Combining Texts

All the ideas for 'Defending the Axioms', 'Elements of Law and Justice' and 'Miscellaneous Observations'

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16 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Delusion and truth differ in their life functions [Novalis]
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]
9. Objects / D. Essence of Objects / 3. Individual Essences
Refinement of senses increasingly distinguishes individuals [Novalis]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Experiences tests reason, and reason tests experience [Novalis]
14. Science / C. Induction / 2. Aims of Induction
Hypotheses come from induction, which is comparison of experiences [Leibniz]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The seat of the soul is where our inner and outer worlds interpenetrate [Novalis]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Only self-illuminated perfect individuals are beautiful [Novalis]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis]