Combining Texts

All the ideas for 'Defending the Axioms', 'Elements of Law and Justice' and 'Grounding Concepts'

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25 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
17729 Examining concepts can recover information obtained through the senses [Jenkins]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
17740 Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins]
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 / a. The Infinite
17730 Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
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 / a. Mathematical empiricism
17719 Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
17717 Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
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 / 6. Logicism / d. Logicism critique
17724 It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17727 We can learn about the world by studying the grounding of our concepts [Jenkins]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
17720 There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG]
7. Existence / E. Categories / 4. Category Realism
17728 The concepts we have to use for categorising are ones which map the real world well [Jenkins]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
17726 Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
17734 It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins]
13. Knowledge Criteria / C. External Justification / 1. External Justification
17723 Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins]
14. Science / C. Induction / 2. Aims of Induction
19387 Hypotheses come from induction, which is comparison of experiences [Leibniz]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
17718 Grounded concepts are trustworthy maps of the world [Jenkins]
17739 The physical effect of world on brain explains the concepts we possess [Jenkins]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
17731 Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins]
19. Language / C. Assigning Meanings / 2. Semantics
17732 Success semantics explains representation in terms of success in action [Jenkins]
19. Language / E. Analyticity / 1. Analytic Propositions
17725 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins]