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All the ideas for 'Thinking About Mathematics', 'The Question of Realism' and 'The Passions'

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58 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom needs both thought and passion, with each reflecting on the other [Solomon]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Philosophy is creating an intellectual conceptual structure for life [Solomon]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K]
2. Reason / A. Nature of Reason / 1. On Reason
Reason is actually passions, guided by perspicacious reflection [Solomon]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on Fine,K]
Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
Grounding relations are best expressed as relations between sentences [Fine,K]
7. Existence / C. Structure of Existence / 2. Reduction
Reduction might be producing a sentence which gets closer to the logical form [Fine,K]
Reduction might be semantic, where a reduced sentence is understood through its reduction [Fine,K]
Reduction is modal, if the reductions necessarily entail the truth of the target sentence [Fine,K]
The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K]
7. Existence / D. Theories of Reality / 3. Reality
What is real can only be settled in terms of 'ground' [Fine,K]
In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K]
Why should what is explanatorily basic be therefore more real? [Fine,K]
Reality is a primitive metaphysical concept, which cannot be understood in other terms [Fine,K]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
We often trust our intuitions as rational, despite their lack of reflection [Solomon]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Distinguishing reason from passion is based on an archaic 'faculty' theory [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
I say bodily chemistry and its sensations have nothing to do with emotions [Solomon]
Emotions are judgements about ourselves, and our place in the world [Solomon]
Emotions are defined by their objects [Solomon]
The heart of an emotion is its judgement of values and morality [Solomon]
Emotions can be analysed under fifteen headings [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
Some emotions are externally directed, others internally [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
The passions are subjective, concerning what is important to me, rather than facts [Solomon]
Emotions are strategies for maximising our sense of dignity and self-esteem [Solomon]
Passions exist as emotions, moods and desires, which all generate meaning [Solomon]
The Myth of the Passions says they are irrational, uncontrolled and damaging [Solomon]
Which emotions we feel depends on our sense of our own powers [Solomon]
It is only our passions which give our lives meaning [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / d. Emotional feeling
Feeling is a superficial aspect of emotion, and may be indeterminate, or even absent [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / e. Basic emotions
There are no 'basic' emotions, only socially prevalent ones [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / f. Emotion and reason
It is reason which needs the anchorage of passions, rather than vice versa [Solomon]
Dividing ourselves into confrontational reason and passion destroys our harmonious whole [Solomon]
The supposed irrationality of our emotions is often tactless or faulty expression of them [Solomon]
19. Language / D. Propositions / 5. Unity of Propositions
A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
Emotions are our life force, and the source of most of our values [Solomon]
22. Metaethics / B. Value / 2. Values / g. Love
Lovers adopt the interests of their beloved, rather than just valuing them [Solomon]
23. Ethics / F. Existentialism / 2. Nihilism
'Absurdity' is just the result of our wrong choices in life [Solomon]
24. Political Theory / D. Ideologies / 1. Ideology
Ideologies are mythologies which guide our actions [Solomon]