Combining Texts

All the ideas for 'works', 'Sets and Numbers' and 'Truth Rehabilitated'

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18 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
Without truth, both language and thought are impossible [Davidson]
Plato's Forms confused truth with the most eminent truths, so only Truth itself is completely true [Davidson]
Truth can't be a goal, because we can neither recognise it nor confim it [Davidson]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Correspondence can't be defined, but it shows how truth depends on the world [Davidson]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Disquotation only accounts for truth if the metalanguage contains the object language [Davidson]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
The master science is physical objects divided into sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Sets exist where their elements are, but numbers are more like universals [Maddy]
Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
7. Existence / D. Theories of Reality / 8. Facts / e. Facts rejected
If we try to identify facts precisely, they all melt into one (as the Slingshot Argument proves) [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Knowing the potential truth conditions of a sentence is necessary and sufficient for understanding [Davidson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
It could be that the use of a sentence is explained by its truth conditions [Davidson]