Combining Texts

All the ideas for 'A Priori Knowledge', 'Defending the Axioms' and 'Truth is not the Primary Epistemic Goal'

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17 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]
10. Modality / A. Necessity / 11. Denial of Necessity
20475 Maybe modal sentences cannot be true or false [Casullo]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
20476 If the necessary is a priori, so is the contingent, because the same evidence is involved [Casullo]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
19566 Epistemology does not just concern knowledge; all aspects of cognitive activity are involved [Kvanvig]
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
19568 Making sense of things, or finding a good theory, are non-truth-related cognitive successes [Kvanvig]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
20471 Epistemic a priori conditions concern either the source, defeasibility or strength [Casullo]
20477 The main claim of defenders of the a priori is that some justifications are non-experiential [Casullo]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
20472 Analysis of the a priori by necessity or analyticity addresses the proposition, not the justification [Casullo]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
19567 The 'defeasibility' approach says true justified belief is knowledge if no undermining facts could be known [Kvanvig]
20474 'Overriding' defeaters rule it out, and 'undermining' defeaters weaken in [Casullo]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
19570 Reliabilism cannot assess the justification for propositions we don't believe [Kvanvig]