Combining Texts

All the ideas for 'Mathematics without Foundations', 'Truth' and 'III.10 On Restraining your Will'

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14 ideas

3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta]
3. Truth / F. Semantic Truth / 2. Semantic Truth
A weakened classical language can contain its own truth predicate [Gupta]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar reappears, even if one insists on propositions instead of sentences [Gupta]
Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta]
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]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue inspires Stoics, but I want a good temperament [Montaigne]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
There is not much point in only becoming good near the end of your life [Montaigne]
25. Social Practice / A. Freedoms / 3. Free speech
Nothing we say can be worse than unsaying it in the face of authority [Montaigne]
25. Social Practice / E. Policies / 1. War / c. Combatants
People at home care far more than soldiers risking death about the outcome of wars [Montaigne]