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All the ideas for 'Defending the Axioms', 'Maxims' and 'Axiomatic Theories of Truth (2013 ver)'

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25 ideas

1. Philosophy / A. Wisdom / 2. Wise People
To try to be wise all on one's own is folly [Rochefoucauld]
3. Truth / A. Truth Problems / 2. Defining Truth
If we define truth, we can eliminate it [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh]
3. Truth / F. Semantic Truth / 2. Semantic Truth
The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
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]
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]
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 / 12. Denial of Properties
We can reduce properties to true formulas [Halbach/Leigh]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
La Rochefoucauld's idea of disguised self-love implies an unconscious mind [Rochefoucauld, by Sartre]
22. Metaethics / B. Value / 2. Values / g. Love
Judging by effects, love looks more like hatred than friendship [Rochefoucauld]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
Supreme cleverness is knowledge of the real value of things [Rochefoucauld]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Realising our future misery is a kind of happiness [Rochefoucauld]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue doesn't go far without the support of vanity [Rochefoucauld]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
True friendship is even rarer than true love [Rochefoucauld]
23. Ethics / F. Existentialism / 4. Boredom
We are bored by people to whom we ourselves are boring [Rochefoucauld]