Combining Texts

All the ideas for 'Defending the Axioms', 'Scientific Objectivity' and 'Specimen inventorum'

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16 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
One view says objectivity is making a successful claim which captures the facts [Reiss/Sprenger]
An absolute scientific picture of reality must not involve sense experience, which is perspectival [Reiss/Sprenger]
Topic and application involve values, but can evidence and theory choice avoid them? [Reiss/Sprenger]
The Value-Free Ideal in science avoids contextual values, but embraces epistemic values [Reiss/Sprenger]
Value-free science needs impartial evaluation, theories asserting facts, and right motivation [Reiss/Sprenger]
Thermometers depend on the substance used, and none of them are perfect [Reiss/Sprenger]
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]
14. Science / A. Basis of Science / 3. Experiment
The 'experimenter's regress' says success needs reliability, which is only tested by success [Reiss/Sprenger]
14. Science / C. Induction / 6. Bayes's Theorem
The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
The cause of a change is not the real influence, but whatever gives a reason for the change [Leibniz]