Combining Texts

All the ideas for 'Mathematics without Foundations', 'Relations' and 'Letters to Bentley'

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19 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 / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
We can talk of 'innumerable number', about the infinite points on a line [Newton]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Not all infinites are equal [Newton]
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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
We want the ontology of relations, not just a formal way of specifying them [Heil]
Two people are indirectly related by height; the direct relation is internal, between properties [Heil]
Maybe all the other features of the world can be reduced to relations [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
In the case of 5 and 6, their relational truthmaker is just the numbers [Heil]
Truthmaking is a clear example of an internal relation [Heil]
If R internally relates a and b, and you have a and b, you thereby have R [Heil]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
If properties are powers, then causal relations are internal relations [Heil]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The principles of my treatise are designed to fit with a belief in God [Newton]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
I do not pretend to know the cause of gravity [Newton]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
The motions of the planets could only derive from an intelligent agent [Newton]
That gravity should be innate and essential to matter is absurd [Newton]