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All the ideas for 'Structures and Structuralism in Phil of Maths', 'The Epic of Gilgamesh' and 'Intro to the Philosophy of Time'

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55 ideas

2. Reason / F. Fallacies / 2. Infinite Regress
Vicious regresses force you to another level; non-vicious imply another level [Baron/Miller]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
A traveller takes a copy of a picture into the past, gives it the artist, who then creates the original! [Baron/Miller]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Grounding is intended as a relation that fits dependences between things [Baron/Miller]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / E. Objects over Time / 2. Objects that Change
How does a changing object retain identity or have incompatible properties over time? [Baron/Miller]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
The gods alone live forever with Shamash. The days of humans are numbered. [Anon (Gilg)]
26. Natural Theory / C. Causation / 1. Causation
Modern accounts of causation involve either processes or counterfactuals [Baron/Miller]
26. Natural Theory / C. Causation / 4. Naturalised causation
The main process theory of causation says it is transference of mass, energy, momentum or charge [Baron/Miller]
If causes are processes, what is causation by omission? (Distinguish legal from scientific causes?) [Baron/Miller]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
The counterfactual theory of causation handles the problem no matter what causes actually are [Baron/Miller]
Counterfactual theories struggle with pre-emption by a causal back-up system [Baron/Miller]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / d. Entropy
There is no second 'law' of thermodynamics; it just reflects probabilities of certain microstates [Baron/Miller]
27. Natural Reality / C. Space / 6. Space-Time
In relativity space and time depend on one's motion, but spacetime gives an invariant metric [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
The block universe theory says entities of all times exist, and time is the B-series [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
How can we know this is the present moment, if other times are real? [Baron/Miller]
If we are actually in the past then we shouldn't experience time passing [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
Erzatz Presentism allows the existence of other times, with only the present 'actualised' [Baron/Miller]
How do presentists explain relations between things existing at different times? [Baron/Miller]
Presentism needs endurantism, because other theories imply most of the object doesn't exist [Baron/Miller]
How can presentists move to the next future moment, if that doesn't exist? [Baron/Miller]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
Most of the sciences depend on the concept of time [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
For abstractionists past times might still exist, althought their objects don't [Baron/Miller]
The error theory of time's passage says it is either a misdescription or a false inference [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / b. Rate of time
It is meaningless to measure the rate of time using time itself, and without a rate there is no flow [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
The C-series rejects A and B, and just sees times as order by betweenness, without direction [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
The A-series has to treat being past, present or future as properties [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / f. Tenseless (B) series
The B-series can have a direction, as long as it does not arise from temporal flow [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
Static theories cannot account for time's obvious asymmetry, so time must be dynamic [Baron/Miller]
The direction of time is either primitive, or reducible to something else [Baron/Miller]
The kaon does not seem to be time-reversal invariant, unlike the rest of nature [Baron/Miller]
Maybe the past is just the direction of decreasing entropy [Baron/Miller]
We could explain time's direction by causation: past is the direction of causes, future of effects [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / h. Change in time
Static time theory presents change as one property at t1, and a different property at t2 [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / j. Time travel
If a time traveller kills his youthful grandfather, he both exists and fails to exist [Baron/Miller]
Presentism means there no existing past for a time traveller to visit [Baron/Miller]
27. Natural Reality / D. Time / 2. Passage of Time / k. Temporal truths
The past (unlike the future) is fixed, along with truths about it, by the existence of past objects [Baron/Miller]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
The moving spotlight says entities can have properties of being present, past or future [Baron/Miller]
The present moment is a matter of existence, not of acquiring a property [Baron/Miller]