Combining Texts

All the ideas for 'Concerning the Author', 'Defending the Axioms' and 'The Nature of Existence vol.1'

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13 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
The demonstrations of the metaphysicians are all moonshine [Peirce]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
I am saturated with the spirit of physical science [Peirce]
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 / B. Unity of Objects / 2. Substance / d. Substance defined
Substance has to exist, with no intrinsic qualities or relations [McTaggart]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
Infallibility in science is just a joke [Peirce]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Association of ideas is the best philosophical idea of the prescientific age [Peirce]
14. Science / B. Scientific Theories / 1. Scientific Theory
Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce]