Combining Texts

All the ideas for 'Demonstratives', 'Introducing the Philosophy of Mathematics' and 'Metaphysics of Morals II:Doctrine of Virtue'

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72 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Moral self-knowledge is the beginning of all human wisdom [Kant]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
For any subject, its system of non-experiential concepts needs a metaphysics [Kant]
2. Reason / A. Nature of Reason / 1. On Reason
Philosophers should not offer multiple proofs - suggesting the weakness of each of them [Kant]
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-realists 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
The number 8 in isolation from the other numbers is of no interest [Friend]
In structuralism the number 8 is not quite the same in different structures, only equivalent [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]
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]
10. Modality / B. Possibility / 1. Possibility
That a concept is not self-contradictory does not make what it represents possible [Kant]
16. Persons / A. Concept of a Person / 4. Persons as Agents
Within nature man is unimportant, but as moral person he is above any price [Kant]
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]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
Indexicals have a 'character' (the standing meaning), and a 'content' (truth-conditions for one context) [Kaplan, by Macià/Garcia-Carpentiro]
'Content' gives the standard modal profile, and 'character' gives rules for a context [Kaplan, by Schroeter]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics
Duty is impossible without prior moral feeling, conscience, love and self-respect [Kant]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
Moral principles do not involve feelings [Kant]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
The love of man is required in order to present the world as a beautiful and perfect moral whole [Kant]
All morality directs the will to love of others' ends, and respect for others' rights [Kant]
22. Metaethics / B. Value / 2. Values / g. Love
The duty of love is to makes the ends of others one's own [Kant]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
A duty of virtue is a duty which is also an end [Kant]
Virtue is strong maxims for duty [Kant]
The supreme principle of virtue is to find universal laws for ends [Kant]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
We are obliged to show the social virtues, but at least they make a virtuous disposition fashionable [Kant]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
If virtue becomes a habit, that is a loss of the freedom needed for adopting maxims [Kant]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
How do we distinguish a mean? The extremes can involve quite different maxims [Kant]
If virtue is the mean between vices, then virtue is just the vanishing of vice [Kant]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
There is one principle of virtues; the virtues are distinguished by their objects [Kant]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
We can love without respect, and show respect without love [Kant]
Respect is limiting our self-esteem by attending to the human dignity of other persons [Kant]
Disrespect is using a person as a mere means to my own ends [Kant]
Respect is purely negative (of not exalting oneself over others), and is thus a duty of Right [Kant]
Love urges us to get closer to people, but respect to keep our distance [Kant]
We must respect the humanity even in a vicious criminal [Kant]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
Humans are distinguished from animals by their capacity to set themselves any sort of end [Kant]
Man is both social, and unsociable [Kant]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Violation of rights deserves punishment, which is vengeance, rather than restitution [Kant]
25. Social Practice / F. Life Issues / 6. Animal Rights
Men can only have duties to those who qualify as persons [Kant]
Cruelty to animals is bad because it dulls our empathy for pain in humans [Kant]