Combining Texts

All the ideas for 'Defending the Axioms', 'Introduction of 'Essence of Christianity'' and 'Sets and Numbers'

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23 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17824 The master science is physical objects divided into sets [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 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
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 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
17825 Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
17826 Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
17828 Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
17827 Sets exist where their elements are, but numbers are more like universals [Maddy]
17830 Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17823 If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
17829 Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
19451 When absorbed in deep reflection, is your reason in control, or is it you? [Feuerbach]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
19450 Reason, love and will are the highest perfections and essence of man - the purpose of his life [Feuerbach]
27. Natural Reality / G. Biology / 5. Species
19448 Consciousness is said to distinguish man from animals - consciousness of his own species [Feuerbach]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
19454 A God needs justice, kindness and wisdom, but those concepts don't depend on the concept of God [Feuerbach]
28. God / C. Attitudes to God / 4. God Reflects Humanity
19452 The nature of God is an expression of human nature [Feuerbach]
28. God / C. Attitudes to God / 5. Atheism
19453 If love, goodness and personality are human, the God who is their source is anthropomorphic [Feuerbach]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
19449 Religion is the consciousness of the infinite [Feuerbach]
19455 Today's atheism will tomorrow become a religion [Feuerbach]