Newton-Smith on Popper]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]