Combining Texts

All the ideas for 'Defending the Axioms', 'Introduction to a Secret Encyclopaedia' and 'Philosophical Naturalism'

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17 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Analysing right down to primitive concepts seems beyond our powers [Leibniz]
3. Truth / A. Truth Problems / 8. Subjective Truth
We hold a proposition true if we are ready to follow it, and can't see any objections [Leibniz]
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]
7. Existence / D. Theories of Reality / 5. Naturalism
Externalism may be the key idea in philosophical naturalism [Papineau]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
How does a dualist mind represent, exist outside space, and be transparent to itself? [Papineau]
17. Mind and Body / C. Functionalism / 8. Functionalism critique
Functionalism needs causation and intentionality to explain actions [Papineau]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
Epiphenomenalism is supervenience without physicalism [Papineau]
Supervenience requires all mental events to have physical effects [Papineau]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Knowing what it is like to be something only involves being (physically) that thing [Papineau]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
If a mental state is multiply realisable, why does it lead to similar behaviour? [Papineau]
19. Language / F. Communication / 4. Private Language
The Private Language argument only means people may misjudge their experiences [Papineau]