Combining Texts

All the ideas for 'Defending the Axioms', 'An Axiomatization of Set Theory' and 'Truthmaking for Presentists'

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18 ideas

3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
If maximalism is necessary, then that nothing exists has a truthmaker, which it can't have [Cameron]
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Determinate truths don't need extra truthmakers, just truthmakers that are themselves determinate [Cameron]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
The facts about the existence of truthmakers can't have a further explanation [Cameron]
3. Truth / B. Truthmakers / 9. Making Past Truths
The present property 'having been F' says nothing about a thing's intrinsic nature [Cameron]
One temporal distibution property grounds our present and past truths [Cameron]
We don't want present truthmakers for the past, if they are about to cease to exist! [Cameron]
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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
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]
All the axioms for mathematics presuppose set theory [Neumann]
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]
8. Modes of Existence / B. Properties / 3. Types of Properties
Being polka-dotted is a 'spatial distribution' property [Cameron]
9. Objects / E. Objects over Time / 2. Objects that Change
Change is instantiation of a non-uniform distributional property, like 'being red-then-orange' [Cameron]
27. Natural Reality / D. Time / 3. Parts of Time / c. Intervals
Surely if things extend over time, then time itself must be extended? [Cameron]