Combining Texts

All the ideas for 'Defending the Axioms', 'Three Grades of Modal Involvement' and 'Against the Ethicists (one book)'

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16 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
22752 Reasoning is impossible without a preconception [Sext.Empiricus]
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 / 1. Ontology of Logic
12219 Whether a modal claim is true depends on how the object is described [Quine, by Fine,K]
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 / G. Quantification / 1. Quantification
10922 Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine]
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]
9. Objects / D. Essence of Objects / 9. Essence and Properties
10923 Aristotelian essentialism says a thing has some necessary and some non-necessary properties [Quine]
10. Modality / A. Necessity / 2. Nature of Necessity
10921 Necessity can attach to statement-names, to statements, and to open sentences [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
10924 Necessity is in the way in which we say things, and not things themselves [Quine]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
22754 Saying the good is useful or choiceworth or happiness-creating is not the good, but a feature of it [Sext.Empiricus]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
22755 Like a warming fire, what is good by nature should be good for everyone [Sext.Empiricus]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
22756 If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus]