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All the ideas for 'The Periodic Table', 'Vagueness, Truth and Logic' and 'Introduction to Mathematical Philosophy'

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93 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K]
2. Reason / D. Definition / 3. Types of Definition
A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell]
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
An argument 'satisfies' a function φx if φa is true [Russell]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Members define a unique class, whereas defining characteristics are numerous [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
We may assume that there are infinite collections, as there is no logical reason against them [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The British parliament has one representative selected from each constituency [Russell]
Choice shows that if any two cardinals are not equal, one must be the greater [Russell]
Choice is equivalent to the proposition that every class is well-ordered [Russell]
We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility: a family of functions is equivalent to a single type of function [Russell]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
Propositions about classes can be reduced to propositions about their defining functions [Russell]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
All the propositions of logic are completely general [Russell]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
In modern times, logic has become mathematical, and mathematics has become logical [Russell]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Logic can only assert hypothetical existence [Russell]
Logic is concerned with the real world just as truly as zoology [Russell]
Logic can be known a priori, without study of the actual world [Russell]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded Middle, and classical logic, may fail for vague predicates [Fine,K]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Asking 'Did Homer exist?' is employing an abbreviated description [Russell]
Russell admitted that even names could also be used as descriptions [Russell, by Bach]
Names are really descriptions, except for a few words like 'this' and 'that' [Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
The only genuine proper names are 'this' and 'that' [Russell]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logic holding between indefinite sentences is the core of all language [Fine,K]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Could a number just be something which occurs in a progression? [Russell, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
A complex number is simply an ordered couple of real numbers [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
Discovering that 1 is a number was difficult [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Infinity and continuity used to be philosophy, but are now mathematics [Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
'0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
A number is something which characterises collections of the same size [Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
There is always something psychological about inference [Russell]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Existence can only be asserted of something described, not of something named [Russell]
7. Existence / D. Theories of Reality / 7. Fictionalism
Classes are logical fictions, made from defining characteristics [Russell]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Vagueness is semantic, a deficiency of meaning [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / e. Higher-order vagueness
A thing might be vaguely vague, giving us higher-order vagueness [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
A vague sentence is only true for all ways of making it completely precise [Fine,K]
Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K]
Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K]
With the super-truth approach, the classical connectives continue to work [Fine,K]
Borderline cases must be under our control, as capable of greater precision [Fine,K]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
If a relation is symmetrical and transitive, it has to be reflexive [Russell]
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vagueness can be in predicates, names or quantifiers [Fine,K]
9. Objects / D. Essence of Objects / 3. Individual Essences
The essence of individuality is beyond description, and hence irrelevant to science [Russell]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell]
All forms of implication are expressible as truth-functions [Russell]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
If something is true in all possible worlds then it is logically necessary [Russell]
14. Science / A. Basis of Science / 4. Prediction
If a theory can be fudged, so can observations [Scerri]
14. Science / B. Scientific Theories / 1. Scientific Theory
Mathematically expressed propositions are true of the world, but how to interpret them? [Russell]
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]
19. Language / D. Propositions / 1. Propositions
Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell]
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
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
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]
Since 99.96% of the universe is hydrogen and helium, the periodic table hardly matters [Scerri]
To explain the table, quantum mechanics still needs to explain order of shell filling [Scerri]