Combining Texts

All the ideas for 'Defending the Axioms', 'reports' and 'The Roots of Romanticism'

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14 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
Romanticism is the greatest change in the consciousness of the West [Berlin]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Most Enlightenment thinkers believed that virtue consists ultimately in knowledge [Berlin]
23. Ethics / B. Contract Ethics / 2. Golden Rule
The Torah just says: do not do to your neighbour what is hateful to you [Hillel the Elder]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
If we are essentially free wills, authenticity and sincerity are the highest virtues [Berlin]
23. Ethics / D. Deontological Ethics / 2. Duty
The Greeks have no notion of obligation or duty [Berlin]
23. Ethics / F. Existentialism / 1. Existentialism
Central to existentialism is the romantic idea that there is nothing to lean on [Berlin]
29. Religion / B. Monotheistic Religion / 2. Judaism
Judaism and Christianity views are based on paternal, family and tribal relations [Berlin]