Combining Philosophers

All the ideas for Friedrich Schlegel, Michèle Friend and Lawrence M. Krauss

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56 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
Irony is consciousness of abundant chaos [Schlegel,F]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Plato has no system. Philosophy is the progression of a mind and development of thoughts [Schlegel,F]
2. Reason / D. Definition / 8. Impredicative Definition
An 'impredicative' definition seems circular, because it uses the term being defined [Friend]
2. Reason / D. Definition / 10. Stipulative Definition
Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend]
2. Reason / E. Argument / 5. Reductio ad Absurdum
Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend]
3. Truth / A. Truth Problems / 8. Subjective Truth
Anti-realist see truth as our servant, and epistemically contrained [Friend]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
In classical/realist logic the connectives are defined by truth-tables [Friend]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Double negation elimination is not valid in intuitionist logic [Friend]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic was developed for fictional or non-existent objects [Friend]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
A 'proper subset' of A contains only members of A, but not all of them [Friend]
A 'powerset' is all the subsets of a set [Friend]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Set theory makes a minimum ontological claim, that the empty set exists [Friend]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Infinite sets correspond one-to-one with a subset [Friend]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The 'integers' are the positive and negative natural numbers, plus zero [Friend]
The 'rational' numbers are those representable as fractions [Friend]
A number is 'irrational' if it cannot be represented as a fraction [Friend]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
Cardinal numbers answer 'how many?', with the order being irrelevant [Friend]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Raising omega to successive powers of omega reveal an infinity of infinities [Friend]
The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
Between any two rational numbers there is an infinite number of rational numbers [Friend]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Is mathematics based on sets, types, categories, models or topology? [Friend]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Most mathematical theories can be translated into the language of set theory [Friend]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend]
The number 8 in isolation from the other numbers is of no interest [Friend]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend]
Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
'In re' structuralism says that the process of abstraction is pattern-spotting [Friend]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Constructivism rejects too much mathematics [Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionists typically retain bivalence but reject the law of excluded middle [Friend]
7. Existence / C. Structure of Existence / 2. Reduction
An understanding of the most basic physics should explain all of the subject's mysteries [Krauss]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
In 1676 it was discovered that water is teeming with life [Krauss]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Poetry is transcendental when it connects the ideal to the real [Schlegel,F]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Studying biology presumes the laws of chemistry, and it could never contradict them [Friend]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
For poets free choice is supreme [Schlegel,F]
22. Metaethics / A. Value / 2. Values / e. Love
True love is ironic, in the contrast between finite limitations and the infinity of love [Schlegel,F]
23. Ethics / F. Existentialism / 3. Angst
Irony is the response to conflicts of involvement and attachment [Schlegel,F, by Pinkard]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
Space itself can expand (and separate its contents) at faster than light speeds [Krauss]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
General Relativity: the density of energy and matter determines curvature and gravity [Krauss]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
Uncertainty says that energy can be very high over very short time periods [Krauss]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss]
27. Natural Reality / C. Space-Time / 1. Space / b. Space
Empty space contains a continual flux of brief virtual particles [Krauss]
27. Natural Reality / D. Cosmology / 3. The Beginning
The universe is precisely 13.72 billion years old [Krauss]
27. Natural Reality / D. Cosmology / 10. Multiverse
It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss]