Combining Texts

All the ideas for 'The Condemnation of 1277', 'Defending the Axioms' and 'The Blank Slate'

expand these ideas     |    start again     |     specify just one area for these texts

22 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]
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
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [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]
7. Existence / C. Structure of Existence / 2. Reduction
7508 Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker]
10. Modality / B. Possibility / 1. Possibility
22142 In future, only logical limits can be placed on divine omnipotence [Anon (Par), by Boulter]
12. Knowledge Sources / D. Empiricism / 2. Associationism
7510 Connectionists say the mind is a general purpose learning device [Pinker]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
7513 Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
16716 It is heresy to require self-evident foundational principles in order to be certain [Anon (Par)]
16. Persons / F. Free Will / 5. Against Free Will
7509 Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
7511 Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker]
7512 There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
7505 Many think that accepting human nature is to accept innumerable evils [Pinker]
25. Social Practice / E. Policies / 5. Education / d. Study of history
1866 It is heresy to teach that history repeats every 36,000 years [Anon (Par)]
27. Natural Reality / G. Biology / 2. Life
7516 In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker]
27. Natural Reality / G. Biology / 3. Evolution
7515 All the evidence says evolution is cruel and wasteful, not intelligent [Pinker]
7514 Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker]
28. God / A. Divine Nature / 3. Divine Perfections
1865 It is heresy to teach that natural impossibilities cannot even be achieved by God [Anon (Par)]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
1864 It is heresy to teach that we can know God by his essence in this mortal life [Anon (Par)]