Combining Texts

All the ideas for 'fragments/reports', 'works' and 'A Structural Account of Mathematics'

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29 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]
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 / 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]
14. Science / B. Scientific Theories / 3. Instrumentalism
Special relativity, unlike general relativity, was operationalist in spirit [Putnam on Einstein]
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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / C. Causation / 1. Causation
Einstein took causation to be the bedrock of physics [Einstein, by Coveney/Highfield]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
General relativity assumes laws of nature are the same in all frames of reference [Einstein, by Close]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
Newton is a special case of Einstein's general theory, with an infinite speed of light [Einstein, by Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
The theory is 'special' because it sticks to observers moving straight, at constant speeds [Einstein, by Farmelo]
Assume the speed of light is constant for all observers, and the laws of physics are the same [Einstein, by Farmelo]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
General Relativity says there is no absolute force or acceleration [Einstein, by Close]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]
27. Natural Reality / B. Modern Physics / 4. Standard Model / d. Mass
Mass is a measure of energy content [Einstein]
27. Natural Reality / C. Space / 6. Space-Time
Space-time arises from the connection between measurements of space and of time [Einstein, by Farmelo]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
28. God / C. Attitudes to God / 5. Atheism
I do not believe in a personal God [Einstein]