Combining Texts

All the ideas for 'Defending the Axioms', 'The Book of Chuang Tzu' and 'Replies on 'Limits of Abstraction''

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36 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Words of wisdom are precise and clear [Zhuangzi (Chuang Tzu)]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Don't even start, let's just stay put [Zhuangzi (Chuang Tzu)]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Concern for rigour can get in the way of understanding phenomena [Fine,K]
2. Reason / C. Styles of Reason / 1. Dialectic
Disagreement means you do not understand at all [Zhuangzi (Chuang Tzu)]
2. Reason / C. Styles of Reason / 3. Eristic
If you beat me in argument, does that mean you are right? [Zhuangzi (Chuang Tzu)]
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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
There is no stage at which we can take all the sets to have been generated [Fine,K]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
We might combine the axioms of set theory with the axioms of mereology [Fine,K]
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 / G. Quantification / 5. Second-Order Quantification
If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
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 / 3. Nature of Numbers / b. Types of number
Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
Why should a Dedekind cut correspond to a number? [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Do not try to do things, or to master knowledge; just be empty [Zhuangzi (Chuang Tzu)]
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
You know you were dreaming when you wake, but there might then be a greater awakening from that [Zhuangzi (Chuang Tzu)]
Did Chuang Tzu dream he was a butterfly, or a butterfly dream he was Chuang Tzu? [Zhuangzi (Chuang Tzu)]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
The perfect man has no self [Zhuangzi (Chuang Tzu)]
To see with true clarity, your self must be irrelevant [Zhuangzi (Chuang Tzu)]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K]
We can combine ZF sets with abstracts as urelements [Fine,K]
We can create objects from conditions, rather than from concepts [Fine,K]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
If words can't be defined, they may just be the chirruping of chicks [Zhuangzi (Chuang Tzu)]
19. Language / D. Propositions / 4. Mental Propositions
Words are for meaning, and once you have that you can forget the words [Zhuangzi (Chuang Tzu)]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Great courage is not violent [Zhuangzi (Chuang Tzu)]
27. Natural Reality / G. Biology / 2. Life
As all life is one, what need is there for words? [Zhuangzi (Chuang Tzu)]
29. Religion / C. Spiritual Disciplines / 2. Taoism
Go with the flow, and be one with the void of Heaven [Zhuangzi (Chuang Tzu)]
Fish forget about each other in the pond and forget each other in the Tao [Zhuangzi (Chuang Tzu)]