Combining Texts

All the ideas for 'Natural Kinds and Biological Realism', 'A Structural Account of Mathematics' and 'The Periodic Table'

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48 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Realists about sets say there exists a null set in the real world, with no members [Chihara]
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]
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 / A. Basis of Science / 4. Prediction
If a theory can be fudged, so can observations [Scerri]
14. Science / B. Scientific Theories / 4. Paradigm
The periodic system is the big counterexample to Kuhn's theory of revolutionary science [Scerri]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Scientists eventually seek underlying explanations for every pattern [Scerri]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
The periodic table suggests accommodation to facts rates above prediction [Scerri]
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 / B. Natural Kinds / 1. Natural Kinds
Some kinds are very explanatory, but others less so, and some not at all [Devitt]
Natural kinds are what are differentiated by nature, and not just by us [Scerri]
If elements are natural kinds, might the groups of the periodic table also be natural kinds? [Scerri]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
The colour of gold is best explained by relativistic effects due to fast-moving inner-shell electrons [Scerri]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]
The stability of nuclei can be estimated through their binding energy [Scerri]
If all elements are multiples of one (of hydrogen), that suggests once again that matter is unified [Scerri]
27. Natural Reality / F. Chemistry / 1. Chemistry
The electron is the main source of chemical properties [Scerri]
A big chemistry idea is that covalent bonds are shared electrons, not transfer of electrons [Scerri]
How can poisonous elements survive in the nutritious compound they compose? [Scerri]
Periodicity and bonding are the two big ideas in chemistry [Scerri]
Chemistry does not work from general principles, but by careful induction from large amounts of data [Scerri]
Does radioactivity show that only physics can explain chemistry? [Scerri]
27. Natural Reality / F. Chemistry / 2. Modern Elements
It is now thought that all the elements have literally evolved from hydrogen [Scerri]
19th C views said elements survived abstractly in compounds, but also as 'material ingredients' [Scerri]
27. Natural Reality / F. Chemistry / 3. Periodic Table
Moseley, using X-rays, showed that atomic number ordered better than atomic weight [Scerri]
Some suggested basing the new periodic table on isotopes, not elements [Scerri]
Elements are placed in the table by the number of positive charges - the atomic number [Scerri]
Elements in the table are grouped by having the same number of outer-shell electrons [Scerri]
Orthodoxy says the periodic table is explained by quantum mechanics [Scerri]
Pauli explained the electron shells, but not the lengths of the periods in the table [Scerri]
Moseley showed the elements progress in units, and thereby clearly identified the gaps [Scerri]
Elements were ordered by equivalent weight; later by atomic weight; finally by atomic number [Scerri]
The best classification needs the deepest and most general principles of the atoms [Scerri]
To explain the table, quantum mechanics still needs to explain order of shell filling [Scerri]
Since 99.96% of the universe is hydrogen and helium, the periodic table hardly matters [Scerri]
27. Natural Reality / G. Biology / 5. Species
The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt]
Species pluralism says there are several good accounts of what a species is [Devitt]