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All the ideas for 'Thinking About Mathematics', 'Travels in Four Dimensions' and 'Ideas: intro to pure phenomenology'

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71 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 / 13. Against Definition
The use of mathematical-style definitions in philosophy is fruitless and harmful [Husserl]
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 / 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 / d. Non-being
A thing which makes no difference seems unlikely to exist [Le Poidevin]
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 / 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 / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
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]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
In addition to causal explanations, they can also be inferential, or definitional, or purposive [Le Poidevin]
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]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
We don't just describe a time as 'now' from a private viewpoint, but as a fact about the world [Le Poidevin]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
Only facts follow from facts [Husserl]
26. Natural Theory / C. Causation / 1. Causation
The logical properties of causation are asymmetry, transitivity and irreflexivity [Le Poidevin]
27. Natural Reality / C. Space / 3. Points in Space
We can identify unoccupied points in space, so they must exist [Le Poidevin]
If spatial points exist, then they must be stationary, by definition [Le Poidevin]
27. Natural Reality / C. Space / 4. Substantival Space
Absolute space explains actual and potential positions, and geometrical truths [Le Poidevin]
27. Natural Reality / C. Space / 5. Relational Space
For relationists moving an object beyond the edge of space creates new space [Le Poidevin]
27. Natural Reality / C. Space / 6. Space-Time
We distinguish time from space, because it passes, and it has a unique present moment [Le Poidevin]
27. Natural Reality / D. Time / 1. Nature of Time / e. Eventless time
Since nothing occurs in a temporal vacuum, there is no way to measure its length [Le Poidevin]
Temporal vacuums would be unexperienced, unmeasured, and unending [Le Poidevin]
27. Natural Reality / D. Time / 2. Passage of Time / b. Rate of time
Time can't speed up or slow down, so it doesn't seem to be a 'process' [Le Poidevin]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
To say that the past causes the present needs them both to be equally real [Le Poidevin]
The B-series doesn't seem to allow change [Le Poidevin]
If the B-universe is eternal, why am I trapped in a changing moment of it? [Le Poidevin]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
Time's arrow is not causal if there is no temporal gap between cause and effect [Le Poidevin]
An ordered series can be undirected, but time favours moving from earlier to later [Le Poidevin]
If time's arrow is causal, how can there be non-simultaneous events that are causally unconnected? [Le Poidevin]
If time's arrow is psychological then different minds can impose different orders on events [Le Poidevin]
There are Thermodynamic, Psychological and Causal arrows of time [Le Poidevin]
Presumably if time's arrow is thermodynamic then time ends when entropy is complete [Le Poidevin]
If time is thermodynamic then entropy is necessary - but the theory says it is probable [Le Poidevin]
27. Natural Reality / D. Time / 2. Passage of Time / i. Time and motion
Instantaneous motion is an intrinsic disposition to be elsewhere [Le Poidevin]
The dynamic view of motion says it is primitive, and not reducible to objects, properties and times [Le Poidevin]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
If the present could have diverse pasts, then past truths can't have present truthmakers [Le Poidevin]
27. Natural Reality / D. Time / 3. Parts of Time / a. Beginning of time
The present is the past/future boundary, so the first moment of time was not present [Le Poidevin]
27. Natural Reality / D. Time / 3. Parts of Time / c. Intervals
The primitive parts of time are intervals, not instants [Le Poidevin]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
If time is infinitely divisible, then the present must be infinitely short [Le Poidevin]
27. Natural Reality / E. Cosmology / 10. Multiverse
The multiverse is distinct time-series, as well as spaces [Le Poidevin]
28. God / A. Divine Nature / 5. God and Time
How could a timeless God know what time it is? So could God be both timeless and omniscient? [Le Poidevin]