Combining Texts

All the ideas for 'Defending the Axioms', 'Theology and Verification' and 'Form, Matter and Substance'

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14 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Much metaphysical debate concerns what is fundamental, rather than what exists [Koslicki]
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 / 1. Unifying an Object / a. Intrinsic unification
Structured wholes are united by the teamwork needed for their capacities [Koslicki]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The form explains kind, structure, unity and activity [Koslicki]
9. Objects / D. Essence of Objects / 3. Individual Essences
Hylomorphic compounds need an individual form for transworld identity [Koslicki]
29. Religion / D. Religious Issues / 1. Religious Commitment / c. Religious Verification
Belief in an afterlife may be unverifiable in this life, but it will be verifiable after death [Hick, by PG]
It may be hard to verify that we have become immortal, but we could still then verify religious claims [Hick, by PG]
29. Religion / D. Religious Issues / 1. Religious Commitment / d. Religious Falsification
Some things (e.g. a section of the expansion of PI) can be verified but not falsified [Hick, by PG]