Combining Texts

All the ideas for 'Defending the Axioms', 'Physiologia' and 'Commentary on the Metaphysics'

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12 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Understanding begins with the notion of being and essence [Avicenna]
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 / A. Existence of Objects / 5. Simples
The simple's whatness is its very self [Avicenna]
9. Objects / C. Structure of Objects / 3. Matter of an Object
The ultimate material of things has the unity of total formlessness [Avicenna]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
The quantity is just the matter, in that it has extended parts and is diffuse [Charleton]
9. Objects / D. Essence of Objects / 2. Types of Essence
An essence can either be universal (in the mind) or singular (in concrete particulars) [Avicenna, by Panaccio]