Combining Texts

All the ideas for 'fragments/reports', 'Reality is Not What it Seems' and 'A Structural Account of Mathematics'

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33 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
We only know relational facts about the empty set, but nothing intrinsic [Chihara]
In simple type theory there is a hierarchy of null sets [Chihara]
Realists about sets say there exists a null set in the real world, with no members [Chihara]
The null set is a structural position which has no other position in membership relation [Chihara]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
A pack of wolves doesn't cease when one member dies [Chihara]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
The mathematics of relations is entirely covered by ordered pairs [Chihara]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
7. Existence / B. Change in Existence / 2. Processes
Quantum mechanics deals with processes, rather than with things [Rovelli]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
Quantum mechanics describes the world entirely as events [Rovelli]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli]
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
The basic ideas of fields and particles are merged in quantum mechanics [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
Because it is quantised, a field behaves like a set of packets of energy [Rovelli]
There are about fifteen particles fields, plus a few force fields [Rovelli]
The world consists of quantum fields, with elementary events happening in spacetime [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
Electrons only exist when they interact, and their being is their combination of quantum leaps [Rovelli]
Electrons are not waves, because their collisions are at a point, and not spread out [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
Quantum Theory describes events and possible interactions - not how things are [Rovelli]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]
Nature has three aspects: granularity, indeterminacy, and relations [Rovelli]
27. Natural Reality / C. Space / 4. Substantival Space
The world is just particles plus fields; space is the gravitational field [Rovelli]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
Only heat distinguishes past from future [Rovelli]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]