Combining Texts

All the ideas for 'Defending the Axioms', 'Intensions Revisited' and 'Introduction to 'Evidentialism''

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15 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Quantified modal logic collapses if essence is withdrawn [Quine]
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]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essences can make sense in a particular context or enquiry, as the most basic predicates [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
Necessity is relative to context; it is what is assumed in an inquiry [Quine]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds are a way to dramatise essentialism, and yet they presuppose essentialism [Quine]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
A rigid designator (for all possible worlds) picks out an object by its essential traits [Quine]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Beliefs can be ascribed to machines [Quine]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
Evidentialism says justifications supervene on the available evidence [Conee/Feldman]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Rational decisions are either taken to be based on evidence, or to be explained causally [Conee/Feldman]