Combining Texts

All the ideas for 'Philosophical Essay on Probability', 'Models' and 'Mathematics without Foundations'

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15 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
13. Knowledge Criteria / C. External Justification / 7. Testimony
The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
14. Science / B. Scientific Theories / 7. Scientific Models
Theoretical models can represent, by mapping onto the data-models [Portides]
In the 'received view' models are formal; the 'semantic view' emphasises representation [Portides, by PG]
Representational success in models depends on success of their explanations [Portides]
The best model of the atomic nucleus is the one which explains the most results [Portides]
'Model' belongs in a family of concepts, with representation, idealisation and abstraction [Portides]
Models are theory-driven, or phenomenological (more empirical and specific) [Portides]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
General theories may be too abstract to actually explain the mechanisms [Portides]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]