Combining Texts

All the ideas for 'fragments/reports', 'Elements of Set Theory' and 'A Future for Presentism'

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27 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
We can only define functions if Choice tells us which items are involved [Enderton]
8. Modes of Existence / A. Relations / 1. Nature of Relations
It is a necessary condition for the existence of relations that both of the relata exist [Bourne]
All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne]
Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
How can presentists talk of 'earlier than', and distinguish past from future? [Bourne]
Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne]
Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne]
B-series objects relate to each other; A-series objects relate to the present [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius]