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All the ideas for 'fragments/reports', 'Nature and Meaning of Numbers' and 'Ideas: intro to pure phenomenology'

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50 ideas

1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenology studies different types of correlation between consciousness and its objects [Husserl, by Bernet]
Phenomenology needs absolute reflection, without presuppositions [Husserl]
There can only be a science of fluctuating consciousness if it focuses on stable essences [Husserl, by Bernet]
Phenomenology aims to validate objects, on the basis of intentional intuitive experience [Husserl, by Bernet]
Husserl saw transcendental phenomenology as idealist, in its construction of objects [Husserl, by Bernet]
Start philosophising with no preconceptions, from the intuitively non-theoretical self-given [Husserl]
Epoché or 'bracketing' is refraining from judgement, even when some truths are certain [Husserl]
'Bracketing' means no judgements at all about spatio-temporal existence [Husserl]
After everything is bracketed, consciousness still has a unique being of its own [Husserl]
Phenomenology describes consciousness, in the light of pure experiences [Husserl]
2. Reason / D. Definition / 9. Recursive Definition
Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
2. Reason / D. Definition / 13. Against Definition
The use of mathematical-style definitions in philosophy is fruitless and harmful [Husserl]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
An infinite set maps into its own proper subset [Dedekind, by Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers are free creations of the human mind, to understand differences [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
Order, not quantity, is central to defining numbers [Dedekind, by Monk]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting we see the human ability to relate, correspond and represent [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Our goal is to reveal a new hidden region of Being [Husserl]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
As a thing and its perception are separated, two modes of Being emerge [Husserl]
7. Existence / D. Theories of Reality / 3. Reality
The World is all experiencable objects [Husserl]
7. Existence / D. Theories of Reality / 4. Anti-realism
Absolute reality is an absurdity [Husserl]
9. Objects / A. Existence of Objects / 3. Objects in Thought
A thing is completely determined by all that can be thought concerning it [Dedekind]
9. Objects / D. Essence of Objects / 5. Essence as Kind
The sense of anything contingent has a purely apprehensible essence or Eidos [Husserl]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Imagine an object's properties varying; the ones that won't vary are the essential ones [Husserl, by Vaidya]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
The physical given, unlike the mental given, could be non-existing [Husserl]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Feelings of self-evidence (and necessity) are just the inventions of theory [Husserl]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Direct 'seeing' by consciousness is the ultimate rational legitimation [Husserl]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
The phenomena of memory are given in the present, but as being past [Husserl, by Bernet]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Natural science has become great by just ignoring ancient scepticism [Husserl]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
We know another's mind via bodily expression, while also knowing it is inaccessible [Husserl, by Bernet]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Pure consciousness is a sealed off system of actual Being [Husserl]
16. Persons / C. Self-Awareness / 2. Knowing the Self
We never meet the Ego, as part of experience, or as left over from experience [Husserl]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett]
We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Only facts follow from facts [Husserl]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
A virtue is a combination of intelligence, strength and luck [Ion]