Combining Texts

All the ideas for 'fragments/reports', 'Subjective and Objective' and 'Defending the Axioms'

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14 ideas

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]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Sense-data are a false objectification of what is essentially subjective [Nagel]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
Inner v outer brings astonishment that we are a particular person [Nagel]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
If you assert that we have an ego, you can still ask if that future ego will be me [Nagel]
16. Persons / F. Free Will / 1. Nature of Free Will
The most difficult problem of free will is saying what the problem is [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]