Combining Texts

All the ideas for 'Defending the Axioms', 'Truth' and 'Against the Ethicists (one book)'

expand these ideas     |    start again     |     specify just one area for these texts


15 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
Reasoning is impossible without a preconception [Sext.Empiricus]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
The fact which is stated by a true sentence is not something in the world [Strawson,P]
Facts aren't exactly true statements, but they are what those statements say [Strawson,P]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
The statement that it is raining perfectly fits the fact that it is raining [Strawson,P]
3. Truth / F. Semantic Truth / 2. Semantic Truth
The word 'true' always refers to a possible statement [Strawson,P]
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]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
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
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
If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus]